PHYSICS LAB MANUAL PHY 114 ENGINEERING SCIENCE & PHYSICS DEPARTMENT

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1 C O L L E G E O F T A T E N I L A N D PHYIC LAB MANUAL ENGINEERING CIENCE & PHYIC DEPARTMENT The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them. --ir William Lawrence Bragg PHY 114 C I T Y U N I V E R I T Y O F N E W Y O R K

2 COLLEGE OF TATEN ILAND PHY 114 PHYIC LAB MANUAL ENGINEERING CIENCE & PHYIC DEPARTMENT CITY UNIVERITY OF NEW YORK

3 ENGINEERING ENGINEERING CIENCE CIENCE & & PHYIC PHYIC DEPARTMENT DEPARTMENT PHYIC PHYIC LABORATORY LABORATORY EXT 2978, 4N-214/4N-215 EXT 2978, 4N-214/4N-215 LABORATORY RULE 1. No eating or drinking in the laboratory premises. 2. The use of cell phones is not permitted. 3. Computers are for experiment use only. No web surfing, reading , instant messaging or computer games allowed. 4. When finished using a computer log-off and put your keyboard and mouse away. 5. Arrive on time otherwise equipment on your station will be removed. 6. Bring a scientific calculator for each laboratory session. 7. Have a hard copy of your laboratory report ready to submit before you enter the laboratory. 8. ome equipment will be required to be signed out and checked back in. The rest of the equipment should be returned as directed by the technician. All equipment must be treated with care and caution. No markings or writing is allowed on any piece of equipment or tables. Remember, you are responsible for the equipment you use during an experiment. 9. After completing the experiment and, if needed, putting away equipment, check that your station is clean and clutter free and push in your chair. 10. Before leaving the laboratory premises, make sure that you have all your belongings with you. The lab is not responsible for any lost items. Your cooperation in abiding by these rules will be highly appreciated. Thank You. The Physics Laboratory taff

4 ENGINEERING CIENCE & PHYIC DEPARTMENT PHYIC LABORATORY EXT 2978, 4N-214/4N EENTIAL of writing laboratory reports ALL students must comply with 1. No report is accepted from a student who didn t actually participate in the experiment. 2. Despite that the actual lab is performed in a group, a report must be individually written. Photocopies or plagiaristic reports will not be accepted and zero grade will be issued to all parties. 3. The laboratory report should have a title page giving the name and number of the experiment, the student's name, the class, and the date of the experiment. The laboratory partner s name must be included on the title page, and it should be clearly indicated who the author and who the partner is. 4. Each section of the report, that is, objective, theory background, etc., should be clearly labeled. The data sheet collected by the author of the report during the lab session with instructor s signature must be included no report without such a data sheet indicating that the author has actually performed the experiment is to be accepted. 5. Paper should be 8 ½ x 11. Write on one side only using word-processing software. Ruler and compass should be used for diagrams. Computer graphing is also accepted. 6. Reports should be stapled together. 7. Be as neat as possible in order to facilitate reading your report. 8. Reports are due one week following the experiment. No reports will be accepted after the "Due-date" without penalty as determined by the instructor. 9. No student can pass the course unless he or she has turned in a set of laboratory reports required by the instructor. 10. The student is responsible for any further instruction given by the instructor.

5 PHY 114 TABLE OF CONTENT The laboratory instructor, in order to adjust to the lecture schedule or personal preference, may substitute any of the experiments below with supplementary experiments. 1. LABORATORY REPORT FORMAT AND DATA ANALYI MA AND DENITY UNIFORM MOTION MOTION OF A BODY IN FREE FALL FORCE AND ACCELERATION MECHANICAL ENERGY FRICTION CENTRIPETAL FORCE CALORIMETRY OHM LAW AND REITANCE THE JOULE EXPERIMENT REFLECTION AND REFRACTION FOCAL POINT AND FOCAL LENGTH OF MIRROR AND LENE OUND WAVE...47 UPPLEMENTARY EXPERIMENT: 15. TANDING WAVE ON A TRETCHED TRING DENITY AND ARCHIMEDE PRINCIPLE ATOMIC PECTRA IMPLE PENDULUM...65

6 19. VERNIER CALIPER - MICROMETER CALIPER EQUILIBRIUM OF A RIGID BODY ACCELERATION FOCAL LENGTH OF A CONVERGING LEN...83 APPENDIX: A1 A2 A3 A4 GRAPHICAL ANALYI FINDING THE BET...89 TECHNICAL NOTE ON VERNIER LABQUET2 INTERFACE...93 TECHNICAL NOTE ON ENOR AND PROBE...97 MULTIMETER AND POWER UPPLIE All diagrams and tables created by Jackeline. Figueroa, enior CLT. Except for diagrams on pages and

7 LABORATORY REPORT FORMAT AND PREENTATION OF DATA The Laboratory Report should contain the following information: 1. Objective of the lab; 2. Physical Principles and laws tested and used; 3. Explanation (rather than a description) of the procedure; 4. Laboratory Data: arranged in tabular form with labeled rows and columns. Note that the data sheet must be signed by the instructor in the presence of the student when the experiment is completed; 5. Computations and graphs of the main quantities and their errors; 6. ummary of Results which includes: discussion of the results and their errors as well as a conclusion based on this discussion as to what extent the lab objective is achieved. 7. Answers to all questions. I. ERROR OF OBERVATION 1. Blunders: Every measurement is subject to error. Obviously, one should know how to reduce or minimize error as much as possible. The commonest and simplest type of error to remove is a blunder, due to carelessness, in making a measurement. Blunders are diminished by experience and the repetition of observations. 2. Personal Errors: These are errors peculiar to a particular observer. For example beginners very often try to fit measurement to some preconceived notion. Also, the beginner is often prejudiced in favor of his first observation. 3. ystematic Errors: Are errors associated with the particular instruments or technique of measurement being used. uppose we have a book which is 9in. high. We measure its height by laying a ruler against it, with one end of the ruler at the top end of the book. If the first inch of the ruler has been previously cut off, then the ruler is like to tell us that the book is 10in. long. This is a systematic error. If a thermometer immersed in boiling pure water at normal pressure reads 215 F (should be 212 F) it is improperly calibrated; if readings from this thermometer are incorporated into experimental results, a systematic error results. 4. Accidental (or Random) Errors: When measurements are reasonably free from the above sources of error it is found that whenever an instrument is used to the limit its precision, errors occur which cannot be eliminated completely. uch errors are due to the fact that conditions are continually varying imperceptibly. These errors are largely unpredictable and unknown. For example: A small error in judgment on the part of the observer, such as in estimating to tenths the smallest scale divisions. Other causes are 1

8 unpredictable fluctuations in conditions, such as temperature, illumination, socket voltage or any kind of mechanical vibrations of the equipment being used. The effect of these errors may be mitigated by repeating the measurement several times and taking the average of the readings. There are two ways of estimating the error due to random independent measurements. One way is to calculate the Mean Absolute Deviation and the other is to calculate the tandard deviation. Both methods are discussed in the appendix. 5. ignificant Figures: Every number expressing the result of a measurement or of computations based on measurements should be written with the proper number of "significant figures." The number of significant figures is independent of the position of the decimal point: i.e cm, 84.48mm, or m has the same number of significant figures. A figure ceased to be a significant when we have no reason to believe, on the basis of measurement made, that the correct result is probably closer to that figure than to the next (higher or lower) figure. In computations, since figures which are not significant in this sense have no place in the final result, they should be dropped to avoid useless labor. e.g. in the measurement of the diameter of a penny we read on the ruler Here the last figure is a very rough guess; hence, for computations we use Reading error: Every instrument has a limitation in accuracy. The markings serve as a guide as to that accuracy. We read the instrument to a fraction of the smallest division. As in the diameter of a penny the 8 is an estimated number. We then have to estimate the error in that number. For most applications the reading error can be taken as +/-2. Therefore the experimental value for that measurement is / cm. The reading error may be taken as a constant error for that instrument. The smallest error associated with a measurement is the reading error. 7. Percent Error: To present the error in a relative manner we calculate the percent error. The Measurement error may be estimated from your measurements a variety of ways. Two simple ways are the standard deviation or the mean absolute error. For most applications the mean absolute error is a good estimate of the measurement error. Percent Error = Measurement Error Average Value 100% 8. Percent Difference: In your laboratory work you will often find occasion to compare a value which you have obtained as a result of measurement, with the standard, or generally accepted value. The percent difference is computed as follows: Percent Difference = tandard Value Experimental Value 100% tandard Value Note: If Percent Difference (PD) is smaller than Percent Error (PE), you can conclude that the experimental value is consistent with the standard (known) value within estimated errors. If, however, PD is larger than PE, the measured value is inconsistent with the standard (known) one. In other words, if PE is estimated correctly, the measured value can be claimed to be a better estimate of the standard one. 2

9 II. ANALYI OF DATA Every measurement is prone to errors leading to deviations of a measured quantity from one measurement to another. For example, length of a pencil measured several times may come out differently depending on how ruler was applied. Personal blunders due to carelessness are also a source of errors. In general, each particular instrument never gives a result precisely. Many external factors such as, e.g., temperature vary and thereby affect results. Thus, errors of measurements and the associated deviations of measured quantity are an inherent part of the measurement process. Patience and experience are required in order to reduce the errors and the deviations. In order to evaluate errors the same quantity should be measured at least several times. As an example, the result of such measurements of a length of one object is given in the table below DL= L - L [cm] N L [cm] The upper row marked by N gives the number of a particular measurement. The second row shows object s length obtained during each measurement (for example, the result of the 4th measurement is 15.4 cm). The bottom row gives absolute deviations DL L L Eq. 1 of each measurement from the average value (mean value) of the length ( ) L avg(l) 15.1cm 9 calculated from 9 measurements. In calculating the average, the result must be rounded off so that the number of significant digits is not more than that for each measurement. The mean absolute deviation DL avg( DL) Eq. 2 indicates how the measured value varied due to all of the factors mentioned above. For our example, DL 02. cm. The final result for the object length is expressed as L L DL Eq. 3 That is, L ( ) cm. This means that in the measurement of the length the result obtained was between 14.9 cm and 15.3 cm with high certainty. 3

10 Errors can also be represented as percent error. It is defined as DL % error 100% Eq. 4 L For our example, it is % 1%. This sort of analysis should be applied to 151. measurements of other physical quantities. ometimes a purpose of the laboratory experiment is to measure a quantity Q whose standard value Qst is well known from theoretical considerations or other measurements. In this case it is important to compare these two quantities Q and Qst in order to make a conclusion on whether your experiment confirmed the value Qst and thereby supported a theoretical concept underlying this value. An important quantity is the percent difference between the measured (mean) value and the standard value: Qst Q % difference 100% Eq. 5 Q We can say that the experiment does confirm the concept within the experimental percent deviation (or percent error), if the percent difference is not bigger than the percent error. The errors should always be estimated for the experimental data. Furthermore, any experimental result for which no errors are evaluated is considered as unreliable. st PROPAGATION OF ERROR ometimes a measured quantity is obtained by using some equation, and the question is how to evaluate fractional (or percent) error for such a quantity. For example, density ρ of some material is obtained as the ratio of mass M and volume V: ρ=m/v. While mass can be measured directly by scale, volume is often obtained from measurements of linear dimensions of a rectangular shaped sample as V=L 1 L 2 L 3. Each four values, M, L 1, L 2, and L 3 have their own errors (mean deviations): M = M ± M L 1 = L 1 ± L 1 L 2 = L 2 ± L 2 L 3 = L 3 ± L 3 Eq. 6 The resulting fractional (or % ) error for ρ can be found as a sum of fractional (%) errors of all multiplicative quantities entering the equation. For our example this means M L L L M M L L L L L L 1 2 3, Eq

11 Let us use particular measurements performed on a piece of wood of mass M with rectangular shape given by dimensions L 1, L 2 and L 3 : M = (7.5±0.2)g L 1 = (2.4±0.1)cm L 2 = (2.0±0.1)cm L 3 = (3.4±0.1)cm Then, the mean volume is =16 cm 3 and the mean density becomes: 7.5/ g cm 3 The fractional error follows from Eq. 7 as That is, % error is %=15%, and the absolute error is g/cm 3 =0.07 g/cm 3. The final answer for the density is ( ) g cm 3 imilar procedure should be followed for other composite quantities. TANDARD DEVIATION The method of estimating errors as the mean of the deviations shown in Eq. 2 to Eq. 4 can be improved by considering these deviations as some random variable. Then, the standard deviation of such variable from its mean is taken as the error. In general, the procedure becomes as follows: If the random variable X takes on N values x1,,xn (which are real numbers) with equal probability, then its standard deviation σ can be calculated as follows: 1. Find the mean, x, of the values. 2. For each value x i, calculate its deviation ( x i x) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance σ Take the square root of the variance. 6. This calculation is described by the following formula: 1 N N i 1 (x i x) 2 5

12 where x is the arithmetic mean of the values x i, defined as: x x 1 x 2... x N N 1 N N i 1 x i Example: uppose we wished to find the standard deviation of the data set consisting of the values 3, 7, 7, and 19 tep 1: Find the arithmetic mean (average) of 3, 7, 7, and 19, tep 2: Find the deviation of each number from the mean, 3 9 = = = = 10 tep 3: quare each of the deviations, which amplifies large deviations and makes negative values positive, (-6) 2 = 36 (-2) 2 = 4 (-2) 2 = = 100 tep 4: Find the mean of those squared deviations, tep 5: Take the non-negative square root of the quotient (converting squared units back to regular units), 36 6 o, the standard deviation of the set is 6. This example also shows that, in general, the standard deviation is different from the mean absolute deviation, as calculated in Eq. 2. pecifically for this example the mean deviation is 5. Despite these differences, both methods of estimating errors are acceptable. 6

13 III. GRAPHICAL REPREENTATION OF DATA: ome essentials in plotting a graph. 1. Arrange the numbers to be plotted in tabular form if they are not already so arranged. 2. Decide which of the two quantities is to be plotted along the X-axis and which along the Y-axis. It is customary to plot the independent variable along the X-axis and the dependent along the Y. 3. Choose the scale of units for each axis of the graph. That is, decide how many squares of the cross-section plotted along a particular axis. In every case the scales of units for the axes must be so chosen that the completed curve will spread over at least one-half of the full-sized sheet of graph paper. 4. Attach a legend to each axis which will indicate what is plotted along that axis and, in addition, mark the main divisions of each axis in units of the quantity being plotted. 5. Plot each point by indicating its position by a small pencil dot. Then draw a small circle around the dot so that each plotted point will be clearly visible on the completed graph. This circle is drawn with a radius equal to the estimated probable error of that particular measurement (you may use the percent difference when calculable). (ee "errors" below). 6. Draw a smooth curve through the plotted points. This curve need not necessarily pass through any of the points but should have, on the average, as many points on one side of it as it has on the other. The reason for drawing a smooth curve is that it is expected to represent a mathematical relationship between the quantities plotted. uch a mathematical relationship ordinarily will not exhibit any abrupt changes in slope, merely indicates that the measurement is subject to some error. A close fit of the experimental points to the smooth curve shows that the measurement is one of small error. 7. Label the graph. That is, attach a legend which will indicate, at a glance, what the graph purports to show. 7

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15 MA AND DENITY Apparatus: - Electronic balance - Vernier caliper or metric ruler - Assorted metallic cylinders - Aluminum bar - Wooden block - Irregular shaped object (mineral/rock sample) - 250ml graduated cylinder Part I. Mass and Weight: The mass of a body at rest is an invariable property of that body. It is a measure of the quantity of matter in a body. A body has the same mass at the equator as at the North Pole, -- the same mass on the earth as on Jupiter or interstellar space. The gravitational force between the earth (or other planet) and a body is called the weight of the body with respect to the earth (or other planet). The gravitational force on a body is a variable quantity even on the surface of the earth, e.g., the weight of a body is larger at the North Pole than at the Equator. E.g., A book transported to the moon would have the same mass (quantity matter) on the moon as it had back on the earth, but the book weighs less on the moon than it did on the earth because the moon's gravitational pull is less than the earth's. The weight of a body is proportional to its mass, the proportionality factor depending on the place at which the weight is determined. If the weight of a body is compared with that of a standard body, at the same place on the earth the ratio of the two weights is equal to the ratio of the two masses. Consequently, if the weight of the body is found to be equal to the weight of a standard body at the same place on earth, the two masses are equal. In order to measure the mass of a body, it is necessary to find a standard mass or a combination of standard masses whose weight equals that of a body at the same place on the earth. The device employed for this purpose is called a balance. Part I - Obtaining the mass: 1.1. Determine the mass of each object using the balance. Record all data in tabular form. Part II - Volume based on measured dimensions: 2.1. Using a metric ruler or vernier caliper, make the necessary measurements to enable you to calculate the volume of the regular bodies. Repeat each measurement at least once and take the average Calculate the volume for each regular object using the applicable formulas below. 9

16 Fig. 1 - Volume Formulas Part III. Measuring the volume with the graduated cylinder: The graduated cylinder used to measure the volume of a liquid has the scale in milliliters. A liter is a unit of volume used in the metric system. There are 3.79 liters to a U.. gallon, but for our purposes it turns out that: or more usefully: 1 Liter = 1000 ml = 1000 cubic centimeters (cm 3 or cc) 1 ml = 1 cc Fig. 2 - Graduated Cylinder If one pours water into a graduated cylinder one notices the top surface of the water is curved (Fig. 2). The curved surface is called a meniscus. The curvature is due to cohesive forces between the inner wall for the graduated cylinder and the water in contact with it. We read the column of water by looking at the correspondence of the bottom of the meniscus with the scale of the cylinder. It was Archimedes who noted that any object of any shape when placed in a liquid displaced its own volume. Thus, placing an object in our graduated cylinder (which now contains some water) we note that the water level rises. 10

17 3.1 Use the graduated cylinder to obtain the volume of the objects applicable to this method. Be ingenious with the wooden block! Part IV. Mass Density: The mass density of a material is defined as the mass of any amount of that material divided by the volume of that amount. The density of a substance is a fixed quantity for fixed external conditions, and, thus, is a means of identifying a substance. E.g., All different shaped solids of aluminum have the same density at room temperature. The units of mass density are g/cm 3 or kg/m 3 in the metric system. When we use centimeter (cm), grams (g), and seconds (s) in measuring quantities we refer to the cgs system. Likewise when we use meters (m), kilograms (kg), and seconds (s) we refer to the mks system Calculate the mass density of each object in the cgs system Identify the unknown object by using the density you calculated and finding a close match in the Density Table shown below. TABLE OF DENITIE OF COMMON UBTANCE* Name Density [g/cm 3 ] Name Density [g/cm 3 ] Name Density [g/cm 3 ] Name Density [g/cm 3 ] Aluminum 2.70 Calcite 2.72 Ash 0.56 Cement 1.85 Brass 8.44 Diamond 3.52 Balsa 0.17 Chalk 1.90 Copper 8.95 Feldspar 2.57 Cedar, red 0.34 Clay 1.80 Iron 7.86 Halite 2.12 Corkwood 0.21 Cork 0.24 Lead Magnetite 5.18 Douglas Fir 0.45 Glass 2.60 Nickel 8.80 Olivine 3.32 Ebony 0.98 Ice 0.92 ilver Mahogany 0.54 ugar 1.59 Tin 7.10 Oak, red 0.66 Talc 2.75 Zinc 6.92 Pine, white 0.38 *ee the American Institute of Physics Handbook for a more extensive list. All values in cgs (g/cc) and at 20 C. 4.3 Calculate the % difference of your density measurements. 11

18 Questions: 1. By Archimedes' observation how would you obtain the volume of the object placed in the cylinder? 2. Which value of the volume is closer to the 'truth'? I.e., Part II or III. Explain your answer. 3. How do you account for the errors in your computed values of the density(ies)? 4. Which type of measurement done in parts I, II and III do you think you made with the least error? i.e., mass or length or volume. Explain. 5. Which of the densities you have just determined would you expect to be the least accurate? 6. What is the benefit, if any, in measuring volumes by using Archimedes observations? 12

19 UNIFORM MOTION Apparatus: - Air track, air supply and hose - Master and accessory photogate timers - Glider with flag - Rubber bumper Introduction: Movement of an object can be seen as a change in its position over some period of time. We will be examining one particular type of motion; uniform motion. Velocity can be defined as the rate of change in the distance an object travels, in a particular direction, per unit time, such as miles per hour, feet per second, meters per second, or centimeters per second. An object traveling with uniform motion maintains the same velocity for the entire time it is observed. Where d is the distance, t is the time and v is the velocity, this relationship can be expressed as: The apparatus we will use in our investigation is the linear air track. The air track has a triangular surface with many small holes, air is pumped through these holes. The air forms a cushion between the track and gliders which "float" on this cushion. This allows the examination of the movement of these gliders with almost no friction. The lack of friction is important as it allows the gliders to move with relatively constant velocity over large distances. et-up: et-up air track as shown on Fig. 1. Turn on the blower unit and allow the air track to warm up. Fig. 1 - Air Track et-up Place the glider on the track and level the track until the glider remains at rest near the center. 13

20 Procedure: Position the start and stop photogates so that the distance between them is 20cm. et the master photogate to pulse mode. With the rubber band set for the smallest separation, launch the glider and record the time. Be sure not to allow the glider to bounce back and trip the start gate before the time is recorded. Repeat two more times for the same distance. Repeat the procedure after moving the stop photogate to give timing distances of 40cm, 60cm, 80cm and 100cm. Reset the timer each time before releasing the glider. Do not forget to do three runs for each distance and record the corresponding times. Data Table d [cm] t [s] t avg [s] v=d/t avg [cm/s] t 1 = 20 t 2 = t 3 = t 1 = 40 t 2 = t 3 = t 1 = 60 t 2 = t 3 = t 1 = 80 t 2 = t 3 = t 1 = 100 t 2 = t 3 = Calculations and Graph: 1. Calculate the average time for each given distance. 2. Use the average time to calculate the average velocity for each position. Compare these velocities are they equal? How much do you trust your results? 14

21 3. Use all the velocities on the 4 th column and find the mean. 4. Use the data from the table to plot a graph of d vs. t avg. 5. Determine the slope of the graph, how does it compare to the mean velocity you obtained on Calculation 3? 15

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23 MOTION OF A BODY IN FREE FALL Apparatus: - Behr Free-Fall apparatus - Pre-made tape from the free fall apparatus - Masking Tape - Ruler and/or meter stick Discussion: In the case of free falling objects the acceleration and the velocity are in the same direction so that in this experiment we will be able to measure the acceleration by concerning ourselves only with changes in the speed of the falling bodies. (We recall the definition of acceleration as a change in the velocity per unit-time and the definition of velocity as the displacement in a specified direction per unit-time.) A body is said to be in free fall when the only force that acts upon it is gravity. The condition of free fall is difficult to achieve in the laboratory because of the retarding frictional force produced by air resistance; to be more accurate we should perform the experiment in a vacuum. ince, however, the force exerted by air resistance on a dense, compact object is small compared to the force of gravity, we will neglect it in this experiment. The force exerted by gravity may be considered to be constant as long as we stay near the surface of the earth; i.e., the force acting on a body is independent of the position of the body. The force of gravity (also known as the weight of the body) is given by the equation: where m is the mass and g is the acceleration due to gravity The direction of g is toward the center of the Earth. As shown by Galileo, the acceleration imparted to a body by gravity is independent of the mass of the body so that all bodies fall equally fast (in a vacuum). The acceleration is also independent of the shape of the body (again neglecting air resistance). Useful Information for Constant Acceleration: 17

24 Fig. 1 - Behr Free-Fall Apparatus This is the Behr Free-Fall apparatus. Initially the body is at the top of the post and held by an electromagnet; when the switch is opened, the magnet releases the body, which then falls. A record is made of the body's position at fixed time intervals by means of a spark apparatus and waxed tape. When the body is released, it falls between two copper wires that are connected to the spark source. The device causes a voltage to be built up periodically between the wires, and this causes a spark to leap first from the high voltage wire to the body and to the ground wire, a mark is burned on the waxed paper by the spark. The time interval between sparks is fixed (here it is 1/60 of a second); thus the time interval between marks on the tape is also fixed and the marks on the tape record the position of the body at the end of these intervals. ee Fig

25 Fig. 2 - ample tape and demonstration of falling bob When you obtain a tape, inspect it and draw a small circle around each mark made by the spark apparatus to help with the identification of the position marks. You will obtain the acceleration of gravity, g, by two methods. The difference in the methods is in the analysis of the data on the tape. Method I: 1. Choose a starting point and from that point on, label your points, 1, 2, 3... n. 2. Obtain the distance Ä in cm between two successive points. For example, assume the distance between points 3 and 4 is: 4.52cm. Thus, Ä=4.52cm. 3. Obtain the average velocity over each of these distances. Note that the time interval Ät between two successive points is s. 4. Obtain the successive changes in average velocities ÄV then use these changes to compute the acceleration for each particular change. 19

26 5. Tabulate your data as follows: n Ä [cm] t= n Ät [s] [cm/s] ÄV [cm/s] [cm/s 2 ] 1 1/60 2 2/ Note: n n/60 6. Obtain g by taking the average of the values of a on the 6 th column of your table. tate g and the % difference of your result. Method II: 1. Plot a graph of velocity V versus time t; the independent variable should be plotted on the abscissa and the dependent variable along the ordinate. 2. Determine g from the slope of the graph, the units should be cm/s Convert your value of g from cm/s 2 to m/s 2. Compare your result with the theoretical value of g = 9.80 m/s 2. Questions: Fig. 3 - ample graph of V vs t 1. What are the advantages in terms of analysis by Method 2 as compared to Method 1? 2. Does any part of the experiment show that all bodies fall with constant acceleration? 3. Why doesn't the graph of V versus t (Method 2) go through the origin? 20

27 FORCE AND ACCELERATION Apparatus: Air track, air supply and hose Master and accessory photogate timers Glider and Air track kit Electronic balance Introduction: The interaction between various objects is responsible for a whole variety of phenomena in our Physical World. If no interaction existed our world would be a bunch of objects performing Uniform Motion in accordance to Newton s 1 st Law. We could not even perceive such a world because out perceptions are associated with out interaction with the external environment. For example, vision is due to interaction with light. In fact, we would not even exist because no forces would bind the constituents of our organisms together. What a boring situation! o force is one of the central physical concepts. It is not possible for us to trace out all the possible means by which various forces act, and what are all the implications. However, we will consider a specific situation which can be studied completely. This is based on the observation that a force applied to a single object produces acceleration of this object. Furthermore, a constant force produces a constant acceleration. In accordance with Newton s 2 nd law of dynamics, the acceleration is proportional to the force. This law can be formulated as the concise equation: F = MA Eq. 1 where A is the acceleration and F is the force. While F is essentially due to other objects, the coefficient M is a property of the accelerating object. This property is called mass. Applying this Fig. 1 - et-up 21

28 equation, we immediately deduce that due to gravity any object of mass m feels the force, m g close to the Earth s surface. Indeed this is a way to verify Eq. 1 experimentally. Unit of force is a Newton, N and mass is measured in kilograms, kg. Accordingly, Experiment: 1N = 1kg m/s 2 A glider is placed on the airtrack with a string and hanging weight attached. The hanging mass M 2 produces the force F on the glider. If M 2 is much smaller than M 1, the relation F=M 2 g holds with good accuracy. The force F should produce the acceleration A in accordance with Eq. 1. If we can measure A, then the Eq. 1 can be verified. In order to measure A, two photogates are placed at a distance d apart so that the recording of time, t the glider moves through this distance can be made. If the glider starts moving from rest with some constant acceleration, A, this acceleration can be computed by the following formula: Eq. 2 Finally, if indeed Eq. 1 is valid, the glider mass M 1 can be found as either the slope of the linear fit of the graph F vs A or as the mean of the ratio: Eq. 3 In order to determine F, we use Newton s 2 nd and 3 rd Laws: mg - F= ma and F=MA from the equations above we can obtain F as follows: F = m (g -A) Eq. 4 ummarizing, the purpose of these measurements is to obtain independently data for F and A, and check that these data are related to each other through the theoretical dependence indicated in Eq. 1. Then, the glider mass M 1 is to be found and compared with the value obtained from the scale. 22

29 Preliminary set-up: Turn on the air supply and allow the track to warm up for several minutes then level the air track. Cut a length of string approximately 130 cm long and tie a small loop at each end. Attach one end of the string to the glider by placing one loop around the connector for the flag, and the other end to the mass hanger. Place the string over the pulley and set the position of the glider so that the mass is just below the pulley. Place the photogates 60-80cm apart making sure that the hanger does not hit the floor before the glider crosses through the gate closer to the pulley. Adjust the position of the start photogate so that it is about to be tripped by the glider. et master photogate to pulse mode. Procedure: 1. Weigh the glider, flag and string and record the total mass as M 1 (units in kg). If you wish for the glider to be heavier there is the option to add 50 g weights, one on each side of the glider. 2. The hanger by itself weighs 2 g (0.002 kg). Place 5 g (0.005 kg) on the hanger to get a total mass M 2 = 7 g = kg. When ready, release the glider and record the time. Repeat two additional times. 3. Combine the small masses to give additional total hanging masses of 12,17, 22, and 27 grams. Take three time measurements for each and record them. 4. Use the table below to tabulate your data or the ForceAccelPlotOnly.ga3 template that is saved on the lab computers: PHY Exp Templates\GAExpTemplates\PHY114L261 folder. d = [m] M 1 = [kg] (mass obtained using the electronic balance) M 2 [kg] t 1 [s] t 2 [s] t 3 [s] t avg [s] F=M 2 g [N] A=2d/t avg2 [ m/s 2 ] M=F/A [kg] Note: For this experiment you will only need to use the hanger plus combinations of the slotted silver masses to obtain the required hanging mass M 2. Your airtrack kit includes the following masses and you must be careful not to lose them: Hanger...2 g x 1 mall lotted ilver Mass...5 g x 1 Large lotted ilver Mass...10 g x 2 23

30 Graph/Calculations: 1. From the table of Procedure 5 plot a graph of F vs. A. Find the slope of the best linear fit for this graph and record it. What should the slope of this graph represent? If you are using the Graphical Analysis template ForceAccelPlotOnly.ga3 click on f(x) on top of the toolbar and select proportional fit to obtain the slope of the line. 2. Compare M 1 (mass of the glider) to the other M values that were obtained based on experimental data. Questions: 1. How close is the value of the glider mass obtained from the slope to the one obtained from the electronic balance? 2. How close is the value of the glider mass obtained from the mean of the F/A ratio (last column of your data table) to the one obtained from the electronic balance? 3. Give a conclusion as to whether this experiment supports Newton s 2 nd Law of dynamics. Discuss the precision of your measurements for the glider mass, and possible reasons for deviations. 24

31 MECHANICAL WORK AND ENERGY Apparatus: Air track, air supply and hose Master photogate timer Glider and Air track kit Electronic balance Objective: The concept of Work and Energy is to be studied. The Law of Conservation of Energy is to be verified for a simple mechanical set-up. Theoretical Background: The concept of Work and Energy is crucial for understanding nature. Its importance is not limited to the mechanics of a single object. This concept can equally be applied to complex systems atoms, molecules, substance, and even organisms. All acts of motion, transformation, and creation in our world are due to Work and Energy. We will begin study of this concept for a simple mechanical system the glider on the airtrack. A very special significance is endowed to the Law of Conservation of Energy which states that the total amount of Energy in the world is constant. That is, Energy can neither be created or destroyed. It can be only transformed from one form to another and redistributed between objects. The process of Energy transformation and redistribution is called Work. How Energy is defined and measured is to be studied in this experiment, though here we will talk only about Mechanical Energy and Work. The first form of energy we will investigate is Kinetic Energy. This is energy or ability to do work, that an object possesses due to its motion. In this case if we know the mass of an object and its velocity, we can calculate its kinetic energy: The larger the object mass, M or the velocity, V, the greater the KE. If two moving bodies are considered then their total kinetic energy is: Eq. 1 The second form of energy we will investigate is Potential Energy. This is the energy or ability to do work, that an object possesses due to its height or position. In our experiment we will only deal with objects raised a certain height above either the ground or some reference point. If we know the mass of an object and its height we can calculate its potential energy: Eq. 2 25

32 The unit of energy is the Joule, J where: If the mechanical system is isolated from the environment, the total Mechanical Energy is: Eq. 3 In other words, the total mechanical energy is conserved, in accordance with the general statement given above. Mechanical energy can be lost or acquired, if it is transformed to or from other forms of energy. Fo example, friction decreased the KE and heats the environment. If, however, no friction is present, Eq. 3 says that any increase in KE occurs at the expense of PE, or conversely any increase of PE occurs at the expense of KE. Reformulated in terms of the change of Kinetic Energy, ÄKE and the change in Potential Energy, ÄPE, the statement becomes Eq. 4 Preliminary set-up: imilar to the previous experiment. Cut a length of string approximately 130 cm long and tie a small loop at each end. Attach one end of the string to the glider by placing one loop around the flag connector, and the other end to the mass hanger. Place the string over the pulley and set the position of the glider so that the hanging mass is just below the pulley. Position the photogate approximately 60 to 80cm from the pulley. A typical value for h is 60 cm. et the photogate to gate mode. Fig. 1 - et-up 26

33 Procedure: 1. Weigh the glider with the flag and string and record the total mass as M 1 with units in kg. If you wish for the glider to be heavier there is the option to add 50 g weights, one on each side of the glider. 2. The hanger by itself weighs 2 g (0.002 kg). Place 5 g (0.005 kg) on the hanger to get a total mass M 2 = 7 g = kg as shown on the table below. When ready release the glider M 1. Record the time. Repeat two additional times. 3. Combine the small masses to give additional total hanging masses of 12,17, 22, and 27 grams. Take three time measurements for each and record them. 4. Use the table below to tabulate your data and calculate ÄKE and ÄPE using Eq. 1 and Eq. 2. You may also use the Graphical Analysis template MechEnergyKEPEPlotOnly.ga3 that is saved on the lab computers in the PHY Exp Templates\GAExpTemplates\PHY114L261 folder. h = [m] M 1 = [kg] d = 0.1 [m] M 2 [kg] t 1 [s] t 2 [s] t 3 [s] t avg [s] V=d/ t avg [ m/s] ÄKE [ J] ÄPE [J] Note: For this experiment you will only need to use the hanger plus combinations of the slotted silver masses to obtain the required hanging mass M 2. Your airtrack kit includes the following masses and you must be careful not to lose them: Hanger...2 g x 1 mall lotted ilver Mass...5 g x 1 Large lotted ilver Mass...10 g x 2 Graph and Calculations: 1. Plot a graph of ÄKE vs ÄPE. 2. Find the slope of the best linear fit for this graph and compare it with its expected value 1. If you are using the Graphical Analysis template click on f(x) on top of the toolbar and select proportional fit to obtain the slope of the line. 27

34 Questions: 1. For a hanging weight of 8 g and a height of 2 m, make a prediction for the velocity of the glider. 2. Discuss possible deviations of the slope in cases when the airtrack was not leveled. 3. How would the slope (if compared to 1) of the best linear fit graph change in the presence of friction. 28

35 FRICTION Apparatus: Friction block Friction board Pulley 50gr hanger lotted weights tring Electronic balance Meter stick or pendulum protractor Fig. 1 - et-up for block on a horizontal plane Theory: For a large class of surfaces the ratio of the (static and kinetic) frictional force, f, to the normal force, N, is approximately constant over a wide range of forces. This ratio defines, for specific surfaces, the coefficient of friction, namely: In the static case when our applied force reaches a value such that the object instantaneously starts to move we obtain the maximum frictional force or limiting value of the frictional force f max. We can now obtain the coefficient of static friction defined as: Fig. 2 - Forces acting on the system When the object is moving it experiences a frictional force, f K which is less than the static. Frictional experiments tell us that we can (analogous to the static case) define a coefficient of kinetic friction given by: 29

36 Procedure: 1. et up the equipment as in Fig Weigh the block, W Increase the weight W 2 until the block is on the point of sliding. Record the value of W Repeat for five other values of W 1 by slowly increasing the block s weight by adding masses to its top. 5. Newton's Laws tell us: a) N = W 1 b) At point of sliding f max = W 2 6. Plot f max versus N. Determine ì s from the slope of your graph. 7. Repeat procedures 1-6 above but this time adjust W 2 so that the block W 1 moves with constant speed after it has been given an initial push. Plot the data and obtain ì k from your graph. 8. et the block on an inclined plane and slowly increase the angle of the plane until the block is on the verge of sliding down. Note the value of the inclined plane angle. 9. Repeat Procedure 8 except hold the inclined plane at a fixed angle (lower than the angle found in above procedure), so that the block moves down the plane with constant speed after it has been given an initial push. Note the value of the angle at which this happens. 10. The data of Procedures 8 and 9 permit us to determine ì s and ì k by analyzing the forces on the block in Fig. 3. By applying Newton s econd Law we see that: From which: Fig. 3 -Forces acting on a block on an inclined plane Use this last formula to obtain ì s from Procedure 8 and ì k from Procedure 9. Estimate errors and compare the % difference of these with the values you obtained in 6 and 7. 30

37 Questions: 1. Which coefficient, ì s, or ì k is usually the larger? 2. What graphical curve should you obtain in part 6? 3. Is it possible to have a coefficient of friction greater than 1? Justify your answer. 31

38 32

39 CENTRIPETAL FORCE Apparatus: Centripetal force apparatus et of slotted weights 50g hanger topwatch Electronic balance Level Ruler Fig. 1 - Centripetal Force Apparatus and Display of tatic Test Theory: A mass m moving with constant speed v in a circular path of radius r must have acting on it a centripetal force F where n is the revolutions per sec. Eq. 1 Description: As indicated in Fig. 1, the shaft, cross arm, counterweight, bob, and spring are rotated as a unit. The shaft is rotated manually by twirling it repeatedly between your finger at its lower end, where it is knurled. With a little practice it is possible to maintain the distance r essentially constant, as evidenced for each revolution by the point of the bob passing directly over the indicator rod. The centripetal force is provided by the spring. The indicator rod is positioned in the following manner: with the bob at rest with the spring removed, and with the cross arm in the appropriate direction, the indicator rod is positioned and clamped by means of thumbscrews such that the tip of the bob is directly above it, leaving a gap of between 2 and 3mm. The force exerted by the (stretched) spring on the bob when the bob is in its proper orbit is determined by a static test, as indicated in Fig. 1(tatic Test). The mass m in Eq. 1 is the mass of the bob. A 100-gm mass (slotted) may be clamped atop the bob to increase its mass. The entire apparatus should be leveled so that the shaft is vertical. 33

40 Procedure: Devise a method for determining whether the shaft is vertical, and make any necessary adjustments of the three leveling screws. The detailed procedure for checking Eq. 1 experimentally will be left to the student. At least three values of r should be used, with two values of m for each r. A method for measuring r should be thought out, for which purpose the vernier caliper may be useful. The value of n should be determined by timing 50 revolutions of the bob, and then repeating the timing for an additional 50 revolutions. If the times for 50 revolutions disagree by more than one-half second, either a blunder in counting revolutions has been made, or the point of the bob has not been maintained consistently in its proper circular path. Fig. 2 - Centripetal Force Apparatus Rotating Results and Questions: 1. Exactly from where to where is r measured? Describe how you measured r. 2. Tabulate your experimental results. 3. Tabulate your calculated results for n, F from static tests, and F from Eq. 1, and the % difference between the F's, using the static F as standard. 4. Describe how to test whether the shaft is vertical without the use of a level. Why should it be exactly vertical? 5. Why is the mass of the spring not included in m? 34

41 CALORIMETRY Apparatus: Calorimeter Metal samples Glass beaker (600mL) Hot plate Tongs Electronic balance Plastic beaker topwatch Multimeter (Fluke) Fig. 1 - Experiment et-up Introduction: Consider a calorimeter of mass m c and specific heat c c containing a mass of water m w. uppose the calorimeter and its contents are initially at some temperature t i. If a hot body of mass m s, specific heat c s, is placed in the calorimeter, then the final equilibrium temperature t f of the entire system can be measured. Eq. 1 Eq. 1 assumes no heat losses. From this equation it is possible to determine the temperature t h the metal sample had before it was immersed in the calorimeter containing water at room temperature. Therefore, Eq. 2 Procedure: 1. Fill a glass beaker with water to about 400ml and carefully place it on the hot plate. Turn on the hot plate and set the temperature to approximately 450 C. Let the water heat up while taking other measurements. Keep the calorimeter away from heat source. 2. Place the empty inner cup and stirrer on the electronic balance. Record the mass m c. 3. With the inner cup still on the scale zero the balance. lowly fill the inner vessel with cool water till the scale reads approximately 150ml. Note that 150ml is equivalent to 150g which is then represented as m w. Carefully and without spilling place the inner cup inside the larger cup. Cover it and place the thermocouple through the center hole. 35

42 4. Obtain the mass of your metal sample. 5. Once the water starts to boil carefully place the metal sample in the beaker. Heat the sample for10 minutes. While the sample is heating note the initial temperature of the water in the calorimeter just prior to immersing the sample. 6. Immerse the hot sample in the calorimeter, cover it and stir gently. Note the final temperature of the system after equilibrium has been reached. 7. Use Eq. 2 to calculate the temperature of the hot metal. Questions: 1. If the final temperature of the calorimeter and its contents was less than room temperature, would the value of t h computed from Eq. 1 be too high or too low? Justify your answer. pecific Heats ample pecific Heat [J/g C] Aluminum Brass Copper Iron Lead teel Water

43 OHM LAW AND REITANCE Apparatus: Variable DC power supply Tubular resistor (100Ù) Tungsten filament lamp (60W) Lamp socket Multimeter set to V DC Multimeter set to ma DC PT knife switch Connecting wires Objective: Fig. 1 - et-up To illustrate the voltmeter-ammeter method of measuring resistance and to verify Ohm's Law. Discussion: Materials containing electric charges which can move freely are called conductors. Thus, applying an electric field on such a material results in the mechanical motion of the charges in one particular direction. This unidirectional motion of electric charges is called electric current. The applied electric field is characterized by the difference of the electric potential V along the conductor. It is measured in Volts, V. The electric current, I is characterized by the amount of charge transferred through the conductor each second. It is measured in Amperes, A. For most conductors, the relation between V and I follows Ohms Law: Eq. 1 where R is the resistance of the conductor, which does not depend on either V or I. Resistance depends on various factors -the material the wire is made of, the length of the wire, its cross sectional area. Resistance also depends on the temperature of the wire. The unit R is the Ohm, Ù. If graphed on axes V vs I, Eq. 1 yields a straight line whose slope is R. However, not all conductors obey Ohm s Law. This means that, if plotted, the data V vs I may be far from that of straight line for such conductors. uch conductors are called non-ohmic. Procedure: 1. et up the equipment as shown in Fig 1. Note the limiting current on the power supply has been set to 5A and must not be changed throughout the experiment. R is the 100Ù tubular resistor. 37

44 The first multimeter will be used to measure the current I in your circuit, set it to ma and press the yellow key for DC Current. et the second multimeter to VDC, this will measure the voltage drop across the resistor. Have your instructor check your connections. Close the circuit and allow current to flow in the circuit. et the power supply, V o to 1, 2, 4, 6, 10, 14, 18, 22, 26 and 30V and record the corresponding readings of I and V from the multimeters. When done, open the circuit. 2. With not current flowing through the circuit remove the tubular resistor and connect the tungsten lamp in its place. Have your instructor check your connections. Close the circuit and allow current to flow in the circuit. et the power supply, V o to 1, 2, 4, 6, 10, 14, 18, 22, 26 and 30V and record the corresponding readings of I and V from the multimeters. Note that when using low voltages give it a few seconds to allow the current, I to stabilize before recording it. When done with the procedure, open the circuit and turn off all the instruments. Calculations and Graphs: 1. From the data of Procedure 1 plot V as the y-axis and I as the x-axis. If you obtain a straight line then Ohm s Law has been verified. Find the slope of the line and compare it to the known resistance. 2. From the data of Procedure 2 plot V as the y-axis and I as the x-axis. Do you obtain a straight line or a parabolic curve? Questions: 1. What is the accuracy of your measurements of R in Procedure 1? 2. What is your explanation for the fact that light bulb does not follow Ohm s Law? 3. From the graph corresponding to the 60W bulb data find the current at 16V. 38

45 THE JOULE EXPERIMENT (Equivalence of Electrical Energy and Heat) Apparatus: Variable power supply 10A ammeter Electric calorimeter with rubber stopper Multimeter (Fluke) Electronic balance topwatch Connecting wires PT switch 600ml plastic beaker Theory: Fig. 1 - Joule Exp. et-up Mechanical Equivalent of Heat: For a long time, motion and heat were thought to be very different kinds of phenomena. But during the last century, several experiment and calculations pointed to the idea that heat is a kind of motion, in fact, a kind of kinetic energy. Crucial to this new evidence were the classic experiments of James Joule (during the 1840's), which led to the principle of general energy conservation. Joule spent years converting several different forms of energy to heat; among these were gravitational potential energy and electrical energy. The former is easier to picture and understand, and therefore the description of this experiment appears in practically all textbooks, but it is difficult to perform. We will perform the electrical version which is much easier, though it requires the use of the laws of electricity. The goal of all these experiments is to obtain the mechanical equivalent of heat of Joule s constant, relating the common unit of mechanical and electrical energy (now called the joule in the metric system) to the common unit of heat, the calorie. Because the idea is so important, let us understand it first by looking at The Joule s Machine (Fig. 2). Joule suspended masses, with the other end of the rope wound around the axle of a paddle wheel. The paddle wheel is immersed in a tank of water which is thermally insulated. When the weight is allowed to fall (slowly), the paddle Fig. 2 - The Joule s Machine wheel turns, it heats the water, and the temperature rises. 39

46 The mass loses potential energy, but heat is added to the water. Joule found that for a given loss of mechanical energy, the same amount of heat always appears, regardless of how fast it is done or how the mechanism is constructed. Moreover, if twice as much mechanical energy is lost, twice as much heat appears; i.e., the heat added is proportional to the mechanical energy given up by the mass; or, the ratio of mechanical energy lost to heat gained is constant. Joule could measure this constant easily because one can calculate independently the mechanical energy lost and the heat gained: Eq. 1 assuming the speed of the mass is negligible at the end, and Eq. 2 where m w is the mass of the water, c w is the specific heat of the water, and ÄT is the change in temperature (for the time being we have neglected the heating of the vessel which contains the water). In the end, Joule found that, regardless of how the experiment was carried out, Eq. 3 This lead to the conclusion that mechanical energy is being converted to heat, M.E.=Q, that the calorie is just another unit of energy, and that therefore the conversion factor between these units if just from Eq. 3: Eq. 4 The Electrical Joule Experiment: Heating water electrically is very similar to heating it mechanically: instead of letting mass be pulled by the force of gravity, we let electrical charges be pulled by an electrical force through a metal (resistor). As the mass lost gravitational potential energy (in moving down from a height), the charges lose electrical potential energy in moving from the positive side (higher potential) to the negative side (lower side) of the battery or other source. This energy loss per time, the electrical power is given by: Eq. 5 where I is the current, V is the voltage, t is time, and W e is the electrical work done (measured in same units as mechanical work). Therefore, in our experiment, Eq. 5 is used just as Eq. 1 in the gravitational version. Here too, heat appears, warming whatever in touches. If the resistor (a heating coil in our case) is immersed in a thermally insulated container of liquid, the heating of the liquid can be measured in 40

47 the usual way, Eq. 2 except that for good accuracy one should include additional terms on the right side to account for heat lost to the container and whatever else is warmed by the current (see Eq. 7). Thus, the ratio, J, is obtained here as W/Q. We can do this for different amounts of electrical energy lost, and heat gained, simply by letting the heating take place for different lengths of time. And we can vary the rate of heating by changing the current. Procedure: 1. Using the electronic scale, weigh the inner cup of the calorimeter with the stirrer. Both must be dry. Denote the mass as m c. 2. Keep the inner cup on the scale and zero the latter. Fill the inner cup with approximately 250ml of cool water. Record the mass of the water as m w. 3. Carefully, place the inner vessel into the calorimeter, insert the heating coil. Place the thermocouple through the hole in the rubber stopper. et the thermocouple so that it is inside the coil not through it. The tip should be past the length of the coil but without touching the bottom. 4. Connect the circuit as shown on Fig Turn on the power supply. Close the switch to allow current to run through the circuit. lowly set the voltage to 6V and record the corresponding current. Immediately, open the circuit to avoid heating the water before starting the experiment. 6. Turn on the multimeter and set to mv and press the yellow key to change the setting to temperature readouts. tir the water, wait a bit for equilibrium, and record the temperature as T i this must be done before closing the circuit again. 7. When ready to start throw the switch to allow current to flow in the circuit again and simultaneously start the timer. 8. Record the temperature at one minute intervals for 12 minutes or till water heats up to 10 to 15 above room temperature. During the process the water must be stirred constantly but gently. Calculations: You now have all the data to calculate, at each of the above points in time, the value of the Joule constant, J. From Eq. 5, obtain the energy dissipated by the coil: Eq. 6 41

48 If I is in amperes, V in volts, and t in seconds, then W e is in Joules. Now calculate the amount of heat added to the water, the vessel, and the stirrer, from the following equation: Eq. 7 where c c is the specific heat of the calorimeter which in this case, it is made of aluminum, c w is the specific heat of water and T i and T f are the initial and final temperatures respectively. Note that T i is the temperature you recorded in procedure 5, thus, it will remain the same throughout the experiment and calculations. Find the average of all values of J=W e /Q thus obtained, and estimate your statistical error as outlined by the instructor. Compare your average J with the accepted value. Is the difference within the experimental error? If not, why not? Plot W e vs Q. Is the curve approximately a straight line? If so, determine the slope of the best straight line through the points which should be J and compare with the known value. Material pecific Heat [cal/g C] Aluminum 0.22 Water

49 REFLECTION AND REFRACTION Apparatus: Laser ray box Trapezoidal acrylic prism 3-sided mirror (plane, concave and convex) LED lamp Ruler, protractor 11x17 paper, masking tape. Objective: To investigate econd Law of Reflection and nell s Law. Discussion: Fig. 1 - Plane Mirror The econd Law of Reflection is basic to the operation of plane and curved mirrors. It will be verified experimentally that the angle of incidence è i is equal to the angle of reflection è r, where è i and è r are measured from the normal to the mirror at the point of reflection as in Fig. 1. è i = è r (Eq. 1) When dealing with refraction, if a light ray traveling in a medium 1 strikes the surface of a second medium 2, in addition to reflection aforementioned, the transmitted ray will be refracted (bent or broken) changing the direction of its propagation. How much it changes its direction will depend on the optical properties of both mediums called their index of refraction, n. The relationship that quantifies this dependence is nell's Law: (Eq. 2) where è 1 is the angle of incidence in the medium n 1 and è 2 is the angle of refraction in medium n 2. Both angles are measured to the normal of the surface separating the two mediums as shown in Fig. 2. In the diagram a light ray enters the left side of trapezoidal prism and exits the right parallel side, having undergone two refractions. Only the first refraction has been labeled for è 1, è 2 and their Normal NN'. Fig. 2 - ingle ray through a trapezoidal prism 43

50 Procedure: 1. et the plane mirror on a sheet of paper and trace its surface. et the ray box to produce a single ray and aim the ray toward the center of the mirror so that the ray is reflected back upon itself. Mark the ray with two points spread far enough apart to insure accuracy. Remove the mirror and trace this ray. This line represents the principal axis of the mirror. 2. Carefully replace the mirror and aim the ray again to strike the mirror at its vertex, but at some angle (say about 30 o or so) with the principal axis. Mark both the incident and reflected rays. The angle between the incident ray and the principal axis is the angle of incidence è i and the angle between the reflected ray and the principal axis is the angle of reflection è r. Measure and record both angles on your paper. Repeat this procedure for 3 different angles. 3. Draw a straight line and set the trapezoidal prism (frosted side down) vertically in such a way that the line goes through the center of the prism as on Fig. 2 line N-N. Trace the outline of the trapezoid. et the ray box to produce a single ray, set it so that the ray passes through the two parallel faces of the trapezoid. Note that the incident ray should enter the trapezoid at the same point where the Normal line, N, meets the first surface of the prism. Carefully mark the incident and emergent rays. Remove the trapezoid and construct the incident and emergent rays, and connect them with a straight line representing the internal ray as in Fig. 2. Measure and record the angles of incidence è 1 and angle of refraction è 2. Calculations: 1. From the results of procedure 2, compare è i and è r for the plane mirror. 2. From the results of Procedure 3, calculate the index of refraction, n 2, of the prism (second medium) and compare to the known index for acrylic (plexi-glass). Note that the index of refraction for the first medium, air, is n 1 = CWC 44

51 FOCAL POINT AND FOCAL LENGTH OF MIRROR AND LENE Apparatus: Laser ray box 3-sided mirror (plane, concave and convex) Diverging and converging lenses LED lamp Ruler 11x17 paper, masking tape. Objective: To find the focal point and focal length of mirrors and lenses. Discussion: Based solely on their refracting properties and shapes, lenses are capable of forming images of objects placed in front of them. Mirrors based their capacity to achieve this on their reflecting properties and shapes. Both lenses and mirrors focus light and have well defined focal points F and focal lengths ƒ. This same, single property generates both of their abilities. We should not be surprised that our treatment, here for lenses, will be strongly similar. When parallel rays of light or light from infinitely distant objects fall on a mirror, the image point, real as in Fig. 1(a) or virtual as in Fig. 1(b), is called the focal point, F of the mirror. The focal length, ƒ is the distance between F and the mirror. These distances are always measured along the so called principal or optic axes of the mirrors, which is the perpendicular bisector of the mirror. Note that the focal points for the rays in Fig. 1(a) and (b) are on this principal axis. The point where the principal axis intersects the mirror is called the vertex of the mirror. Fig. 1 - Focal points for concave and convex mirrors 45

52 As with mirrors, there are two distinctly different types of lenses that can be identified. They are correctly referred to as converging and diverging lenses, not convex and concave. Each lens has two focal points, which are determined by passing a parallel beam of light through a lens, as shown on Fig. 2. Fig. 2 - Converging and Diverging Lenses Procedure: 1. Locate and draw the principal axis of your concave mirror. Trace the mirror. et the ray box to produce a bundle of parallel rays. Aim the rays at the mirror, parallel to its optic axis, so that the reflected rays cross each other back on the axis. Label this point F. Measure the distance of F the mirror in centimeters. This distance is the focal length, ƒ. 2. Repeat this procedure using the convex mirror. Here the reflected ray will have to be extended back behind the mirror to the principal axis. ince F is now behind the mirror, the focal length ƒ is negative. 3. On a new page, draw a line along its length, near the middle of the page. This line will represent the principal axis for your lens. Place the center of the converging lens at the middle of the axis and perpendicular to it. Trace the lens on the paper. Be careful not to let the lens move off of its trace, throughout the procedure. et the ray box to produce a bundle of parallel rays. Locate and mark the first focal point F by directing these rays along the optic axis and marking their point of convergence. Measure and record the focal length ƒ. 4. Repeat Procedure 3, using the diverging lens. Note that this time the focal point will be behind the lens. Refer to Fig. 2b. CWC 46

53 OUND WAVE Apparatus: 1000ml graduated cylinder Acrylic tube Tuning forks (various frequencies) Rubber activator Objective: To determine the wavelengths in air of sound waves of different frequencies by the method of resonance in closed pipes and to calculate the speed of sound in air using these measurements. Discussion: The speed of sound can be measured directly by timing the passage of a sound over a long, known distance. To do this with an ordinary watch requires a much longer distance than is available in the laboratory. It is convenient, therefore, to resort to an indirect way of measuring the speed of sound in air by making use of its wave properties. For all waves the following relationship holds: where v is the speed of the wave, f is its frequency of vibration, and ë is its wavelength. In this Eq. 1 experiment, you are going to measure the wavelength of a sound of known frequency. You will then compute the speed of sound. You will use the principle of resonance to determine the wavelength produced by a tuning fork of known frequency. When a tuning fork is sounded near the open end of a tube closed at the other end, a strong reinforcement of the tuning fork sound will be heard if the air column in the tube is the right length. This reinforcement is known as resonance. It is caused by the fact the waves reflected from the closed end of the tube return to the top of the tube in phase with the new direct waves being made by the fork. The direct and reflected waves thus combine their effects. To find the length of the air column which produces resonance for a given tuning fork, it is necessary to vary the length of the tube. Fig. 1 shows one of the methods to accomplish this purpose. In Fig. 1 an acrylic tube is inserted inside the 500ml graduated cylinder. The cylinder is then filled with water being careful not to spill. A tuning fork will start vibrating when stricken with a rubber mallet. This is placed right above the graduated cylinder, then the tube is raised to change the length of the air column in the tube until Fig. 1 - Resonance Tube 47

54 the sound intensity is at a maximum. For a tube closed at one end, whose diameter is small compared to its length, strong resonance will occur when the length of the air column is one-quarter of a wavelength, ë/4, of the sound waves made by the tuning fork. A less intense resonance will also be heard when the tube length is 3/4ë, 5/4ë, and so on. ince the shortest tube length for which resonance occurs is L=ë/4, it follows that ë. Practically, this relationship must be corrected for the diameter d of the tube. This gives: In this experiment ë, L, and d will be measured in meters. Procedure: Eq Measure the inner diameter of the hollow tube and record it. Record the room temperature. 2. Choose a tuning fork of known frequency. Record the frequency. 3. Place the acrylic tube, with the 0 mark atop, inside the graduated cylinder and fill it with water. The water level should be as high as possible but without spilling, making the air column as short as possible. 4. trike the fork on the rubber activator and bring the tuning fork over the open end of the tube. Hold the tuning fork so that the tines vibrate toward and away from the surface of the water in the tube. lowly raise the tube until you hear strong resonance. At this point measure the length L, of the air column in the tube in meters and record it in your date table. 5. Using several other tuning forks of different frequencies, make the same measurements as in Procedures 2 through 4. Record all your measurements on your data table. Table 1 Frequency f [Hz] Length of Air Column L [m] Diameter of Tube d [m] Wavelength ë [m] Room Temperature T [ C] peed v [m/s] 48

55 Calculations: 1. Using the values of L and d in Table 1, calculate the value of the wavelength ë from Eq. 2. Enter this value of wavelength in the table. 2. Using Eq. 1 calculate the value of the speed of sound in air and record this value in the table for each of the tuning forks used. 3. Calculate the value of the speed of sound in air from the following relation: Eq. 3 where T is the temperature in degrees centigrade and 331m/s is the speed of sound in air at 0 C. 4. Compare the result obtained by resonance measurement with the calculated value obtained by using Eq. 3. Questions: 1. How could you use the method and the results of this experiment to determine whether the speed of sound in air depends upon its frequency? What do your results indicate about such a relationship? 2. If we assume that the speed of sound at any temperature is known from Eq. 3, how can this experiment be used to measure the frequency of an unmarked tuning fork? 49

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57 UPPLEMENTARY EXPERIMENT 51

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59 TANDING WAVE ON A TRETCHED TRING Apparatus: Electric string vibrator Pulley C-clamp Wooden board Elastic cord Meter stick and 30cm ruler Friction block 50g hanger and slotted weights Objective: Fig. 1 - et-up To demonstrate standing waves on a stretched string and to determine the dependence of wave velocity on the tension in the string and its mass per unit length. Discussion: The velocity v of transverse waves in a stretched string depends on the stretching force of tension T and the mass per unit length ì (mu) of the string according to the relation: Eq. 1 The frequency of the waves f depends on their source, in our experiment, a 60Hz electric vibrator will be used. Once the frequency and wave velocity are chosen the wavelength of the waves will be fixed by the requirement that: Eq. 2 It should be noted that Eq. 2 provides us with a means of calculating the wave velocity if the wavelength and frequency of the waves are known. Waves traveling on a string fixed at both ends will be reflected back at those boundaries and combine with the incident waves. Under the right conditions, namely, when the length of the string L satisfies the requirement: Eq. 3 the incident and reflected waves will combine to form standing waves, i.e. waves that "appear" stationary on the string (Fig. 2) The wavelengths of these stationary waves may be measured directly, and their wave velocities calculated from Eq. 2. In the experiment a means of separately varying the tension and mass per unit length of the string will be provided, and Eq. 1 will be verified. 53

60 Fig. 2 - tanding Waves on a tretched tring Procedure: 1. et up equipment as in Fig. 1. Cut approximately 1½ meters of elastic string. Tie one end of the string to the vibrator and the other to the weight hanger. 2. Record the mass per unit length ì of the elastic string provided for this experiment. 3. Place the 50g hanger on the string over the pulley. Plug in vibrator to the outlet. The string will start vibrating immediately. 4. Vary the mass to form a standing wave pattern made up of 8 nodes. Note that a node is a point along a standing wave where amplitude is zero. Avoid the "nodes" located at the vibrator or at the pulley. These are not true nodes. 5. Measure the distance between the nodes in meters, this distance represents ë/2. Determine ë. 6. Vary T to create 7, 6, 5 and 4 nodes, recording T and the wavelength of each new standing wave pattern formed. Data Table N m [kg] T=mg [N] [m] ë [m] v=ëf [m/s] v 2 [m 2 /s 2 ] [kg/m 3 ]

61 Calculations: 1. Calculate tension T = mg. 2. Obtain the wavelength ë in meters. 3. Calculate velocity using Eq. 2 where f=60hz. 4. Plot T as ordinate against v 2 as abscissa. Fit the plotted data with a straight line that passes through the origin. Record the slope and compare to the known value of ì. 5. Use Eq. 1 to determine ì for each set of nodes. Calculate the average of ì and compare to the known value of ì. 55

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63 DENITY AND ARCHIMEDE' PRINCIPLE Apparatus: Electronic balance Hook stand and beaker base 600ml plastic beaker Aluminum cylinder with hook Brass pendulum bob (2.54cm) tring 500ml graduated cylinder with water Ruler or Vernier caliper Fig. 1 - et-up Introduction: Archimedes's principle states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid (Fig. 2). Imagine now that a body is suspended in water as shown in Fig. 3b. The effective weight of the body (W eff ) as measured by the masses on the scale is given by: Eq. 1 but the effective weight is equal to the weight of the object minus the buoyant force. Fig. 2 Eq. 2 Fig. 3 - (a) Object in air (b) Object submerged in water 57

64 By Archimedes's principle: Eq. 3 ubstituting Eq. 3 into Eq. 2: Eq. 4 Eq. 5 Eq. 6 Eq. 7 If the cross sectional area is constant, Eq. 7 reduces to: Eq. 8 Where: M = mass of the cylinder when it is partially submerged in water. ñ H2O = density of water. ñ = density of the object L = total length of the object L i = length of the part of the cylinder that is submerged in water M = mass of the object Note that Eq. 8 is of the form y=mx + b where the slope, When M vs L i is plotted and fitted to the function as in Eq. 8 the slope can be used to determine the density, ñ of the object. Procedure: 1. Measure the diameter and length of the aluminum cylinder (Fig. 4a). Obtain the mass of the cylinder (Fig. 4b). Calculate the density of your object by direct measurement of mass and volume, compare to the known density. 2. Carefully add water to the beaker varying L i in steps of 1cm and recording the corresponding M each time (Fig. 4c). Do this from 1cm up to 7cm. Plot a graph of M' vs. L i (Eq. 8). Determine the density ñ of the object from the slope of your line and compare to the known density. 58

65 Fig. 4 - (a) Obtaining cylinder dimensions, (b) Obtaining mass, M of cylinder, (c) Obtaining mass M of cylinder corresponding to L i 3. If the body is completely submerged in water, V i = V, Eq. 7 reduces to: Eq. 9 Use a brass ball as your object. Weigh the ball (Fig. 5a). Carefully add water to the beaker till the ball is completely submerged (Fig. 5b). Be sure the ball is not touching the bottom of the beaker. Record the mass M' in grams. Using Eq. 9 determine the density of the brass ball and compare it to the known value. Fig. 5 - Applying Archimedes Principle to a Brass ball Questions: 1. How do the two values of density ñ from Procedures 1 and 2 compare with each other? 2. Derive Eq How do the errors in procedure 1 and 2 compare to the error in procedure 3? 4. Archimedes is supposed to have discovered the principle which bears his name when he was asked whether a certain crown was made of gold. How could you solve Archimedes' problem using an unmarked balance (i.e. you cannot read weight; you can only balance two objects against each other). Use Archimedes' principle in your solution. 59

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67 ATOMIC PECTRA Apparatus: Meter stick Diffraction grating Grating holder cale with a slit Meter stick supports pectrum tube power supply pectrum tubes (He, H 2 ) Objective: To use the effect of light interference to measure the wavelengths of light emitted by various atoms. Theory: Every chemical element or compound, upon being (by delivering energy to it), emits a unique pattern of wavelengths of light (or colors, each color corresponds to a particular wavelength of the light wave). In fact, such a pattern makes it possible to recognize unambiguously the element presence even in a very tiny amount. Therefore, to analyze the pattern precisely, the wavelengths of light should be measured. This direct measurement would be difficult to perform because of very small values of visible light ( nm). However, the exploitation of the wave properties interference and diffraction turns out to be very helpful. The interference effect has already been used to measure the wavelength of a sound wave (see the experiment on ound Waves). In fact, standing waves can also be formed by light similarly to what happened with sound in the resonating pipe. In this experiment, another device the diffraction grating will be used to explore the interference of light. A key element of the grating are the very tiny parallel lines set on the transparent slide. The distance d between these lines is a very important parameter. Normally, each grating is labeled as to how many line per mm it has, from which the distance d can be determined. Light striking the grating splits into many rays which, then interfere with each other. As a result, the interference antinodes (bright lines) are formed on the screen. The position of each antinode depends on the wavelength ë and the parameter d. This dependence is given by the following equation Eq. 1 Where a is the angle of diffraction (Fig. 2) and n=0,1,2,3 stands for the order of the antinode. 61

68 By measuring, the distance from the grating to the screen, and x, the distance from the zero order antinode to the n-th order antinode, the angle a, can be found as: Eq. 2 Fig. 2 - Diffraction and interference of light due to the diffraction grating From Eq. 1 the wavelength can then be determined as Eq. 3 ubstituting the sin(a) from Eq. 2, we arrive at: Eq. 4 You will use Eq. 4 to determine the wavelengths corresponding to the colored lines you will observe in the spectrum of each tube under study. Procedure: Note: Each chemical element is excited by a HIGH VOLTAGE ELECTRIC DICHARGE which is dangerous if handled improperly. Never touch the spectrum tube or its holders. (HOCK HAZARD!) 1. et up the equipment as shown in Fig The human eye will play the role of the screen in this experiment. The scale with the slit is to be aimed at the spectrum tube containing the glowing element. 62

69 3. Before you start, make sure that you can find the spectrum of colors by looking through the grating at the light emitted by the element. You will see the colored lines at the sides of the light source. These lines form a group which repeats itself as one looks farther from the center line. Each group corresponds to a different n in Eq. 1 and Eq. 3. Only the first group of lines for which n=1 is to be analyzed in this experiment. 4. Note the name of the element whose spectra you will analyze. Aim the set-up toward the light source and observe the spectrum of the element in use. Record the color and the distance x along the scale for each distinct colored line, keeping the distance along the meter stick fixed. For this experiment you will use a grating having 600 lines per mm. Fig. 3 - chematic of the meter stick set-up with the spectrum tube set in the center. Develop a data table with the following columns: Element: : d: Line # Color of the line x [cm] ë [nm] (Using Eq. 4) ë [nm] (From chart) Percent difference in ë 5. Repeat Procedure 4 for another spectrum tube of different element. 6. For each element you used, identify its spectrum from an Atomic pectra chart and record the corresponding wavelengths. 7. For each element compare your calculated values of ë to the values obtained from the chart. 63

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71 THE IMPLE PENDULUM Apparatus: Table clamp teel rod Pendulum clamp (silver) Pendulum bob (various sizes) tring Electronic balance Master photogate timer (set to pendulum mode) Meter stick Pend. Protractor align center of ball with infrared beam Introduction: Fig. 1 - et-up A simple pendulum consists of a small mass (the bob) suspended by a non-stretching, massless string of length L. The period T of oscillation is the time for the pendulum bob to go from one extreme position to the other and back again. Consider the variables that determine the period of oscillation of a pendulum: The amplitude θ of oscillation. The amplitude of the pendulum s swing is the angle between the pendulum in its vertical position and either of the extremes of its swings. The length L of the pendulum. The length is the distance from the point of the suspension to the center (of mass) of the pendulum bob. The mass m of the bob. The acceleration due to gravity g. L θ Resting position Fig. 2 - imple Pendulum One period m mg From unit analysis we can show: T L g m, or by units, m s 2 = s 2 = s Where T = period of oscillation; m = mass of bob; L = length of string; g = acceleration due to gravity 65

72 ince an oscillation is described mathematically by cos ωt and knowing that ω=2πf where f = 1/T we then have: Equation 1 can be re-writen as: T = 2π ω T = 2π L g Eq. 1 Eq. 2 Procedure: Make the following measurements: 1. Turn on the photogate and set it to pendulum mode. In addition, make sure the memory switch on as well. et-up the pendulum so that when it is in resting position it blocks the photogate as shown on Fig Period as a function of amplitude (plot T vs. θ). Perform this procedure for amplitudes of 5 to 30 in steps of 5. The length and mass will remain constant. At each given angle allow the pendulum to swing through the photogate, be careful not to strike the photogate with the pendulum. Record the period displayed on the photogate that corresponds to the amplitude. 3. Period as a function of length (plot T vs. L). Use a small angle such as 10. Change the length 6 times. Each time a new length L is set, the length must be measured from the center of the bob to the pivot point. The amplitude and the mass will remain constant. Allow the pendulum to swing through the photogate and record the period displayed on the photogate. Fit the data to Eq. 2. How does the obtained g value from the fit compare to the known value of g? Note: An alternate method for this procedure is to plot T 2 vs L and use the best linear fit to determine the slope. Then use the slope to obtain g and compare to the known value. The linear fit would be of the form: T 2 = 4π g L. 4. Period as a function of mass (plot T vs. m). Use a small angle such as 10. Use 4 different masses but keep amplitude and length constant. For each mass record the period as displayed on the photogate. Questions: 1. For the simple pendulum where is the maximum for: displacement, velocity and acceleration? 2. Would the period increase or decrease if the experiments were held on : a) the top of a high mountain? b) the moon? c) on Jupiter? 66

73 VERNIER CALIPER - MICROMETER CALIPER Apparatus: - Two metal cylinders - One wire - Vernier caliper, 0-150mm, 0.02 least count - Micrometer caliper, 0-25mm, 0.01mm least count Part I: The Vernier Caliper When you use English and metric rulers for making measurements it is sometimes difficult to get precise results. When it is necessary to make more precise linear measurements, you must have a more precise instrument. One such instrument is the vernier caliper. The vernier caliper was introduced in 1631 by Pierre Vernier. It utilizes two graduated scales: a main scale similar to that of a ruler and a especially graduated auxiliary scale, the vernier, that slides parallel to the main scale and enables readings to be made to a fraction of a division on the main scale. With this device you can take inside, outside, and depth measurements. ome vernier calipers have two metric scales and two English scales. Others might have the metric scales only. ENGLIH CALE Fig. 1 - Parts of a Vernier Caliper Fig. 2 - Dimensions that can be measured with a vernier caliper 67

74 Notice that if the jaws are closed, the first line at the left end of the vernier, called the zero line or the index, coincides with the zero line on the main scale (Fig. 2). Fig. 3 - Vernier caliper with closed jaws The least count can be determined for any type of vernier instrument by dividing the smallest division on the main scale by the number of divisions on the vernier scale. The vernier caliper to be used in the laboratory measurements has a least count 0.02mm. Instructions on how to read the measurements on this particular model can be found in: The link below has a caliper simulator, practice with it before the lab session: mm.html For our experiment will be using a caliper with English and Metric scales. The top main scale is English units and the lower main scale is metric. For our experiment will be concentrating on metric only. In our model the metric scale is graduated in mm and labeled in cm. That is, each bar graduation on the main scale is 1mm. Every 10 th graduation is numbered (10mm). The vernier scale divides the millimeter by fifty (1/50), marking the 0.02mm (two hundredths of a millimeter), which is then the least count of the instrument. In other words, each vernier graduation corresponds to 0.02mm. Every 5 th graduation (0.1mm) is numbered. Having first determined the least count of the instrument, a measurement may be made by closing the jaws on the object to be measured and then reading the position where the zero line of the vernier falls on the main scale (no attempt being made to estimate to a fraction of a main scale division). We next note which line on the vernier coincides with a line on the main scale and multiply the number represented by this line (e.g., 0,1,2, etc.) by the least count on the instrument. The product is then added to the number already obtained from the main scale. Occasionally, it will be found that no line on the vernier will coincide with a line on the main scale. Then the average of the two closest lines is used yielding a reading error of approximately 0.01mm. In this case we take the line that most coincides. 68

75 Let us review the steps on how to use a vernier caliper (Fig. 4), note that we are only interested in metric measurements. Before taking a measurement make sure the vernier reads zero when the jaws are fully closed. If this is not the case, request another caliper, as it could be damaged. Fig. 4 - ample reading on vernier caliper tep 1: The main metric scale is read first. In our example there are 21 whole divisions (21mm) before the 0 line on the vernier scale. Therefore, the first number is 21. tep 2: On the vernier scale, find the first line that lines up with any line on the main scale. This is shown by the arrow pointing in the example (lower vernier scale) to the 16 th line. tep 3: Multiply 16 by the least count 0.02, thus resulting in 0.32 (remember, each division on the hundredths scale (vernier scale) is equivalent to 0.02mm. Thus, 16 x 0.02=0.32mm. tep 4: Add 21 and 0.32, that is, =21.32mm. Thus, your final reading is 21.32±0.01mm. Alternatively, it is just as easy to read the 21mm on the main scale and 32 on the hundredths scale, therefore resulting in as your measurement. That is, 21.32±0.01mm. Procedure: 1. Make six independent measurements of the diameter of each metal cylinder. 2. Make six independent measurements of the length of each metal cylinder 3. Make six independent measurements of the diameter of the wire. Questions: 1. Why did you take six independent measurements in each procedure above? 2. What does the smallest division on the main scale of the vernier caliper correspond to? 3. What is the error of your measurements? 69

76 Part II. The Micrometer Caliper: The micrometer caliper, invented by William Gascoigne in the 17 th century, is typically used to measure very small thicknesses and diameters of wires and spheres. It consists of a screw of pitch 0.5mm, a main scale and another scale engraved around a thimble which rotates with the screw and moves along the scale on the barrel. The barrel scale is divided into millimeters, on some instruments, such as ours, a supplementary scale shows half millimeters. The thimble scale has 50 divisions. ince one complete turn of the thimble will produce an axial movement of 0.5mm. One scale division movement of the thimble past the axial line of the scale on the barrel is equivalent to 1/100 times 1.0 equals 0.01mm. Hence readings may be taken directly to one hundredth of a millimeter and by estimation (of tenths of a thimble scale division) to a thousandth of a millimeter. The object to be measured is inserted between the end of the screw (the spindle) and the anvil on the other leg of the frame. The thimble is then rotated until the object is gripped gently. A ratchet at the end of the thimble serves to close the screw on the object with a light and constant force. The beginner should always use the ratchet when making a measurement in order to avoid too great a force and possible damage to the instrument. The measurement is made by noting the position of the edge of the thimble on the barrel scale and the position of the axial line of the barrel on the thimble scale and adding the two readings. The micrometer should always be checked for a zero error. This is done by rotating the screw until it comes in contact with the anvil (use the ratchet) and then noting whether the reading on the thimble scale is exactly zero. If it is not, then this "zero error" must be allowed for in all readings. Fig. 5 - Micrometer Caliper 70

77 To read a measurement (Fig. 6), simply add the number of half-millimeters to the number of hundredths of millimeters. In the example below, we have 2.620±0.005mm, that is 5 half millimeters and 12 hundredths of a millimeter. If two adjacent tick marks on the moving barrel look equally aligned with the reading line on the fixed barrel, then the reading is half way between the two marks. Fig. 6 - ample Reading on Micrometer In the example above, if the 12 th and 13 th tick marks on the moving barrel looked to be equally aligned, then the reading would be 2.625±0.005mm. You may use this java applet to practice the use and reading of a micrometer. Procedure: 1. Repeat all measurements that are possible of part I (vernier caliper) using the micrometer. 2 Make six independent measurements of the diameter of a human hair. 3. What is the error of your measurements? Questions: 1. Would you use the vernier to measure the diameter of a human hair? Explain your answer. 2. What does one division on the barrel of the caliper correspond to? 3. What does one division on the rotating thimble correspond to? 4. Define metric scale. 5. What does pitch 0.5 mm mean? 6. What type (name) of error is the "zero error" of the micrometer assuming it enters a calculation 71

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79 EQUILIBRIUM OF A RIGID BODY Apparatus: - Meter stick - One knife-edge meter stick clamp without clips - Two knife-edge meter stick clamps with clips - Two 50gr hangers - lotted weights - Meter stick support stand - Large friction box - Electronic balance Introduction: If a rigid body is in equilibrium, then the vector sum of the external forces acting on the body yields a zero resultant and the sum of the torques of the external forces about any arbitrary axis is also equal to zero. tated in equation form: ΣF = 0 Στ = 0 Eq. 1 In this lab work force is defined as the mass m times gravitational acceleration g: F = mg Eq. 2 where m is in kg and g in m/s 2 therefore, force F is in newtons N. Torque is a measure of how effective a given force is at twisting or turning the object it is applied to. Torque is defined as the force F times the moment arm or lever arm r of the force with respect to a selected pivot point x. In other words r is the distance from the pivot to the point where a force is applied. If the force is perpendicular to r, then τ = Fr Eq. 3 The unit of torque is Newton-meter, N m. The sign for torque is defined as positive (+) when rotating in counter-clockwise direction and negative (-) when rotating in a clockwise direction. In this experiment a meter stick is used as a rigid body to illustrate the application of the equations of equilibrium. The torque equation will be verified for a balanced system of two masses. The torque equation will also be applied to determine the mass of the meter stick and compare to the known value. For this experiment it is not only important to familiarize yourself with the equations, but also with sketching free-body diagrams (FBD). Next are examples of balanced systems and application of the torque equation. The equations must be solved as a pre-lab exercise. 73

80 1. Meter stick in equilibrium, fulcrum at its center and masses on opposite sides of the balance point. x 1 x o x 2 Fulcrum m 1 m 2 N x 1 x o x 2 r 1 r 2 m 1 *g M*g m 2 *g Fig. 1 Balanced system with two masses and corresponding FBD ince Στ=0 and knowing that τ=fr we can develop the equation of equilibrium based on the FBD taking into account the sign of the torque. r is the distance from the pivot point to the point where the force is applied. In the case above we have F 1 acting at point x 1 that will cause a counterclockwise rotation with respect to the pivot point x o therefore, torque is positive. F 2 is acting at point x 2 and will cause a clockwise rotation with respect to the pivot point x o thus making the torque negative. Therefore, Στ = τ 1 τ 2 = 0 Eq. 4 or τ 1 = τ 2 Eq. 5 Rewriting in terms of F and r: (F 1 )(r 1 ) = (F 2 )(r 2 ) Eq. 6 where F=mg Then: (m 1 g)(r 1 ) = (m 2 g)(r 2 ) Eq. 7 (m 1 g)(x o x 1 ) = (m 2 g)(x 2 x o ) Eq. 8 Let us assume that in this system we have: m 1 =0.110 kg (includes the mass of the clamp) suspended at x 1 =0.223 m, m 2 =0.081 kg (includes the mass of the clamp) suspended at x 2 =0.890 m and the pivot point is located at x o =0.506 m. ubstitute the given values along with g=9.8 m/s 2 into the equation above. How does τ 1 compare to τ 2? 74

81 Note that the location x is read from the inside edge of the meter stick clamp. In the case of Fig. 2 the location is 41.5 cm or m. Fig. 2 Meter stick clamp 2. Balanced meter stick with one mass. Determining the mass of the meter stick. x o x' o x 1 CG New pivot point Fulcrum m 1 N x o x' o x 2 r o r 1 m 1 *g m s *g M*g Fig. 3 - ystem with one mass and balanced at new pivot point plus corresponding FBD Fig. 3 shows one mass suspended on the right side of the meter stick and a new pivot point was determined in order for the system to be in equilibrium. The torque equation will be applied with respect to the new pivot point x o and use it to calculate the experimental mass of the meter stick. Rewriting: Στ = τ o τ 1 = 0 Eq. 9 τ o = τ 1 Eq. 10 (Mg)(r o ) = (m 1 g)(r 1 ) Eq. 11 (Mg)(x o x o ) = (m 2 g)(x 1 x o ) Eq. 12 olving for M: M = (m 1g)(x 1 x o ) (g)(x o x o ) = (m 1)(x 1 x o ) (x o x o ) Eq

82 In this system we have: m 1 =0.061 kg (includes the mass of the clamp) suspended at x 1 =0.792 m, M acting at the original pivot point x o =0.506 m, New pivot point x o is located at x o = m. The mass of the meter stick obtained by means of an electronic scale is kg. Calculate the experimental mass and compare to the known value by means of the percent difference formula. Procedure: Part I. Balancing the meter stick without masses to determine the pivot point: 1. Weigh the meter stick by itself on the electronic balance and record its mass. 2. Determine and record the mass of the clamps with clips. 3. Put the meter stick through the clamp that has no clips (the clamp should be upside down so that the lock screw is on the bottom). lide the clamp to a point near the center of the meter stick. Position the clamped meter stick on the support stand. Gently slide the meter stick through the clamp till the rigid body is in equilibrium. Once it is, lock the clamp in place (Fig. 4). Record the location of pivot point by reading from the inside edge of the knife-edge clamp. x o CG Fulcrum Fig. 4 Balanced meter stick Part II. Balancing the rigid body with two masses on opposite sides of the fulcrum: 1. ecure one clamp at the 5 cm mark (left of the fulcrum) and suspend a mass of 50 g. 2. ecure the second clamp at an arbitrary point to the right of the fulcrum. 3. Hang 100 g from the second clamp. 4. Adjust the position of m 2 till the system is in equilibrium. 5. Record the masses and positions. Do not forget to include the mass of the clamps to each mass. 6. Draw the corresponding FBD and write the torque equation about the pivot point. 7. Compare and express the percent difference between the torques. 8. lide m 1 to the 15 cm position and adjust the location of m 2 so that the system is equilibrium. 9. Repeat steps lide m 1 to the 25 cm position and adjust the location of m 2 so that the system is equilibrium. 11. Repeat steps

83 Part III. Obtaining the mass of the meter stick by method of torques: 1. Balance the meter stick by itself. 2. Position one clamp at the 5 cm mark and suspend 100 g from it. 3. Find a new pivot point that will bring the system to equilibrium. Record the location. 4. Using the torque equation calculate the mass of the meter stick. 5. Compare the obtained value with the value you found when weighing the meter stick. Questions: 1. A meter stick is balanced at its center. If a 3 kg mass is suspended at x=0 m, where would you need to place a mass of 5 kg to have the system in equilibrium? 2. What will happen if the meter stick is not strictly horizontal? 3. Can we apply the torque balance equation if the stick is not horizontal? What must be changed in Eq. 3, 6, 7, 8, 11, 12 and 13 in this case? 77

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85 ACCELERATION Apparatus: Air Track Air supply and hose Master photogate timer Accessory photogate timer Glider Flag Air Track support blocks Introduction: When an object accelerates it experiences a change in its velocity, either in magnitude or direction. We will only be examining the case of a change in the magnitude of the velocity not its direction. We will also limit our investigation to one particular type of acceleration, constant acceleration. Acceleration can be defined as the rate of change in the velocity of an object per unit time. The units of acceleration are velocity per unit time, such as feet per second per second, meters per second per second, or feet per second squared, meters per second squared. An object traveling with constant acceleration maintains a constant rate of change in velocity for the entire time it is observed. Where a is the acceleration, v is the final velocity, v 0 is the initial or starting velocity and t is the time this relationship can be expressed as: The apparatus we use in our experimental investigation is the linear air track. In order to provide constant acceleration we will create an incline by raising one end of the track. In the particular case of constant acceleration with the initial velocity equal to zero, if d is the distance, a is the acceleration and t is the time; the acceleration can be calculated using the equation: Preliminary et-up: et-up the Air Track as shown in Fig. 1 but without the block under one of the legs. Turn on the blower unit and allow the air track to warm up. Place the glider on the track and adjust the level of the track until the glider remains at rest near the center of the track. 79

86 Fig. 1 - Air Track et-up Procedure 1: Raise one end of the track by placing a block under the single leg. et the timing gates at a convenient timing distance at the high end of the track. Photogates must be set to pulse mode. Position the glider so that it is about to trip the timer, release the glider very carefully, being sure not to give it a push in either direction. Record the time, reset the timer and repeat the procedure with each group member releasing the glider once. Move the timing gates to a new location closer to the center of the track, be sure not to change the timing distance. As above, each group member release the glider and record the time. Move the timing gates once more toward the bottom of the track, again maintaining the timing distance, and repeat the procedure. For each position use a table as below to record your data. Table 1.1 d [cm] t [s] t avg [s] a=2d/t avg2 [cm/s 2 ] t 1 = t 2 = t 3 = Procedure 2: With the glider very close to the top of the track, set the timing gates to a distance of 20 cm. Each group member launch the glider once and record the time. Repeat the procedure after increasing the timing distances to 40 cm, 60 cm, 80 cm and 100 cm. Do not move the starting gate only the stop gate. 80

87 Table 2.1 d [cm] t [s] t avg [s] t avg2 [s 2 ] a=2d/t avg2 [cm/s 2 ] t 1 = 20 t 2 = t 3 = t 1 = 40 t 2 = t 3 = t 1 = 60 t 2 = t 3 = t 1 = 80 t 2 = t 3 = t 1 = 100 t 2 = t 3 = Calculations: 1. For each step in each procedure calculate the average time. 2. For Procedure 2 use the second equation, the distance and the average time squared to calculate the average acceleration for each position. Compare these accelerations, are they equal? How much do you trust your results? Discuss the answers in your conclusion. Graphs: 1. Plot a graph of d vs. t avg 2. Plot a graph of d vs t avg2 Discuss these graphs in your conclusion. Use the slope of the second graph to find the acceleration, how does this acceleration compare to the average acceleration from Procedure 1? 81

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89 Apparatus: FOCAL LENGTH OF A CONVERGING LEN (Adapted from Advanced Physics with Vernier - Beyond Mechanics Manual) Vernier dynamics system track Vernier optics expansion kit containing: - light source - 20cm converging lens - screen. Ruler LED lamp Fig. 1 - et-up Objective: Explore how lens characteristics and the position of the object affect the appearance, orientation and size of real images. Determine the relationship between object distance, image distance, focal length and magnification in real images produced by converging (bi-convex) lenses. Discussion: Fig. 2 - ample Image Formation by a Converging Lens In this experiment we will have the opportunity to see the real images produced by a converging lens by projecting that image on a movable screen of an optical bench. ee Fig

90 Fig. 3 - Object and Image Distances The metric scale on the bench, will allow us to accurately determine object distances d o and image distances d i, providing us a means of verifying the lens equation: Eq. 1 where f is the focal length of the lens. We will also be able to check the validity of the magnification relationship: Eq. 2 where h o and h i are the heights of the object and image respectively. Fig. 4 - Magnification Eq. 1 can also be written as: Eq. 3 84

91 To illustrate the basis for our graphical approach, let us set 1/d i equal to y, 1/d o equal to x, and 1/f equal to b, so that Eq. 3 becomes: y = -x + b Eq. 4 which is clearly, the equation of a straight line. The slope of this line is equal to -1 and its y-intercept b equals 1/f. If we plot y (that is, 1/d i ) against x (that is, 1/d o ), we should get a downward sloping straight line that intercepts the y axis at b (that is, 1/f). Note that the x-intercept also equals 1/f. We therefore have a graphical method for determining the focal length of our converging lens. Procedure: 1. Attach the light source assembly on the track. Position it so that the pointer at the base is at the 2cm mark and the light source faces the other end of the track. 2. Turn the light source wheel until the number 4" is visible in the opening. This will be the object for this experiment. Note that the height of the object h o is 2.0cm. 3. Place the 20cm bi-convex lens at the 35cm mark. 4. Place the screen at the 120cm mark of the track so that the light from the light source passes through the lens and strikes the screen. 5. lowly adjust the position of the lens along the track to find two positions where the image of the object 4" on the screen is in focus (see Fig. 2) that is it produces a sharp image of the object. One image should be magnified up and the other magnified down. 6. Note the orientation of the object and its image. Measure the height of the image, remembering that inverted images are conventionally negative and should be recorded as such. 7. Record the distance between the light source and the lens as d o and the distance between the lens and the screen as d i. 8. Move the screen to the 110cm mark and repeat steps 5 through Repeat measurements for the screen at the 100cm mark. Data Table d o [cm] d i [cm] h o [cm] h i [cm] 1/d o [cm -1 ] 1/d i [cm -1 ] 1/fexp [cm -1 ] fexp [cm]

92 Calculations: 1. Using the data from Procedure 1, plot 1/d i on the vertical axis, against 1/d o on the horizontal axis. Draw the best straight line through your plotted points and determine the slope. How does it compare to the expected value of 1.0? 2. Extend the best-fit line to where it crosses both axes. Read off the value of the two intercepts, and record them. Take the reciprocal of these two intercept values to obtain the two values for the focal length f. Report both f s along with their average. 1/f (from vertical axis) [cm -1 ] f (from vertical axis) [cm] 1/f (from horizontal axis) [cm -1 ] f (from horizontal axis) [cm] f (average) [cm] 3. Compare the f average to the known focal length of the lens you used. 4. Use the values you obtained in Procedure 7 to verify Eq. 1. How does f compare to the known value? 5. Calculate h i /h o and d i /d o for each image that you found. 6. Pick one h i /h o and its corresponding d i /d o ratio when the image is larger than the object and compare them. Is Eq. 2 verified? 7. Pick one h i /h o and its corresponding d i /d o ratio when the image is smaller than the object and compare them. Is Eq. 2 verified? 86

93 APPENDIX 87

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95 A1. GRAPHICAL ANALYI PLOTTING YOUR DATA POINT AND FINDING THE BET FIT 1. Click on the GA 3.4 icon 2. The Graphical Analysis screen will be displayed: 3. On the Data et Table with X and Y columns click on either column to start entering your data. Use either the arrow keys or the mouse to move to the next cell. 4. As you enter data you will notice a graph will develop as the data is plotted. Just continue entering your data till you are finished. 5. To delete the line that is connecting the points either double click on the graph window. elect the Graph Options tab. 1 Adapted from Vernier oftware & Technology Graphical Analysis User s Manual 89

96 Click on Connect Lines to delete the original line on your graph. To add a title, click on the Title window. This window also gives the option to add a legend to your graph or change the grid style. 6. Finding the Best Linear Fit for your graph: On the graph window click and drag the mouse across the segment of interest. The shaded area marks the beginning and end of the range. You may also select the segment of interest on your data columns and then clicking on the graph window to activate it. 7. With the graph window activated, select the Regression option either by clicking the Linear Fit icon, on the toolbar or by selecting it from the Analyze Menu. To remove the regression line click the box in the upper corner of the helper object. The Linear Fit function fits the line y = m*x + b to the selected region of a graph and reports the slope (m) and y-intercept (b) coefficients. If more than one column or data set is plotted, a selection dialog will open for you to which set you want to fit. You may select more than one column for regression; in this case, a separate fit line will be applied to each graphed column. As aforementioned, you can fit a line either to the whole graph or to a region of interest. Drag the mouse across the desired part of the graph to select it. Black brackets mark the beginning and end of the range. 8. If you wish to graph a fit other than y=mx+b, such as proportional, quadratic, cubic, exponential, etc, click on the Curve Fit icon from the toolbar. A Curve Fit dialog window will pop-up: 90

97 elect the function you wish to use. Click Try Fit. Then click OK. 9. To change the labels of your X and Y axes and include their respective units click on the column you wish to change and the dialog window below will pop-up: On this dialog window, you will be allowed to give your column a name other than the default name. You may also include units such as m/s, cm/s 2, etc. The drop down arrows allows you to enter a symbol, subscript or superscript. 10. To change the scaling of your graph, right click on the desired graph and select autoscale or autoscale from zero. To modify manually, click on the highest or lowest number of the axis you wish to change and enter the new number, press Enter. 91

98 11. elect the orientation of your page. This is done by using Page etup under the File menu. 12. To print the entire screen select Print from the File menu or click the icon on the toolbar. A dialog window will pop-up allowing you to enter your name or any comments you wish to add. 13. If you wish to print just the graph select it first and then go to the File menu and select Print Graph You may also print data table alone by selecting Print Data Table. For more information go to: Note: These basic graphing instructions can also be applied to LoggerPro. 92

99 A2. TECHNICAL NOTE ON VERNIER LABQUET2 INTERFACE 1 Once the LabQuest interface is connected to AC power or the battery has been charged, press the power button located on the top of the unit, near the left edge. LabQuest will complete its booting procedure and automatically launch the LabQuest App by default, as shown above. If the screen momentarily shows a charge battery icon or does not light after a moment when used on battery power, connect the power adapter to LabQuest and to an AC power source, then try the power button again. Fig. 1 - LabQuest2 Interface Power Button Power on If the screen is off for any reason (LabQuest is off, asleep, or the screen has turned off to conserve battery power), press and release the power button to turn LabQuest back on. If LabQuest was off, LabQuest will also complete its booting procedure that takes about a minute and then display LabQuest App. leep/wake When LabQuest is on, press and release the power button once to put LabQuest into a sleep mode. Note that the sleep mode does not start until you release the power button. In this mode, LabQuest uses less power but the battery can still drain. This mode is useful if you are going to return to data collection again soon, in which case waking LabQuest from sleep is quicker than restarting after shutdown. To wake LabQuest from sleep, press and release the power button. A LabQuest that is left asleep for one week will automatically shutdown. hut down To shut down LabQuest, hold the power button down for about five seconds. LabQuest displays a message indicating it is shutting down. Release the power button, and allow LabQuest to shut down. To cancel the shutdown procedure at this point, tap Cancel. You can also shut down LabQuest from the Home screen. To do this, tap ystem and then tap hut Down. Emergency shutdown If you hold the power button down for about eight seconds, while it is running. This is not recommended unless LabQuest is frozen, as you may lose your data and potentially cause file system corruption. 1 Adapted from Vernier oftware & Technology LabQuest2 User s Manual. 93

100 Touch creen LabQuest has an LED backlit resistive touch screen that quickly responds to pressure exerted on the screen. LabQuest is controlled primarily by touching the screen. The software is designed to be finger-friendly. In some situations, you may desire more control for precise navigation. In such cases, we recommend using the included stylus. If you are having trouble viewing the color screen or are using LabQuest outside in bright sunlight, we recommend changing to the High Contrast mode. Tap Preferences on the Home screen, then tap Light & Power. elect the check box for High Contrast to enable this mode. Hardware Keys In addition to using the touch screen, the three hardware keys can also be used to control your LabQuest. Collect tart and stop data collection within LabQuest App Home Launch the Home screen to access other applications Escape Close most applications, menus, and exit dialog boxes without taking action (i.e., cancel dialog boxes) Fig. 2 - LabQuest2 Control Buttons ensor Ports LabQuest has three analog sensor ports (CH 1, CH 2, and CH 3) for analog sensors such as our ph ensor, Temperature Probe, and Force ensor. Also included is a full-size UB port for UB sensors, UB flash drives, and UB printers. In addition to the power button, the top edge of LabQuest has two digital sensor ports (DIG 1 and DIG 2) for Motion Detectors, Drop Counters, and other digital sensors. Fig. 3- LabQuest2 ensor Ports 94

101 Audio ports are also located adjacent to the digital ports, as well as a microd card slot for expanding disk storage. On the side opposite of the analog ports, there is a stylus storage slot, an AC power port for recharging the battery, and a mini UB port for connecting LabQuest to a computer. In between these ports, there is a serial connection for charging the unit in a LabQuest Charging tation. Fig. 4 - LabQuest2 Additional Ports For more information on the LabQuest2 interface please go to: 95

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103 A3. TECHNICAL NOTE ON ENOR AND PROBE UTILIZED IN ELECTED EXPERIMENT FROM THI MANUAL 1,2 1. PHOTOGATE Photogates allow for extremely accurate timing of events within physics experiments, for studying air track collisions, pendulum periods, among other things. The PACO ME-9215B Photogate Timer (Fig. 1) is an accurate and versatile digital timer for the student laboratory. The ME-9215B memory function makes it easy to time events that happen in rapid succession, such as an air track glider passing twice through the photogate, once before and then again after a collision. Fig. 1 - Photogate timer with memory Fig. 2 - Photogate head The Photogate Timer uses PACO s narrow-beam infrared photogate (Fig. 2) to provide the timing signals. An LED in one arm of the photogate emits a narrow infrared beam. As long as the beam strikes the detector in the opposite arm of the photogate, the signal to the timer indicates that the beam is unblocked. When an object blocks the beam so it doesn t strike the detector, the signal to the timer changes. Timing Modes: Gate Mode: In Gate mode, timing begins when the beam is first blocked and continues until the beam is unblocked. Use this mode to measure the velocity of an object as it passes through the photogate. If an object of length L blocks the photogate for a time t, the average velocity of the object as it passed through the photogate was L/t. Pulse Mode: In Pulse mode, the timer measures the time between successive interruptions of the photogate. Timing begins when the beam is first blocked and continues until the beam is unblocked and then blocked Fig. 3 - Photogate timer with memory 1 Technical notes adapted from Vernier oftware & Technology User s Manual and Pasco cientific User s Manual 2 ome equipment may be for demo purposes only and might not be part of experiments in this manual. 97

104 again. With an Accessory Photogate plugged into the Photogate Timer, the timer will measure the time it takes for an object to move between the two photogates. Pendulum Mode: In Pendulum mode, the timer measures the period of one complete oscillation. Timing begins as the pendulum first cuts through the beam. The timer ignores the next interruption, which corresponds to the pendulum swinging back in the opposite direction. Timing stops at the beginning of the third interruption, as the pendulum completes one full oscillation. Manual topwatch: Use the TART/TOP button in either Gate or Pulse mode. In Gate mode the timer starts when the TART/TOP button is pressed and it stops when the button is released. In Pulse mode, the timer acts as a normal stopwatch. It starts timing when the TART/TOP button is first pressed and continues until the button is pressed a second time. Memory Feature: When two measurements must be made in rapid succession, such as measuring the pre- and post-collision velocities of an airtrack glider, use the memory function. It can be used in either the Gate or the Pulse mode. To use the memory: 1. Turn the MEMORY switch to ON. 2. Press REET. 3. Run the experiment. When the first time (t 1 ) is measured, it will be immediately displayed. The second time (t 2 ) will be automatically measured by the timer, but it will not be shown on the display. 4. Record t 1, then push the MEMORY switch to READ. The display will now show the TOTAL time, t 1 + t 2. ubtract t 1 from the displayed time to determine t 2 2. MART-PULLEY YTEM: A mart-pulley system is made up of a Vernier Ultra Pulley and a photogate to monitor motion as a string passes over a pulley. Note that the pulley has low friction and low inertia. When properly positioned, the spokes of the pulley will block the photogate s infrared beam each time they pass by. In the mart-pulley systems one arm of the photogate emits a thin beam of infrared light which is detected by the other arm. The LabQuest2 interface discerns whether the beam strikes the detector (Fig. 4a) or is blocked by a spoke (Fig. 4b) in the pulley sheaf. The small LED light illuminates when the beam is blocked. By accurately timing the signals that arrive from the photogate, the computer is able to track the motion of any object linked to the pulley. As the mart-pulley system performs motion timing it provides a Position vs Time graph; based on the data a Velocity vs Time graph can be developed as well as an Acceleration vs Time graph. For our experiment we will only be using the Velocity vs Time graph to obtain the required accelerations. (a) (b) Fig. 4 mart-pulley ystem 98

105 3. MOTION DETECTOR The Motion Detector is used to collect position, velocity and acceleration data of moving objects. tudents can study a variety of motions with the Motion Detector, including: Walking toward and away from the Motion Detector. Dynamics carts moving on track. Objects in simple harmonic motion, such as a mass hanging on a spring. Pendulum motions. Objects dropped or tossed upward. A bouncing object. Fig. 5 - Vernier Motion Detector Fig. 6 - ample motion data of a bouncing ball How the Motion Detector Works This Motion Detector emits short bursts of ultrasonic sound waves from the gold foil of the transducer. These waves fill a cone-shaped area about 15 to 20 off the axis of the centerline of the beam. The Motion Detector then listens for the echo of these ultrasonic waves returning to it. The equipment measures how long it takes for the ultrasonic waves to make the trip from the Motion Detector to an object and back. Using this time and the speed of sound in air, the distance to the nearest object is determined. Fig. 7 - Cone of action 99

106 Note that the Motion Detector will report the distance to the closest object that produces a sufficiently strong echo. The Motion Detector can pick up objects such as chairs and tables in the cone of ultrasound. The sensitivity of the echo detection circuitry automatically increases, in steps, every few milliseconds as the ultrasound travels out and back. This is to allow for echoes being weaker from distant objects. Features of the Motion Detector The Motion Detector is capable of measuring objects as close as 0.15 m and as far away as 6 m. The short minimum target distance (new to this version of the Motion Detector) allows objects to get close to the detector, which reduces stray reflections. The Motion Detector has a pivoting head, which helps you aim the sensor accurately. For example, if you wanted to measure the motion of a small toy car on an inclined plane, you can lay the Motion Detector on its back and pivot the Motion Detector head so that it is perpendicular to the plane. The Motion Detector has a ensitivity witch (Fig. 8), which is located under the pivoting Motion Detector head. To access it, simply rotate the detector head away from the detector body. lide the ensitivity witch to the right to set the switch to the Ball/Walk setting. This setting is best used for experiments such as studying the motion of a person walking back and forth in front Fig. 8 - ensitivity witch of the Motion Detector, a ball being tossed in the air, pendulum motion, and any other motion involving relatively large distances or with objects that are poor reflectors (e.g., coffee filters). The Track sensitivity setting works well when studying motion of carts on tracks like the Dynamics Cart and Track ystem, or motions in which you want to eliminate stray reflections from objects near to the sensor beam. 4. TEMPERATURE PROBE Fig. 9- Vernier Temperature Probe The tainless teel Temperature Probe can be used as a thermometer for experiments in chemistry, physics, biology, Earth science, environmental science, and more. Note: Vernier products are designed for educational use. Our products are not designed nor recommended for any industrial, medical, or commercial process such as life support, patient diagnosis, control of a manufacturing process, or industrial testing of any kind. pecifications: Temperature range: 40 to 135 C ( 40 to 275 F) Maximum temperature that the sensor can tolerate without damage: 150 C 100

107 Typical Resolution: o.17 C ( 40 to 0 C) o.03 C (0 to 40 C) o.1 C (40 to 100 C) o.25 C (100 to 135 C) Temperature sensor: 20 kω NTC Thermistor Accuracy: ±0.2 C at 0 C, ±0.5 C at 100 C Response time (time for 90% change in reading): o 10 seconds (in water, with stirring) o 400 seconds (in still air) o seconds (in moving air) Probe dimensions: o Probe length (handle plus body): 15.5 cm o tainless steel body: length 10.5 cm, diameter 4.0 mm o Probe handle: length 5.0 cm, diameter 1.25 cm 101

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109 A4. MULTIMETER AND POWER UPPLIE DIGITAL MULTIMETER A digital multimeter (DMM) is a test tool used to measure two or more electrical values principally voltage (volts), current (amps) and resistance (ohms). It is a standard diagnostic tool for technicians in the electrical/electronic industries 1. Fig. 1 Fluke Multimeter Dial ettings To perform measurements required in experiments in this manual set the dial to the desire mode To measure DC ( ) Voltage set the dial to the proper setting (Fig. 1). The probes or wires must be connected as shown on Fig. 2a. To measure Resistance (Ω) set dial to the proper setting and connect probes as on Fig. 2a. To measure small DC ( ) Current (ma) (0-400mA) set the dial to the proper setting. Press the shift key to obtain DC readings. This setting will be used for Ohm s Law experiment. The probes or connecting wires must be connected as shown on Fig. 2b. To measure large DC ( ) Current (A) with current ranges 0-10 A set the dial to the proper setting as shown on Fig. 1 and press the shift key to obtain DC readings. This setting will be used for Joule experiment. The probes or connecting wires must be connected as shown on Fig. 2b. To measure temperature turn dial to Millivolt/Temperature setting. Press the yellow key to read temperature. By default the temperature will be set to degrees Celcius. If Fahrenheit is preferred, press the Range key. A thermocouple will be inserted in the V and COM inputs instead of probes. 1 Definition from Fluke Multimeter User s Manual. 103

110 Fig. 2 Probe Connections Note: Exercise caution when using the multimeters to avoid burning a fuse or causing irreparable damage to the devices. To check if a fuse is burnt connect the red probe into the V Ω input, set the dial to resistance (Ω) and place the tip of the probe into the either the 400 ma or 10 A input. For the 400 ma the resistance should read less than 12 Ω while the 10 A input should read a less than 0.5 Ω. If the reading is OL then the fuse must be replaced. POWER UPPLIE 0-30 DC V Power upply: This power supply will supply DC Voltage/Current to various experiments in this manual such as Ohm s Law and Joule experiments. Pay close attention to voltage and current settings as designated by each experiment. Fig. 3 Extech 0-30 DC Volts Power upply The voltage knob will display voltage and current readings in 0.1 V steps (0.8 V). Press the voltage knob once when whole number steps are desired such as 1.0 V, 2.0 V and so forth. 104

111 0-12 DC V Power upply This power supply has various small DC Voltages settings such as 3 V, 4.5 V, 6 V, 7.5 V, 9 V and 12 V. Fig. 4 0 to 12 V Power upply 105