AP PHYSICS 1 SUMMER PREVIEW

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1 AP PHYSICS 1 SUMMER PREVIEW Name: Your summer homework assignment is to read through this summer preview, completing the practice problems, and completing TASK 1 and Task 2. It is important that you read through the notes provided before attempting to answer the questions in Task 1 and Task 2. There are several practice questions embedded in the notes to help you learn the material. Task 1 and Task 2 are due the first day of class and will be counted as your first two homework grades. You can expect a quiz during the first few days of school that is based solely upon the material contained in this summer preview. All of the work and calculations necessary to solve the problems in Task 1 and Task 2 must be shown to receive credit for this assignment. This is an individual assignment. As such, you may not copy any part of the solutions to this assignment from another student nor may you allow any other student to copy any of your work.

2 WHAT IS PHYSICS? Physics is the most basic of the experimental sciences. Physics provides the foundation for the other scientific and technical disciplines. As a science that deals with matter and energy, physics explores a wide variety of fields. We will study the area of Newtonian Mechanics in this course as follows: Newtonian Mechanics Kinematics: The study of how things move Dynamics: The study of the causes of motion Circular Motion and Gravitation Oscillations Conservation Laws Rotational Motion Introduction to Electricity Units, Standards and The SI System The base units that will be used in this course are: kilogram (kg) meter (m) second (s) All physical quantities are expressed in terms of base units. For example, the velocity is usually given in units of m/s. All other units are derived units and may be expressed as a combination of base units. For example: force is expressed in Newtons (1 N = 1 kgm/s 2 ) SI PREFIXES Power Prefix Abbreviation tera- T 10 9 giga G 10 6 mega M 10 3 kilo k 10-2 centi c 10-3 milli m 10-6 micro μ 10-9 nano n pico p

3 MATHEMATICAL NOTATION Many mathematical symbols will be used throughout this course. = denotes equality of two quantities denotes a proportionality < means less than > means greater than means two quantities are approximately equal to each other x (read as delta x ) indicates the change in quantity x represents a sum of several quantities, also called summation PHYSICS VOCABULARY A variable refers to a quantity in an equation. Examples: time, velocity, force Symbols are used to represent variables: t, v, F A unit refers to an accepted standard of measurement. For example: time is measured in seconds, velocity is measured in meters per second, force is measured in Newtons UNIT CONVERSION 1 km = 1000 m 1 m = 100 cm 1 m = 1000 mm 1 h = 60 min 1 min = 60 s 1 h = 3600 s 1 kg = 1000 g 1 g = 1000 mg PRACTICE: 1.1 Convert 15 km/h to m/s 1.2 Convert 450 m/s to km/h

4 PHYSICS SKILLS I. GRAPHICAL ANALYSIS One of the most effective tools for the visual evaluation of data is a graph. The investigator I usually interested in a quantitative graph that shows the relationship between two variables in the form of a curve. For the relationship y = f(x), x is the independent variable and y is the dependent variable. The rectangular coordinate system is convenient for graphing data, with the values of the dependent variable plotted along the vertical axis and the values of the independent variable plotted along the horizontal axis. Positive values of the dependent variable are traditionally plotted above the origin and positive values of the independent variable to the right of the origin. This convention is not always adhered to in physics, and thus the positive direction along the axes will be indicated by the direction the arrow head points. The choice of dependent and independent variables is determined by the experimental approach or the character of the data. Generally, the independent variable is the one over which the experimenter has complete control the dependent variable is the one that responds to the change in the independent variable. An example of this choice might be as follows. In an experiment where the given amount of gas expands when heated at a constant pressure, the relationship between variables, V and T, may be graphically represented as follows: By established convention it is proper to plot V = f(t) rather than F = f(v), since the experimenter can directly control the temperature of the gas, but the volume can only be changed by changing the temperature.

5 CURVE FITTING When checking a law or determining a functional relationship, there is a good reason to believe that a uniform curve or straight line will result. The process of matching an equation to a curve is called curve fitting. The desired empirical formula, assuming good data, can usually be determined by inspection. Curve fitting by inspection requires an assumption that the curve represents a linear or simple power function. If data plotted on the rectangular coordinates yields a straight line, the function y = f(x) is said to be linear and the line on the graph could be represented algebraically by the slope-intercept form: y = mx + b where m is the slope and b is the y-intercept PRACTICE: 1.3 Consider the following graph of velocity vs. time: The curve is a straight line indicating a linear relationship. (a) Write the equation of the line

6 (b) Write the expression for the slope (c) Calculate the slope and write the answer with appropriate units (d) What is the meaning of the y-intercept? (e) Rewrite the mathematical expression with appropriate values and units.

7 1.4 Consider the following graph of pressure vs. volume: (a) What type of curve is this and how are the variables related? The graph can be linearized by plotting P vs 1/V. The resulting graph is shown below: (b) Write the mathematical expression for the line:

8 1.5 Consider the following graph of distance vs. time: (a) What type of curve is this and how are the variables related? The graph can be linearized by plotting d vs t 2. The resulting graph is shown below: (b) Calculate the slope. (c) Write the mathematical expression for the line.

9 1.6 Consider the following graph of distance vs height: The graph can be linearized by plotting d 2 vs h. The resulting graph is: (a) Calculate the slope. (b) Write the mathematical expression for the line:

10 TASK 1 Graphing is Fun Name: 1. A student performed an experiment with a metal sphere. The student shot the sphere from a slingshot and measured its maximum height. Six different trials were performed with the sphere being shot at a different angle from the horizontal for each trial. (a) What is the relationship being studied? (b) What is the independent variable in this experiment? (c) What is the dependent variable in this experiment? (d) What variable must be held constant throughout the experiment? 2. The following data were collected were collected during an experiment. On the last column calculate the average time for each mass, using the correct number of significant figures. Mass (kg) Time (s) Trial 1 Time (s) Trial 2 Time (s) Trial 3 Time (s) Trial ` Average Time (s)

11 3. The following data are based on charges for membership in a CD purchasing club. (a) What is the average price of a compact disc? (b) What is the mathematical equation that states the relationship described by the graph?

12 4. The graph below shows the relationship between scores on the SAT exam and the number of years of science that students study. (a) What is the mathematical equation that states the relationship described by the graph? (b) Write a clear sentence that describe the meaning of the slope. (c) What would be the SAT score of a student who took seven science classes?

13 5. (a) What type of relationship does this graph suggest? (b) What variables would you plot to linearize the data? 6. Below is a graph of the relationship between scholarship awards and the effort students exerted trying to win scholarships.

14 (a) Write a mathematical equation that states the relationship described by the graph. (b) What does the y-intercept illustrate? (c) Using the mathematical model, how many applications would be needed to earn $8000?

15 II. SIGNIFICANT FIGURES Laboratory investigations usually involve the taking of and interpreting of measurements. All physical measurements obtained by means of instruments (i.e. metersticks, stopwatches, etc.) are to some extent uncertain. The degree of uncertainty on physical measurements can be indicated by means of significant figures. Consider, for example, a measurement of the length of the object as indicated below, with three differently calibrated metersticks. Observe that when measuring the length of the object with the uncalibrated meterstick (top stick) the actual length of the object can only be estimated, and then only to the nearest tenth of a meter, or as 0.3 meter (one significant figure). Measuring the length of the object, with a meterstick calibrated in tenths of a meter (center stick) it is obvious that the length of the object is greater than 0.2 m by less than 0.3 m. it would seem reasonable to estimate the length of the object to the nearest tenth of the nearest calibration or to the nearest hundredth of a meter; thus 0.27 m. it might actually be as short as 0.26 m or as long as 0.28 m. this measurement has two significant figures indicating less uncertainty than the first measurement made. Measuring the length of the object with a meterstick calibrated in hundredths of a meter (lower stick), the length of the object could be estimated in tenths of the smallest calibrations or to the nearest millimeter; nearer to m than m or m. Note that this measurement has three significant figures indicating less uncertainty in this measurement than in either of the two preceding measurements. Thus, the number of significant figures in a measurement indicates the precision of the measurement and not the absolute measurement of the object. Once the logic of significant figures is accepted, some simple rules are useful for their implementation. Rule 1 which digits are significant: the digits in a measurement that are considered significant are all of those digits that represent marked calibrations on the measuring device plus one additional digit to represent the estimated digit.

16 The zero digit is used somewhat uniquely in measurements. A zero might be used as an indication of uncertainty or simply as a placeholder. For example, the distance from the earth to the sun us commonly given as 1,500,000,000 km. The zeroes in this measurement are not intended to indicate that the distance is accurate to the nearest km, rather these zeroes are being used as place holders only and are thus not considered significant. Rules for zeroes: 1. All non-zero digits in a measurement are considered to be significant. 2. Zeroes are significant if bounded by non-zero digits; e.g. the measurement 4003 has four significant figures. 3. If a decimal point is expressed, all zeroes following non-zero digits are significant; e.g., the measurement kg has four significant figures. 4. If a decimal point is not explicitly expressed, zeroes following the last non-zero digit are not significant, they are lace holders only; e.g. the measurement 160 N has two significant figures. 5. Zeroes preceding the first non-zero digit are not significant, they are place holders only; e.g., the measurement has three significant figures. Rules for addition and subtraction with significant figures: 1. Change the units of all measurements so that all are expressed in the same units. 2. The sum or difference of measurements may have no more decimal places than the least number of decimal places in any measurement. Example: m m m m = m Since the last measurement (13.2 m) is expressed to only one decimal place, the sum may be expressed to only one decimal place. Thus m is rounded to 29.8 m. Rules for multiplication and division with significant figures: 1. When multiplying or dividing, the number of significant figures retained may not exceed the least number of digits in either of the factors. Example cm x cm. The calculator displays A more reasonable answer is 22.4 cm 2. This product has only three significant figures because one of the factors (0.304 cm) has only three significant figures, therefore the product can have only three. Example g 8.50 L. The calculator displays 0.02 g/l, while numerically correct, leaves the impression that the answer is not known with much certainty. Expressing the density as g/l leaves the reader with the sense that very careful measurements were made.

17 TASK 2 What significant figure? Name: The zero rules for significant figures are as follows: (1) Zeroes are significant when bounded by non-zero digits (2) Zeroes preceding the first non-zero digit are never significant (3) If a decimal point is explicitly expressed, all zeroes after the first non-zero digit are significant (4) If a decimal point is not explicitly expressed, zeroes following the last non-zero digit are not significant For exercises 1 10, give the number of significant digits. Measurement Number of significant figures Measurement s 405 kg m 7600 cm kg g ml mg m 500 ml Number of significant figures For each of the following problems, in the blank record the correct measurement followed by the appropriate explanation of the rule(s) utilized. For example:

18 A graph of velocity and time is plotted below. 14. Estimate the value of v when t = Estimate the value of t when v = Determine the slope of the line with appropriate units. For each of the following problems, express your answer to the appropriate number of significant figures g g g g = s 10 m/s = 19. Determine the volume of a block with dimensions 2.56 cm by cm by 8.0 cm m/s 450 s =