AP Physics Summer Assignment For School Year

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AP Physics Summer Assignment For 014-15 School Year Name : College Major? : You MUST PASS a College Physics course if you want a career in any of the following majors: 1. Any Medical Field: a.

1 AP Physics Summer Assignment For School Year Name : College Major? : You MUST PASS a College Physics course if you want a career in any of the following majors: 1. Any Medical Field: a. Nursing b. Pediatrics c. Dentistry d. Surgeon e. Nuclear Medicine f. Veterinarians g. Pharmacists h. Any Pre med career track. Biological Sciences 3. Psychologists 4. Engineering: a. Civil Engineers b. Mechanical Engineers c. Chemical Engineers d. Electrical Engineers e. Nuclear Engineers f. Aerospace Engineers g. Computer Engineers h. Biomedical Engineering i. Electrical Diagnostics 5. Astronomy and Geosciences 6. Architects 7. Computer Programmers 8. Computer scientists 9. Mathematicians 10. Statisticians These all require a minimum of 1 courses in college physics (Excluding 4-10)

2 Much of the work we will be doing during the year will require a bit of foreknowledge, while succeeding in physics is not dependent upon being an expert in this foreknowledge. Having a general understanding of this knowledge certainly Reduces the work load Increases understanding Creates a firmer understanding of the material Reduces the time spent doing homework Increases the odds of scoring higher on the AP Test In short taking the time during your summer vacation to simply look over the following material will have a real benefit. Of course at the same time this is your first assignment that is due the first day of school and will be worth a generous amount of points. Note: Mr. Marsili will be in his Office during the summer months to assist any student with questions or assist with difficulties. To reach Mr. Marsili simply me at jmarsili@access.k1.wv.us By signing this, I accept the responsibility to complete the summer packet. I understand that this packet will be graded and that I will be tested on this material within the first week or two of school. I realize that knowledge of its content is a course requirement. Signed By: Date:

3 Table of Contents: 1. Significant Digits Page 4 a. Significant Figures Homework Page 5. Scientific Notation Page 6 a. Scientific Notation Homework Page(s) Factor Label Unit Conversion Page 9 a. Metric Conversion Factors Page 10 b. Units and Dimensional Analysis Homework Page Unit Analysis Page 1 5. Solving for Variables Page a. Solving for Variables Homework Page 15 b. Solving for Variables Practice Page(s) Graphing Page(s) a. The Cartesian Coordinate system Page 0 b. The Cardinal Directions Page 1 7. Trigonometry Page a. Introduction to trigonometry Homework Page 3 8. Vectors Page(s) 4 5 a. Triangles and Vectors Page(s) 6 7 b. Adding Vectors Mathematically Page(s) 8 9 c. Adding Vectors Graphically Page 30 d. Vectors homework Page 31 3

4 Significant Digits (also known as significant figures) Rules for deciding which digits are significant: 1. Nonzero digits are always significant.. All final zeros after the decimal point are significant. 3. Zeros between two other significant digits are always significant. 4. Zeros used solely for spacing the decimal point are not significant. Examples: Using the rules above, mm has 3, 960 kg has, and 70,080 s has 4 significant figures m m m = m = m (In addition or subtraction, work with the numbers as they are written, but the final answer must have the same level of precision as the least precise number in this case, precision to the tenths place.) = = 3.45 (In multiplication or division, work with the numbers as they are written, but the final answer must have the same number of significant digits as the number with the least amount of digits in this case, 3 significant digits.) =.1 m (In multiplication or division, units are multiplied and divided like numbers.) Exercises 1. State the number of significant digits in each of the following measurements. a kg b. 0.0 km c m d. 006 s e m f km g kg h. 809 g. Solve the following problems and give the answers to the correct number of significant digits. (All numbers must be written with the correct units.) a cm cm = b. 8.9 g g g = c. 8.3 m x 1.54 m = d. (1. x 106 m)(3.5 x 104 m) = e. = f. = g. = h. 5.5 cm x 1.3 cm = i. 9.0 cm cm cm = j g g = 4

5 Significant Figures 1. Indicate how many significant figures there are in each of the following measured values m m m m m m m m m m m m. Calculate the answers to the appropriate number of significant figures, and state the significant figures in each measurement. a m m m = b kg kg kg = c mm mm mm = 3. Calculate the answers to the appropriate number of significant figures, and state the significant figures in each measurement. a cm + 7.4cm cm cm = b m m m = c kg kg kg = 4. Calculate the answers to the appropriate number of significant figures, and state the significant figures in each measurement. a. 3.7 cm x 3.8 cm = b A x 0.5 A = c g x g = 5. Calculate the answers to the appropriate number of significant figures, and state the significant figures in each measurement. a L 64.5 L = b L 64.1 L = c L 0.4 L = 5

6 Scientific Notation Scientific notation is a compact way of writing large or small numbers while using only significant digits and powers of ten. The normal form for scientific notation is: A x 10 b a is a number in the form of 0.00 (i.e. a digit in the ones, tenths, and hundredths place) b is the powers of ten telling us which direction to move the decimal place and how many times. Examples: written in scientific notation would be.65 x (The negative three power of ten indicates that the decimal point should be moved three places to the left.) 7.68 x 10 5 expanded would be 768,000. (The positive power of five indicates that the decimal point should be moved five places to the right. In this case, zeros are needed as placeholders.) = 3.0 x (Divide the decimals while keeping the correct number of significant figures. When dividing powers of ten, subtract the bottom power of ten s exponent from the top power of ten s exponent. If multiplying, add powers of ten.) (4.5 x 10 - ) + (8. x 10-3 ) = 4.5 x x 10 - = 5.3 x 10 - = 5.3 x (Before adding or subtracting numbers in scientific notation, all numbers need to have the same power of ten) Exercises: Write the following numbers in scientific notation 1) 5800 ) ) ) 560 5) ) ) ) ).004 Expand the following numbers: 10) 1.0 x ).34 x ).00 x ) 1.99 x 10 4 m 14) 9.80 x ) 6.65 x 10 5 Solve the below mathematical operations (using the correct number of significant figures) 16) 5 x x 10 6 = 17) 7.0 x x 10 3 = 18) (6.66 x 10 4 ) (5.0 x 10 8 ) = 19) (6.00 x 10 8 ) (.00 x 10 4 ) = 0) (3.14 x 10 4 ) (. x 10 6 ) = 6

7 Scientific Notion 1) Express the following measurements in scientific notation. a m b m c m d m ) a kg b kg c kg d kg 3) a s b s c s 4) a m b m c m 5) a kg b s c. 6 m d s 7

8 Addition and Subtraction in Scientific Notation: 6) a. 5 x 10 7 m + 3 x 10 7 m = b. 6 x 10 8 m + x 10 8 m = c. 4. x 10 4 m x 10 4 m = d. 1.8 x 10 9 m +.5 x 10 9 m = 7) e. 6.0 x 10 8 m + 4 x 10 7 m = f. 7.0 x 10 4 kg + x 10 3 kg = g. 4 x 10 4 kg x 10 5 kg = h. 6.0 x m x m = Multiplication and Division in Scientific Notation: 8) i. ( x 10 4 m)(4 x 10 8 m) = j. (3 x 10 4 m)( x 10 6 m) = k. (6 x 10 4 m)(5 x 10 8 m) = l. (.5 x 10 7 m)(.5 x m) = 9) m. (6 x 10 8 kg) / ( x 10 4 m 3 ) = n. (6 x 10 8 kg) / ( x 10 4 m 3 ) = o. (6 x 10 8 m) / ( x 10 4 s) = p. (6 x 10 8 m) / ( x 10 4 s) = 8

9 Factor-Label Unit Conversion Common Prefixes: nano has the symbol, n, and means 10 9 (or ) micro has the symbol, µ, and means 10 6 (or ) milli has the symbol, m, and means 10 3 (or 0.001) centi has the symbol, c, and means 10 (or 0.01) kilo has the symbol, k, and means 10 3 (or 1000) For the problems below, show all conversion factors, work. And do not use the conversion factor feature on your calculator to do these problems. 1. Carry out the following conversions using the prefix information shown above. a. 35 nm ( ) b. 450 cm ( ) c µg ( ) d. 50 km ( ) e. 346 ms ( ) f. 543 mg ( ) g g ( ) h. 39 mm ( ) i. 48 ml ( ) j. 38 kg ( ) 9

10 Metric Prefixes Order of Magnitude Prefix Abbreviation exa - E Peta - P 10 1 Tera - T 10 9 Giga - G 10 6 Mega - M 10 3 Kilo - K 10 Hecto - H 10 1 Deka - da 10 0 BASE deci - d 10 - centi - c 10-3 milli - m 10-6 micro nano - n 10-1 pico - p femto - f atto - a 10

11 Units and Dimensional Analysis 1. Compute the number of seconds in an hour, day, and year.. The maximum sodium intake for a person on a 000 calorie diet should be 400 mg/day. How many grams of sodium is this per day? 3. The recommended daily allowance (RDA) of the trace element chromium is 10 μg/day. Express this dose in grams per day 4. An intake of vitamin C up to 500 mg/day is considered safe. Express this intake in grams per day. 5. The electrical resistance of the human body is approximately 1500 ohms when it is dry. Express this resistance in Kilohms. 6. An electrical circuit of about 0.00 amps can cause muscular spasms so that a person cannot, for example let go of a wire. Express this current in milliamps. 7. Starting with the definition 1.00 inches =.54cm, find the number of kilometers in 1.0 miles. 8. In medicine, volumes are often expressed in milliliters; prove that a milliliter is the same as a cubic centimeter. 9. How many cubic centimeters are there in a 1.00 liter bottle of drinking water? (Hint: 1 cm 3 = 1 ml) 10. Bacteria vary somewhat in size, but a diameter of.0μm is not unusual. What would be the volume (in cubic centimeters) and the surface area (in square millimeters) of such bacterium assuming that it is spherical? (Consult Appendix A of your book for assistance) 11

12 Unit Analysis Unit analysis involves the placement of units in an equation to check for unit agreement on both sides of the equals sign. When substituting values into an equation in physics, you must state the units as well as the numerical values. Including units in your calculations helps you keep units consistent throughout and assures you that your answer will be correct in terms of units. The proper units for variables are included in the table below. Quantities Units (d) displacement (v o ) original velocity (v f ) final velocity ( ) average velocity (a) acceleration (t) time Equation with Unit Disagreement Examples Equation with Unit Agreement The equation being inspected is indicate that its units The units on the left are equal to the units on the right of the equal sign. This equation is correct in terms of units. The equation being inspected is its units indicate that ( ) ( ) (Notice that coefficients, such as the number, in the equation are ignored in dimensional analysis) The units on the left are Units (m) Meters (meters per second) m/s (meters per second squared) m/s s (seconds) but the units on the right turn out to be The units do not agree. This final velocity equation is incorrect in terms of its units. Problems Use the method described above to determine if the following equations have unit agreement. Show your work and write correct next to the equation if it is correct and incorrect if it is incorrect in terms of its units. 1.. ( )

13 Solving for Variables PROBLEM SOLVING When solving motion problems, or, indeed, any physics problem, use an orderly procedure like the one listed below. 1. Identify the quantities that are given in the problem.. Identify the quantity that is unknown, the one you have to find. 3. Select the equation that contains the given and unknown quantities. 4. Solve the equation for the unknown quantity using algebra. 5. Substitute the values given in the problem, along with their proper units, into the equation and solve it. 6. Check to see if the numerical value of your answer is reasonable and make sure that the answer has the correct units. Example Solve for each variable in the equation below. The variable should be placed alone on the left side of the equation. (It is already solved for v f, so it only needs to be solved for v o, a, and t.) Problems 1. In the equation, ( ), solve for v f and t.. In the equation,, solve for v o and a. 3. In the equation,, solve for v f, v o, and d. 13

14 Solving for Variables Examples Solve the following equation for c. (Divide both sides by m) (Take the square root of both sides and there will be a positive and negative solution for c) Solve the following equation for k. (Multiply both sides by g) (Divide both sides by 3) or finally, (square both sides of the equation) Problems Solve the following equations for the variable(s) requested. 1. E = ½mv for m and v. for d 3. E = mgh for h 4. E = hf - W o for W o and h 5. = for s i 6. ax + b = c for x Solve for x in the following problems

15 Solving For Variables Directions: Solve for the following for the variable a please show all of your work in a step by step method, and circle your answers

16 Solve for 1. d. t in this equation. d v t d v t 3. m F = ma 4. a v v at f o 5. t v v at f o 6. a 1 d v o t at 7. v o 1 d v o t at 8. d v v ad f o 9. v o v v ad f o 10. a v v ad f o 11. v o v f vo d t 1. t v f vo d t 13. v f v f vo d t 14. m KE = ½ mv² 15. v KE = ½ mv² 16. v mv F c r 16

17 17. r mv F c r Gm1m 18. r F g r Gm1m 19. m F g r 0. L T P L g 1. g T P L g. k 3. m T S T S m k m k I1 R 4. R 1 I R I1 R 5. R I R 6. x μmgd = mgh + ½ mv + ½ kx m μmgd = mgh + ½ mv + ½ kx 17

18 Graphing Plotting Graphs These steps will help you plot graphs from data tables. 1. Your graph should be titled Y vs. X (or the vertical information versus the horizontal information).. Decide on the scales needed for the x and y axes. Choose scales that will spread out the data. Do not choose scales that compress the data points into a tiny portion of the graph paper. Your graph should fill up the graph paper. 3. Number and label the x and y axes (including necessary units). 4. Draw the best straight line (using a straight edge) or smooth curve that passes through as many data points as possible. Do not just connect the data points together with a series of straight line segments. Graphing Data Values The steps listed above were followed to set up the plotting of the data shown below. Time (s) Speed (m/s) Exercises 1. Plot the data values on the graph provided above and draw one straight line that best fits the data (use a straight edge to make the line).. What is the slope of the line of best fit (find the number)? m/s (Slope = rise/run) 3. What is the speed at 3 s? m/s 4. Using the graph, what is the speed at 6 s? m/s 5. At what time is the speed 0 m/s (using your graph) s 18

19 Graphing There are three relationships that occur frequently in physical processes. They are depicted in the three graphs shown below. Speed (m/s) Radius (m) Exercises 1. Plot the data values on the graph provided above and connect the points together with a smooth curve that follows the data.. Approximately what is the radius when the speed is 5 m/s? m. 3. This type of curve is known as a. 4. This graph follows an equation of the form radius = k(speed). Radius and speed squared are related. The Cartesian Coordinate system 19

20 The Cartesian coordinate system is the linear Cardinal Directional Handout system we will be using most often when creating graphs and plots, or when describing the directions of a vector. This system should be familiar to you. Angles and reference points: The angles increase in a counter clockwise rotational direction. Negative angles are rotating in the clockwise direction. An important point to be aware of is that whenever measuring an angle we ALWAYS use the x axis as the reference axis. When measuring an angle from the positive x axis your calculator will know exactly where that specific angle is. When measuring an angle from the negative x axis your calculator will automatically assume the angle is in the first quadrant (So do not allow your calculator to make a fool out of you.) Make sure you know your positive directions from your negative directions. There are four Quadrants: I. From 0 o to 90 o x = positive values, y = positive values II. From 90 o to 180 o x = negative values, y = positive values III. From 180 o to 70 o x = negative values, y = negative values IV. From 70 o to 360 o or 0 o x = positive values, y = negative values 90 o 180 o 0 o Draw the following approximate angles. I. 45 o II. 150 o III. 110 o IV. 335 o V. 40 o 70 o 0

21 The Phrase: 40 o North of West Meaning: The first direction North tells us the direction the angle will be revolving from our reference axis (This direction tells us that our angle is turning from the Western axis in the Northern direction) The second direction West is the axis of reference. (It is from this axis that our angle will start) 40 o The Phrase: 45 o West of South Meaning: The first direction West tells us the direction the angle will be revolving from our reference axis (This direction tells us that our angle is turning from the Southern axis in the Western direction) The second direction South is the axis of reference. (It is from this axis that our angle will start) 1 45 o

22 Trigonometry Trigonometry is an extremely useful branch of mathematics that deals with the relationships between the sides and angles of right triangles. The Pythagorean Theorem is a method for finding missing sides of right triangles. It states that the hypotenuse (the longest side) is related to the other two sides of a triangle by the following equation. (where c is the length of the hypotenuse and a and b are the lengths of the other two sides) The three commonly used trigonometric functions are The sine: The Cosine: The Tangent (Memorizing SOH CAH TOA is one way of memorizing these trigonometric functions.)

23 Introduction to Trigonometry 1. Using the Triangle to the right please do the following: a. Find the length of side c two ways and justify your answer. b. Find the angle of each corner of the triangle c 4 3. If the angle theta is 35 degrees find the length of a. Side y b. Side x 10 θ y x 3. Using the triangle on the right proved the following: a. The tangent ratio of the sides b. The cosine ratio of the sides c. The sine ratio of the sides z θ y 4. The diagram to the left illustrates the path a raft would follow across a 40 meter river that has a strong upward current. (The current moves towards the top of the page) a. What does the hypotenuse represent? b. How far down the river does the raft travel? c. How far is the raft displaced? x 3 45 o

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25 Vectors Calculations 1. Find the horizontal and vertical components of the velocity vector shown below. (Please show your work.) 5

26 Triangles and Vectors Show ALL of your work! 1. Find the length of the missing side and then find the following for the triangle shown at the right: θ 17 m a. sinθ b. cosθ c. tanθ? d. sinγ e. cosγ f. tanγ 14 m γ. Find the angles θ and γ in the triangle above. 3. In the triangle shown to the right, find the following: a. Angle θ θ 165 km b. Side A c. Side B B A 6 6

27 4. In the triangle shown at the right, find the following without the Pythagorean Theorem: a. Angle α R β 68. cm b. Angle β α c. Side R 64.8 cm 5. Break the Following vectors into their horizontal (X) component and (Y) vertical Component. A. 45 m/s at 5 o B. 67 km at 56 o 6. Add the Vectors from Number 5 to obtain the magnitude of the resultant vector. 7. Break the Following vectors into their horizontal (X) component and (Y) vertical Component. A. 57 N at 16 o B. 13 N at 337 o 8. Add the Vectors from Number 7 to obtain the magnitude of the resultant vector. 9. Break the Following vectors into their horizontal (X) component and (Y) vertical Component. A. 45 m/s at 0 o B. 145 m/s at 45 o C. 3 m/s at 50 o 10. Add the Vectors from Number 9 to obtain the magnitude of the resultant vector. 7

28 Adding Vectors Mathematically 1.. a. X components using, 1. Clearly determine the: a. Magnitude of the Vectors. b. Direction of the Vectors.. Break Each Vector into its: a. X components using, b. Y components using, b. Y components using, 3. a. 3. Sum up all of the components in each direction (remember to apply + and - ) a. Sum all the X components b. 4. Determine the magnitude of the Resultant Vector b. Sum all the Y components 4. Use the Pythagorean theorem to determine the magnitude of the Resultant Vector 5. Direction / Angle. Second Quadrant: ( ) 5. To determine the direction of the Resultant Vector in reference to the Positive X axis we must use the Arc Tangent. ( ) 8

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30 Adding Vectors Graphically 1.. A 1. Clearly determine the: a. Magnitude of the Vectors. b. Direction of the Vectors.. Draw the first Vector to scale on the coordinate system. a. Make sure that the Vector is in the correct direction and quadrant. θ 3. B 3. Draw a mini coordinate system at the head of the first Vector. a. Draw the next vector head to tail of the last vector. θ A θ 4. This problem only has two vectors. 4. Repeat step 3 for each Vector 5. B 5. After drawing all vectors, draw the Resultant Vector from the origin to the head of the last vector. C A θ θ 30

31 Directions: Answer the following assigned questions on a separate sheet of paper. Be sure to answer each question using scientific notation and to the best of your ability. Don t forget to circle your answer! 43. If a vector has the following components, use trigonometry to find its magnitude and the counterclockwise angle it makes with the + x axis. a. b. c. d., Vector Classwork sheetz 44. Compute the x and y components of vectors = (1.0 m), = (15.0m), and = (6.0m) shown in the figure below. 37 o 60 o 40 o 45. Vector has components ; vector has components. Find a. The components of the sum b. The magnitude and direction of c. The components of the vector difference d. The magnitude and direction of 46. A plane leaves Seattle, flies 85 mi at o north of east, and then changes direction to 48 o south of east, After flying at 115 mi in this new direction, the pilot must make an emergency landing. a. In what direction and how far should the emergency crew fly to go directly to the site of the emergency landing? b. Check the reasonableness of your answer by graphically adding the vectors. 49. A disoriented physics professor drives 3.5 km north, then 4.75 km west, and then 1.50 km south. a. Use components to find the magnitude and direction of the resultant displacement vector of this poor professor. b. Check the reasonableness of your answer by graphically adding the vectors. 31

Pittsfield High School Summer Assignment Contract Intensive 9 / Honors 9 / Honors Physics

Pittsfield High School Summer Assignment Contract Intensive 9 / Honors 9 / Honors Physics Welcome to Physics! The study of physics takes us on a journey investigating matter, energy, and how they interact.