AP Physics 1 Mr. Perkins June 2014 SUMMER WORK FOR 2014-2015 AP PHYSICS 1 STUDENTS 1. Read Chapter 1 of Textbook (Giancoli pp.1-17). Make a list of questions about any topics you would like clarified on day 1. 2. Read Chapter 2, Section 1 through Section 6 (pp. 21-32): At the end of each chapter, there are a set of questions, followed by MisConceptual Questions, followed by a set of problems. Complete Questions Q1-4 and Problems P1-4, 7-9. 3. Math Skills: All AP Physics 1 students must be familiar with the basic math skills of Algebra, Geometry and Trigonometry. Solve all of the problems in this packet thoroughly, showing all of your work next to each problem. Write all of your final answers on the answer sheet, which is at the end of the packet. You may consult textbooks and notebooks. You will have a test on the second class over this material (Chapter 1, Chapter 2 Sections 1-6, and Math Skills packet). Subpar results may result in a recommendation to take Physics instead of AP Physics 1. A. Rounding B. Multiplying fractions using the calculator C. Areas of rectangles and volumes of rectangular blocks D. Exponents E. Cross multiplication & division F. Simple Algebra problems G. Literal equations in Algebra H. Complex fractions I. Unit conversion J. Trigonometry and Geometry K. Sample Physics Problems 1
A. Rounding If the next digit is 5 or higher, then round up; if the digit is less than 5, then round down. Round only once; do not round twice. e.g. e.g. If you want to round to whole number, then a) 24.45 = 24 b) 23.67 = 24 c) 1.443 = 1 If you want to round to 1 decimal place, then a) 24.45 = 24.5 b) 23.67 = 23.7 c) 1.443 = 1.4 Do Problems: 1. Round the following numbers to 3 decimal places: (i) 58.3382 (ii) 2.5546 (iii) 729.5005 (iv) 4.8898 B. Multiplying fractions using the calculator The parentheses are often used to indicate multiplication. e.g. (2.5)(4.6)(6.7) means 2.5 is multiplied by 4.6, which is then multiplied by 6.7 For a fraction, multiply the value above the fraction line and divide the value below the fraction line. e.g. = 0.33 (a) I suggest you solve the problem above by looking at one pair of parentheses at a time. So on your calculator, press: 1.2 2.3 x 3.4 4.5 x 5.6 6.7 It is also correct to (b) multiply all the numbers above the fraction line first, then divide by all the numbers below the fraction line; so on your calculator, press: 1.2 x 3.4 x 5.6 2.3 4.5 6.7 or (c) press: 1.2 x 3.4 x 5.6 (2.3 x 4.5 x 6.7) (note: the parenthesis) (d) when multiplying and/or dividing with scientific notation, use parenthesis, or treat each part of the notation separately. (4.25) (6.20 x 10 12 ) = (4.25) (6.20) (10 12 ) (3.42 x 10 6 ) (3.42) (10 6 ) AP Physics 1, Summer Assignment - Summer 2014 2
2. Use method (a) above and your calculator to evaluate the following expressions. (i) (ii) (iii) (2.96 x 10 5 ) (4.3 x 10 2 ) (iv) (6.67 x 10-11 ) (423) (570) (8.58 x 10 3 ) (640 x 10-6 ) 2 C. Areas of rectangles and volumes of rectangular blocks Area of rectangle = length x width Area of volume of a rectangular box = length x width x height Note that the units multiply and divide also. e.g. If length = 5.02 cm, width = 2.34 cm, then area = (5.02 cm)(2.34 cm) = 11.7 e.g. If length = 5.02 cm, width = 2.34 cm, height = 1.23 cm, then volume = (5.02 cm)(2.34 cm)(1.23 cm) = 14.4 3. If the length of a rectangle measures 35.6 cm and the width measures 2.30 cm, what is the area? (Don t forget to write the unit.) Show work (setup) clearly. 4. A box measures 12.5 cm in length, 8.67 cm in width, and 3.30 cm in height. What is the volume? Show work (setup) clearly. AP Physics 1, Summer Assignment - Summer 2014 3
D. Exponents a) The value of any power expression with exponent zero is equal to 1, i.e., =1. e.g. =1 =1 =1 etc. b) To multiply two powers having the same base, add the exponents, i.e. e.g. c) To divide one power by another having the same base, subtract the exponents, i.e. e.g.1. e.g.2. d) To evaluate the power to another power, multiply the exponents, i.e. e.g. = 5. Evaluate the following expressions. Express your answer in exponent form. (for example: 2 3. 2 2 = 2 5 ) (i) (ii) (iii) (iv) (v) (vi) e) Ten to a negative power gives a number less than 1. Therefore ten to a large negative power will give a small decimal number. 10-12 < 10-9 < 10-3 < 1 < 10 3 < 10 9 < 10 12 < sign means less than i.e. = 0.000001 6. Which number is larger in each of the following? (i) 10-8 or 10-5? (ii) 10-4 or 0.1? (iii) 10-3 or 0.01? AP Physics 1, Summer Assignment - Summer 2014 4
E. Cross multiplication & division e.g. If D = 3.42 g/ml and V = 12.2 ml, then upon substitution, 3.42 = is the same as thus: (1)M = (3.42) (12.2) = 41.7 g The idea is to put the unknown on one side and everything else on the other side of the equal sign. Cross multiply 3.42 and 12.2. This is the same as multiplying 12.2 on both sides and then canceling. 3.42 = (3.42) (12.2) = M M = 41.7 g e.g. If D = 3.42 g/ml and M = 45.6 g, then upon substitution, 3.42 = 45.6 (3.42) V = 45.6 V = 45.6 V = 13.3g V 3.42 7. If and M = 2.1 and V = 3.8, calculate n. 8. If and M = 2.1 and n = 5.5, calculate V. AP Physics 1, Summer Assignment - Summer 2014 5
F. Simple Algebra problems e.g. v = v 0 + (a)(t) If v = 15 m/s, v 0 = 10 m/s, t = 8 s, then write 15 m/s = 10 m/s + a(8 s) a = (15-10) m/s a = 0.625 m/s 2 8 s 9. GPE = m g h and GPE = 450 m = 24 g = 9.81 Solve for h. 10. v = v 0 + (a)(t) and v = 8 m/s v 0 = 2 m/s a = 3.5 m/s 2 Solve for t. G. Literal equations in Algebra Express one variable in terms of other variables, without numbers. e.g. For the expression, PV = nrt (a) express P in terms of the other variables: (b) express T in terms of the other variables: T = (c) express n in terms of the other variables: n = 11. If, express (i) in terms of the other variables. (ii) in terms of the other variables. AP Physics 1, Summer Assignment - Summer 2014 6
12. If, express (i) n in terms of the other variables (ii) V in terms of the other variables H. Complex fractions The fraction line is a division line. Since means A B, = = x Do the same for units. 13. Evaluate the following expressions (i) (ii) AP Physics 1, Summer Assignment - Summer 2014 7
I. Unit conversion (AKA Dimensional Analysis AKA Factor-Labeling Method) Example 1: Change 26.2 miles to meters. 26.2 mi. x 1609 m = 42155.8 m 1 mi. Example 2: Change 4.75 liters to milliliters 4.75 liters x 1 milliliter = 4750 ml = 4.75 x 10 3 ml.001 liter Solve the following conversion problems using the fraction technique. Equivalent measurements and metric prefixes can be found on the next page. 14. 45 cm = inches 15. 100 yards = meters 16. 1 mile = kilometers 17. 180 pounds = newtons 18. 1,000,000 newtons = tons 19. 2 liters = quarts 20. 10 gallons = liters 21. 400 m = km 22. 500µm = cm 23. 65 kg = grams A rectangular box measures 12 centimeters by 8 centimeters by 3 centimeters. Use this information for problems 24, 25 and 26. 24. Find the volume in cm 3. 25. Find the volume in m 3. 26. Find the volume in liters. AP Physics 1, Summer Assignment - Summer 2014 8
27. How many cm 2 are in 1 m 2? 28. How many meters/second (m/s) are equal to 1 mile/hour (mi/hr)? Equivalents and Conversion Factors Metric Prefixes Tera T 1,000,000,000,000 10 12 Giga G 1,000,000,000 10 9 Mega M 1,000,000 10 6 kilo k 1,000 10 3 deci d.1 10-1 centi c.01 10-2 milli m.001 10-3 micro µ.000 001 10-6 nano n.000 000 001 10-9 pico p.000 000 000 001 10-12 femto f.000 000 000 000 001 10-15 Length Force Volume 1 in = 2.54 cm 1 ft = 30.48 cm =.3048 m 1 yd = 91.44 cm =.9144 m 1 mi = 1609 m 1 pound = 4.45 newtons 1 ton = 8896 newtons 1 liter = 1000 ml = 1000 cm 3 1 liter = 1.0576 quarts 1 gallon = 4 quarts 1 gallon = 3.79 liters 1 m 3 = 1000 liters AP Physics 1, Summer Assignment - Summer 2014 9
J. Trigonometry and Geometry Sine, cosine and tangent functions are essential in the study of physics in two dimensions. Read through the examples and complete all practice problems. Make sure your calculator is in DEG mode, and not in RAD mode. What do Sine, Cosine and Tangent mean? SOH CAH hypotenuse (hyp) opposite (opp) TOA θ Pythagorean Theorem: adjacent (adj) 29. Using your calculator to evaluate the functions, complete the following table. Make sure your calculator is set in degree mode (not radian mode). θ = 30º θ = 60º θ = 45º Sin 30º = Sin 60º = Sin 45º = Cos 30º = Cos 60º = Cos 45º = Tan 30º = Tan 60º = Tan 45º = Do you notice any pattern in the numbers above? Using Sin, Cos and Tan to find the sides or angles of a triangle. Example 1: 20 opp 30º adj AP Physics 1, Summer Assignment - Summer 2014 10
Example 2: 18 12 θ adj Solve for the unknown side lengths and angles in the following triangles. Show your work. Write the answers (2 for each question) on the line for that question on the answer sheet. 30. 31. 32. hyp 5 6 opp θ 45º 60º 8 adj 4.5 33. 34. 35. hyp 35º 6.5 18º 3.6 2.3 y θ 1.8 AP Physics 1, Summer Assignment - Summer 2014 11
K. Sample Physics Problems The following are ordinary physics problems. Place the answer in scientific notation when appropriate and simplify the units (Scientific notation is used when it takes less time to write than the ordinary number does. As an example 200 is easier to write than 2.00x10 2, but 2.00x10 8 is easier to write than 200,000,000). Do your best to cancel units, and attempt to show the simplified units in the final answer. a. b. c. d. e. Often problems on the AP exam are done with variables only. Solve for the variable indicated. Don t let the different letters confuse you. Manipulate them algebraically as though they were numbers. f. l. g. h. i. j. m. n. o. p. k. AP Physics 1, Summer Assignment - Summer 2014 12
Answer Sheet 1. (i) (iii) (iv) 2. (i) (iii) (iv) 3. 4. 5. (i) (iii) (iv) (v) (vi) 6. (i) (iii) 7. 8. 9. 10. 11. (i) 12. (i) 13. (i) 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. K) a. b. c. d. e. K) f. g. h. i. j. k. l. m. n. o. p. AP Physics 1, Summer Assignment - Summer 2014 13