AP Physics 1 NAME ______________________________________

APPh ysics 1S ummer Work 2018

The exercises below are a review of the math skills we willbe usingregularly in AP Physics 1. Make sure to read alldirections throughoutthe packet. Final answers can be in fractions and in terms of mathematical constants (π, e, i,etc.). Your work must be writtenoutclearly so that allsteps are easy to follow. Attach extra pages if you need more space. Markyour finalanswers by either circling or boxing them.

Your completed summer work is due the first week ofclass. During the first two weeks of classtherewill beaquiz with problems similar to those found in this review. Please do not hesitate to email me with any questions at knewton@cpsd.us.

Join the following Google classroom pages for links to videos and/or websites that you mightfind helpful or interesting.

Fall Semester Class (S504A-001) – Google Classroom Code: wxa907kSpring Semester Class (S504A-002) – Google Classroom Code: 1zylul

Significant Figures an dScientific N otationRevi ew

1.) How many significant figures do the following numbers have?

a.) 6.001 Answer: ___________ c.)206,000 Answer: ___________

b.) 0.0080 Answer: ___________ d.) 27.00 Answer: ___________

Find the following. Final answers should be in scientific notation with the correct number ofsignificant figures. 2.) (5.0 ×10−8)(2.9 ×102) 3.) (3.25 ×104 + 7.4 ×103 )

6.000 ×10−11 1.00 ×1026 8400

4.) 2.00 ×107 5.) 1.2 ×107

Unit Conversions Review

6.) Finish the SI prefix table below. Follow the example of the centi-prefix.Symbol Name Numerical

Equivalent n

µ

m

c centi 10-2

k

M

G

7.) 16.7 kilograms is how many grams? 8.) 560 nm is how many meters?

9.) 15 years is how many seconds? 10.) 8.99 ×109 seconds is how many years?

11.) 2.998 ×108 m/s is how many kilometers per hour?

12.) Complete the table below. (Do as much as you can without using a calculator.)

θ 0° 30° 45° 60° 90° sin θ cos θ tan θ

13.) 360 degrees = _________ radians. 14.) 4.5 revolutions = ________ radians.

15.) Find the length of an arc with a radius of 6.0 m swept across 2.5 radians.

16.) Find the length of an arc with a radius of 10.0 m swept across 100 degrees.

Trigonometry ReviewUsethefigurebelow toanswerproblems 17-24. Simplify as much as you can.

c

θ

a

ifgiven a

b

17.) Solvefor c and b. 18.) Solvefor a ifgiven b and c.

19.) Solvefor a ifgiven c and θ. 20.) Solvefor b ifgiven a and θ.

21.) Solvefor θ ifgiven b and c. 22.) Solvefor θ ifgiven a and b.

23.)If a = 2.0 and c = 7.0, whatis b? 24.)If c = 10.0 and θ = 60°,whatis b?

25.)Usingthepropertiesoftriangles,provethat ∠A≅ ∠C in the drawing below.

Answer:

Algebra ReviewSolve the following equations for the given variable and conditions. Simplifyifneeded.

Example: 2x + xy = z .Solvefor x. x(2 + y) = z

zx = 2 + y

v v1 + v2 = 0.Solvefor v1. 27.) a = .Solvefor t.26.) t

28.) �! = �!! + 2�(� − �!)A.) Solvefor v0. B.) Solvefor x.

29.) � = �! + �!� + !!��!

A.) Solvefor vo. B.) Solvefor t,if vo = 0. C.) Solvefor t,if x = x0.

30.) ac = v 2

Solvefor v. 31.) mgsinθ = µmgcosθ .Solvefor θ. r .

mv f + mghf = 12mvi

2 + mghi32.)

A.) Solvefor hf,if hi = 0 and vf = 0. B.) Solve for vf,if hf = 0.

12

1 1 133.) = + .Solvefor RT. 34.) Fg = G m1m2 .Solve for r. r2RT R1 R2

Lmv 2

= G Mm T = 2π 35.) R R2 .Solvefor v. 36.) g .Solvefor g.

37.) 12

1 2kx2

12 2 + mghi.Solvefor x if vf = 0. mv f mvi+ = 2

16

14

Miscellaneous Simplify without using a calculator. Remember to show all of your work.

139.) 13 + 18

38.) +

2

Systems of equations

s2x40.) Consider z = , c = ab,or r = t 2 . y

a.) As x increasesand y stays constant, z _____________________.

b.) As y increasesand x stays constant, z _____________________.

c.) As x increasesand z stays constant, y _____________________. d.) As a increasesand c stays constant, b _____________________.

e.) As c increases and b stays constant, a _____________________.

f.) As b increasesand a stays constant, c _____________________. g.) If s istripled and t stays constant, r is multiplied by _____________________.

h.) If t isdoubledand s stays constant, r is multiplied by _____________________.

Conceptual Question:41.) How many equations are neededtosolve…

a.) for 1 unknownvariable?_________ b.) for 2 unknownvariables?_________ c.)for3unknownvariables?________

Usetheequationsineach problem to solve for the specified variable in the given terms. Simplify.42.) Ff = µFN and FN = mgcosθ .Solvefor µ in terms of Ff, m, g,and θ.

v 2

43.) Fc = mac and ac = .Solvefor r in terms of Fc, m,and v. r

L 144.) T = 2π and T = .Solvefor L in terms of π, g,and f. g f

GraphingEquation s

45.)If r = c – b*t was graphed onan r vs. t graph,whatwouldthefollowingbe? Slope:_____________ y-intercept:________________

46.) Onthe yvs.xgraphs below,sketch the relationships given.

a.) y= mx+ b,if m > 0 and b = 0. b.)y= mx+ b,if m < 0 and b > 0.

c.)y=x2 d.) y = x

e.)y=1/x f.)y=1/x2

1g.) y = h.) y=sin(x) x

Marbles in Cylinder Lab

You received a graduated cylinder with three identical marbles and an unknown amount of wateralready in it. You placed extra identical marbles in the cylinder and obtained the data below. Usethe datato graph abest-fit line showing the relationship between the water level and the numberof marbles. The y-intercept shouldbevisibleonthegraph. Find the slope of the line. Remember thatyouneed to use the bestfitline – notthedatapoints – to find the slope. Label your axes and includeunits.

From the graph, determine a mathematical formula for the water level for any number of marbles.Lastly, give an explanation of your formula in words. Make sure to give an explanation of theslope and y-intercept of your formula.

Number of Marbles inWater

Water level (mL)

3 58 4 61 5 63 6 65 7 68

Formula: ___________________________________

Explanation of the formula in words: (Include the meaning of the slope and y-intercept.)

PendulumLab

You are doing an experiment to find out how the length of a pendulum affects its period. (Period isthe time it takes for one backand forth swing).Youcollectthe databelow.Use Google Sheets to do the following:

• Copy the data into a Google Sheet file (oryoucanstart withtheGoogleSheet filethat is shared on Google Classroom).

• Set up a formula to calculate the average period for each length • Make ascatter plotof the datawith length onthe x-axis and period onthe y-axis • Add a trendline using a power series • Setthelabeltoshowtheequationonthegraph • Attach the Google Sheet file to the Summer Assignment post on Google Classroom.

Period (s) length (m) trial 1 trial 2 trial 3

0.10 0.64 0.63 0.65 0.20 0.91 0.90 0.89 0.30 1.10 1.11 1.09 0.40 1.27 1.25 1.28 0.50 1.42 1.45 1.41 0.60 1.55 1.53 1.56 0.70 1.68 1.67 1.65 0.80 1.79 1.81 1.78 0.90 1.90 1.92 1.89 1.00 2.01 2.02 1.99