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AP Physics 1 Summer Assignment

2014-2015

Concepts and Connections of Math in Physics: Review

This assignment is designed to refresh the student with an understanding of conceptual math problems that will have connections to physical applications in the course. All content should have been learned successfully by the student prior to taking this course. The math in review is a large portion of the understanding behind the physical phenomena we will investigate, and therefore it is the expectation that the student will review the material in detail, where necessary, in order to be prepared for the connections we will make in class. These math topics will be reviewed once we return, but no time is available to reteach the content in class.

Have a wonderful summer and I will see you in the fall!

Mr. Turkett (bturkett@aacps.org)

Due by end of day: August 29, 2014

Part 1: /5

Part 2: /12

Part 3: /7

Part 4: /8

Part 5: /6

Part 6: /12

TOTAL: /50

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Part 1 - Solving Equations: Manipulating Variables

Often in Physics you will find that solving for one variable is necessary. This will require you to review your algebra skills. For each of the following, solve for the indicated variable, but don’t let the different letters confuse you! Just follow the order of operations and solve as if they were numbers you were moving. (1 point for each correct answer)

a. 𝒂 = 𝒎𝒈(𝒔𝒊𝒏𝜽 − 𝝁𝒄𝒐𝒔𝜽), Solve for μ

b. 𝑻 = 𝟐𝝅�𝒍𝒈

, Solve for g

c. 𝑭𝒄 = 𝒎𝒗𝟐

𝒓, Solve for v

d. 𝒙 = 𝑭𝒐𝒄𝒐𝒔(𝝎𝒕)𝒎(𝝎𝒐

𝟐−𝝎𝟐), Solve for Fo

e. 𝑭 = 𝑮𝒎𝒂𝒎𝒃𝒓𝟐

, Solve for ma

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Part 2 – Scientific Notation

Many physics problems will deal with numbers so ridiculously large or small that it is just not convenient to write out all the zeroes. Scientific notation is the saving grace in these cases. Below are some ordinary physics problems. Write the answer in scientific notation and simplify the units. You may use (π = 3). (1 point for each correct answer, 1 for each correct unit)

a. 𝟏.𝟑𝟑𝒔𝒊𝒏(𝟐𝟓.𝟎°) = 𝟏.𝟓𝟎𝒔𝒊𝒏𝜽, θ = ______________________

b. 𝑭 = (𝟗𝒙𝟏𝟎𝟗 𝑵𝒎𝟐

𝑪𝟐) (𝟑.𝟐𝒙𝟏𝟎−𝟗𝑪)(𝟗.𝟔𝒙𝟏𝟎−𝟗𝑪)

(𝟎.𝟑𝟐𝒎)𝟐, F = ______________________

c. 𝑲𝑬 = 𝟏𝟐

(𝟔.𝟔𝒙𝟏𝟎𝟐𝒌𝒈) �𝟐. 𝟏𝟏𝒙𝟏𝟎𝟒 𝒎

𝒔�𝟐

, KE = _____________________

d. 𝟏𝑹𝒑

= 𝟏(𝟒.𝟓𝒙𝟏𝟎𝟐𝛀)

+ 𝟏(𝟗.𝟒𝒙𝟏𝟎𝟐𝛀)

, Rp =

______________________

e. 𝜸 = 𝟏

�(𝟏−𝟐.𝟐𝟓𝒙𝟏𝟎𝟖𝒎/𝒔𝟑.𝟎𝟎𝒙𝟏𝟎𝟖𝒎/𝒔

)

, γ = ______________________

f. 𝑻𝒔 = 𝟐𝝅� (𝟒.𝟓𝒙𝟏𝟎−𝟐𝒌𝒈)(𝟐.𝟎𝒙𝟏𝟎𝟑𝒌𝒈/𝒔𝟐)

, Ts = ______________________

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Part 3 – Unit Conversions

Science uses the KMS system (have you heard of SI: System Internationale??). KMS stands for kilogram, meters, seconds. These are the units of choice in physics. Each equation depends on these unit agreements, sooooooooooo…. YOU MUST(!!!) convert to KMS in most problems to arrive at the correct answer.

What happens if I don’t know a conversion factor? Colleges (and most employers) want students who can find their own information, sooooooooooooooo…take a hint and look it up yourself!!! A good dictionary might have it in say the “measure” or “measurement” section, or the Internet is useful from time to time…Enjoy!

(1 point for each correct conversion)

a. 0.77 m = _______________ cm

b. 298 K = _______________°C

c. 6.23x10-7m = ________________ nm

d. 1.5x1011g = ________________kg

e. 25.0 μs = _________________ s

f. 823 mL = __________________m3

g. 1.2 atm = __________________Pa

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Part 4 – Geometry

Solve the following geometric problems (1 point for each problem)

a. Line B touches the circle at a single point. Line A extends through the center of the circle. i. What is line B in reference to the circle (what kind of line is it)? ________________

ii. How large is the angle between lines A and B? ________________

b. In the triangle what is angle C?

c. What is angle θ?

d. How large is θ?

e. The radius of a circle is 5.5 cm.

i. What is the circumference in meters?

ii. What is the area in square meters?

f. What is the area under the curve at the right?

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Part 5 – Trigonometry

Using the generic triangle in the upper right, Right Triangle Trigonometry and Pythagorean Theorem solve the following (if you use a calculator make sure you are in degree mode). (1 point for each correct problem)

a. Θ = 55° and c = 32 m, solve for a and b. b. Θ = 45° and a = 15 m/s, solve for b and c. c. b = 17.8 m and Θ = 65°, solve for a and c. d. a = 250 m and b = 180 m, solve for θ and c. e. a = 25 cm and c = 32 cm, solve for θ and b. f. b = 104 cm and c = 65 cm, solve for a and θ.

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Part 6 - Vectors

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(1 point for each correct answer/drawing)

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(1 point for each correct answer)

See you in the fall!

~ Mr.T