AP Physics 1 Summer Assignment DUE THE FOURTH DAY OF SCHOOL- 2018 Purpose: The purpose of this packet is to make sure that we all have a common starting point and understanding of some of the basic concepts that are used throughout physics. Some of the exercises in the packet will seem very simple (this is good!), some more complicated (ok!) and others totally foreign (still ok!). I am not asking you to learn all of the mathematics or concepts that you will need for this course over the summer. What I am trying to do is to make sure you are familiar with some of them and that I can quickly evaluate your strengths and weaknesses in these areas. Mathematics is the language of the sciences and in no other discipline is mathematics integrated more than in physics. (Sir Isaac Newton created calculus to better explain physics). So I think it is a good idea that we all have a common understanding of some basic math. Algebra, geometry, and trigonometry are the required subjects for this course, but we will use and refer to calculus occasionally. Scientific Notation and Converting Directions: Find the following. Final answers should be in scientific notation. 1.) (5.0 10-8 )(2.9 10 2 ) 2.) 3.25 10 4 + 7.4 10 3 3.) 6.000 10-111.00 10 26 2.00 10 7 4.) ( ) 8400 1.2 10 7 Unit Conversions Review 5.) Finish the SI prefix table below. Follow the example of the centi- prefix. You will need to memorize these. Symbol Name Numerical Equivalent n m c centi 10-2 k M G 6.) 16.7 kilograms is how many grams? 7.) 560 nm is how many meters? 8.) 15 years is how many seconds? 9.) 8.99 10 9 seconds is how many years? 10.) 2.998 10 8 m/s is how many kilometers per hour?
Trigonometry Review Directions: Use the figure below. Simplify as much as you can. a b c 11.) Find c if given a and b. 12.) Find a if given b and c. 13.) Find a if given c and. 14.) Find b if given a and. 15.) Find c if given b and. 16.) Find if given b and c. 17.) Find if given a and b. 18.) If a = 2.0 and c = 7.0, what is b? 19.) If c = 10.0 and = 60, what is b? 20.) If a = 12.0 and = 30, what is b? 21.) Using the properties of triangles, prove that A C in the drawing below. Answer: 22.) For what angles (in degrees) does sin? Describe why mathematically.
Algebra Review Directions: Solve the following equations for the given variable and conditions. Simplify if needed. Example: 2x + xy = z. Solve for x. x(2 + y) = z x = z 2 + y 23.) v + v = 1 2 0. Solve for v1. 24.) a = v. Solve for t. t 25.) v 2 f = v 2 i + 2ad A.) Solve for vi. B.) Solve for d. 26.) d f = d i + v o t + 1 2 at 2 A.) Solve for vo. B.) Solve for t, if vo = 0. C.) Solve for t, if di = df. 27.) F = m v f - v i t f - t i A.) Solve for vf, if ti = 0. B.) Solve for tf, if vf = 0 and ti = 0. 28.) a c = v 2 r. Solve for v. 29.) mgsinq = mmgcosq. Solve for θ. 30.) 1 2 mv f 2 + mgh f = 1 2 mv i 2 + mgh i A.) Solve for hf, if hi = 0 and vf = 0. B.) Solve for vf, if hf = 0.
31.) F g = G m 1m 2 r 2. Solve for r. 32.) L - Lcosq = v2 2 Solve for L. 33.) mv 2 R = G Mm R. Solve for v. 2 34.) T = 2p L. Solve for g. g Systems of equations Use the equations in each problem to solve for the specified variable in the given terms. Simplify. 35.) F f = mf N and F N = mgcosq. Solve for in terms of Ff, m, g, and. 36.) F 1 + F 2 = F T and F 1 d 1 = F 2 d 2. Solve for F1 in terms of FT, d1, and d2. 37.) F c = ma c and a c = v 2. Solve for r in terms of Fc, m, and v. r 38.) T = 2p L g and T = 1. Solve for L in terms of, g, and f. f
Marbles in Cylinder Lab You received a graduated cylinder with three identical marbles and an unknown amount of water already in it. You placed extra identical marbles in the cylinder and obtained the data below. Use the data to graph a best-fit line showing the relationship between the water level and the number of marbles. The y-intercept should be visible on the graph. Label your axes and include units. 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 the slope and y-intercept of your formula. 58.) Graph below Number of Marbles Water level (ml) in Water 3 58 4 61 5 63 6 65 7 68 49.) Formula: 50.) Explanation of the formula in words: (Include the meaning of the slope and y- intercept.)
Vectors Many quantities in physics are vectors. This makes proficiency in vectors extremely important. Magnitude: Size or extent. The numerical value. Direction: Alignment or orientation of any position with respect to any other position. Scalars: A physical quantity described by a number and units. Examples: time, mass, and temperature - 90 minutes Vector: A physical quantity described by a number, its units, and a direction. Examples: velocity, acceleration, force 30 m/s, north Distinguish between a scalar or a vector. 1. 263 days until the AP physics exam 2. 300 students in the graduating class 3. 95 miles per hour north 4. 6 feet above the ground 5. 6 feet Vectors are often represented by variables with arrows above them or bold letters in books. Ex: A, B, C,...a, b, c,...,,...,,,... Vectors are often represented by arrows and right triangle trigonometry is used to resolve the vectors from their components. This arrow represents a vector. Let s call it. How far does vector How far does vector move to the right? move up? The part of vector that moves in the horizontal direction is its x component, x. The part of vector that moves in the vertical direction is its y component, y. Using trigonometry, find the length of and the angle it is above the + x-axis.
In the previous example we resolved a vector from its components. It s your turn to practice. 1. Find the length of and its angle below the x- axis. 2. A vector has the following components: 9 m east and 30 m south. Find the resultant displacement vector and the angle measured from the positive x axis. You can also work the opposite way to find the components of a vector if you are given its magnitude (length) and direction (angle). Find the components of vector Q = 13 m at 45 degrees above the + x-axis. (It s always a good idea to draw a sketch of the vector to make sure that you have the components in the proper direction to make sure you label them with the proper sign + or -) Qx = 13 cos 45 = 9.2 m Q 45º Qy Qy = 13 sin 45 = 9.2 m Qx
Practice: Find the x & y components of the following vectors. 1. Vector V = 55 m at 30 degrees below the x-axis. 2. Vector Z = 40 m/s at 70 degrees above the + x- axis. Here is the Greek alphabet. You should learn it because many symbols in physics are represented by them. Also, if you plan to join a fraternity or sorority you will need to learn them. Take a look at this packet over the summer when you are extremely bored or there is bad weather. I do not want you to concern yourself with it right now~! I would rather you wait until the day before school starts and do it then. Enjoy your summer, and I look forward to teaching you next year. Capital Low-case Greek Name English Alpha a Beta b Gamma g Delta d Epsilon e Zeta z Eta h Theta th Iota i Kappa k Lambda l Mu m Nu n Xi x Omicron o Pi p Rho r Sigma s Tau t Upsilon u Phi ph Chi ch Psi ps Omega o Mr. Peppard