Physics 218 (Mechanics)Final ExamDecember 10, 2008Please print neatly in ink.Family Name:First Name:Student ID Number:Your Section Number:Signature:IMPORTANT• You have 120 minutes to complete 8 problems totaling 200 points. Make sure you have allthe pages. Work each problem on the page the problem is on. You may use the back of thesheet it is written on, if needed, but indicate it in the front side.• Formulas are provided on a separate sheet at the end of this exam paper. You may use acalculator.• Mark your answers clearly by drawing boxes around them. Write the procedure to solvethe problem.• You may use a pencil from this page.[1] Answer the following questions. Write your answer only in the box. (There is NO partialcredit for this problem.)(a) [ 3 points]Write 1 N (Newton; the unit of force) in terms of kg, m, and s.(b) [3 points] A transverse wave on a string is represented by the wave function y(x, t) =A sin(kx + ωt), where k and ω are positive. Which one of the following statementsabout this wave is correct?(A) This wave is propagating toward +x direction.(B) This wave is propagating toward −x direction.(C) This wave is a standing wave.(D) The above information is not enough to determine the direction of the wave motion.(c) [3 points] Consider the gravity exerted on the earth by the sun and moon. They arealigned on a straight line.Case(I): The system is aligned in the order of Sun-Earth-Moon.Case(II): The system is aligned in the order of Sun-Moon-Earth.The distance between the sun and the earth is R1and that between the earth and themoon is R2. The values of R1and R2do not change in both cases. The gravityexerted on the earth is F1for Case(I) and F2for Case(II). Which one of the followingstatements is correct?(A) F1/F2is larger than 1.(B) F1/F2is smaller than 1.(C) F1/F2equals to 1.(D) F1/F2equals to 0.(E) The given information is not enough to know the ratio of F1/F2.(d) [4 points] Write the two conditions for a rigid body to be in equilibrium.1(e) [3 points] Which of the following situations is impossible?(A) An object has constant nonzero acceleration and changing velocity.(B) An object has constant velocity directed east and acceleration directed west.(C) An object has velocity directed east and acceleration directed north.(D) An object has constant nonzero velocity and changing acceleration.(E) An object has zero velocity but nonzero acceleration.(f) [3 points] Which of the following is an accurate statement for a motion of a rigid body?(A) All points on a rotating disk have the same angular velocity.(B) The vector sum of the tangential acceleration and the centripetal acceleration canbe zero for a point on a rotating disk.(C) All points on a rotating disk experience the same radial acceleration.(D) All points on a rotating disk have the same linear speed.(E) None of the above(g) [3 points] Which, if any, of the following statements concerning the work done by aconservative force is NOT true?(A) It is reversible.(B) It can always be expressed as the difference between the initial and final values ofa potential energy function.(C) When the starting and ending points are the same, the total work is zero.(D) It is independent of the path of the body and depends only on the starting andending points.(E) Its time derivative gives the force as a function of time.(h) [3 points] When is the angular momentum of a system constant?(A) when no torque acts on the system(B) when the moment of inertia is constant(C) when no net external force acts on the system(D) when the total kinetic energy is constant(E) when the linear momentum and the energy are constant2[2] A skier is sliding on a slope. He starts from rest at the height of H. Then he passes ahorizontal region of height h and falls to the ground. Obtain the horizontal distance R.Neglect any friction force in this motion. The gravitational acceleration is g. [25 points]3[3] A conical pendulum is made of a pendulum bob with mass m at the end of a thin wire oflength L. The bob moves in a horizontal circle with constant speed, with the wire makinga constant angle β with the vertical direction. Therefore, the angle β is constant. Findthe tension F in the wire and the period T in terms of given quantities. The gravitationalacceleration constant is g. (Hint: Draw free-body diagram for the bob and use the formulasfor circular motion given in the formula sheet.) [25 points](R is defined in the figure only to help you analyze the problem. Do not use R in your finalanswer.)4[4] Consider an elastic collision in an isolated 1-dimensional space. The body A has mass mAand is moving with velocity v1. The body B of mass mBis at rest. After the collision, Ahas velocity vAand the velocity of B is vB. Express vAand vBin terms of the two massesand v1. [25 points]5[5] There is a wheel of radius R and mass M. This wheel is released from rest at point A on a30◦incline as shown in the figure. The wheel rolls without slipping and moves L to pointB in time T . In this motion, the acceleration of the center of mass of the wheel is constant.The gravitational acceleration is g. (Use the formula sheet for trigonometric functions.)(a) [10 points] Show that the angular speed of the wheel at B is ω =2LRT. (Hint: Usethat the acceleration of its center of mass is constant. Then you have a one-dimensionmotion for the CM of the wheel and you can express the linear acceleration in terms ofL and T .)(b) [15 points] Use energy consideration, find the moment of inertia of the wheel in termsof M, R, L, T and g. (You may use the result of (a) even if you fail to prove it. Youdo not know the structure of the wheel, so you cannot calculate the moment of inertiaof the wheel from its definition.)6[6] There are two satellites of mass m1and m2moving around the earth. The circular orbitof m1has radius R1and that of m2has radius R2. The mass of the earth is MEand thegravitational constant is G.(a) [10 points] Obtain the total energy of the satellite m1in terms of given quantities.(b) [7 points] The satellite of mass m1has the orbital period T1and the satellite of massm2has the orbital period T2. If R2/R1= 4 and m2/m1= 2, what is the ratio ofT2/T1?(c) [8 points] The satellite of mass m1is going to escape from the earth. How muchadditional work should be done to make this satellite escape from the earth?7[7] A block of mass m1is attached to a horizontal spring with force constant k. The block ismoving with simple harmonic motion having amplitude A1so that the