Dr. Galeazzi PHY205 Final Exam December 12, I.D. number:

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1 Signature: I.D. number: Name: 1 You must do the first two problems which consists of five multiple choice questions each. Then you must do four of the five long problems numbered 3-7. Clearly cross out the page and the numbered box of the problem omitted. Do not write in the other boxes. If you do all the problems, only problems 1-6 will be graded. Each problem is worth 25 points for a total of 150 points. TO GET CREDIT IN PROBLEMS 3 7 YOU MUST SHOW GOOD WORK CHECK DISCUSSION SECTION ATTENDED: [ ] Dr. Ghandour 1O, 9:30 10:20 a.m. [ ] Dr. Ghandour 1P, 11:00 11:50 a.m. [ ] Dr. Zuo 1Q, 12:30 1:20 p.m. [ ] Dr. Mariano 1R, 2:00 2:50 p.m. [ ] Dr. Mariano 1S, 3:30 4:20 p.m. [ ] Dr. Cohn 1T, 5:00 5:50 p.m. [ ] Dr. Zuo 2O, 9:30 10:20 a.m. [ ] Dr. Cohn 2Q, 12:30 1:20 p.m. [ ] Dr. Nepomechie 2T, 5:00 5:50 p.m TOTAL THE EQUATION SHEET IS PROVIDED ON THE LAST PAGE WHICH YOU CAN TEAR OFF. 1

2 [1.] This problem has five multiple choice questions. Circle the best answer in each case. [1A.] The motion of an airplane leaving from Miami can be described using a Cartesian coordinate system with due East coincident with the positive x-direction and due North with the positive y-direction. The position of the plane as a function of time can then be written as At what positive time is the airplane s velocity exactly in the North-East direction? [a] t = 0 s [b] t = 2 s [c] t = 4 s [d] t = 12 s [e] t = 12 s [1B.] A mass M is at rest, attached to a vertical spring with constant k. How stretched is the spring? [a] [b] [c] [d] [e] [1C.] A solid cylinder with moment of inertia, a hollow cylinder with moment of inertia and a solid sphere with moment of inertia all have a uniform density, the same mass and the same radius. They are placed at the top of an inclined plane and allowed to roll down the inclined plane without slipping. Rank them in order of total kinetic energy at the bottom of the incline, from higher to lower. [a] sphere(1st), hollow cylinder(2nd), solid cylinder(3rd) [b] sphere(1st), solid cylinder(2nd), hollow cylinder(3rd) [c] hollow cylinder(1st), sphere(2nd), solid cylinder(3rd) [d] hollow cylinder(1st), solid cylinder(2nd), sphere(3rd) [e] they all have the same kinetic energy [1D.] In the figure shown, both pulleys are massless. What must be the magnitude of the static friction force on mass for the masses to be in equilibrium? [a] [c] [e] [b] [d] 2 [1E.] Adam ( 80 ) and Barbara ( 60 ) are initially together at rest on an ice rink. When they push each other part, Adam moves with velocity 3 9. Assuming that there is no friction from the ice, what is Barbara s velocity? [a] 4 12 [b] 4 12 [c] [d] 3 9 [e]

3 3

4 [2.] This problem has five multiple choice questions. Circle the best answer in each case. [2A.] A disk is accelerated from rest with constant angular acceleration. The disk completes the first full revolution in 1 s. What is the value of the angular acceleration of the disk? [a] 1 [b] [c] 2 [d] 4 [e] 2 [2B.] If 3 4 and 2 3, find. [a] [b] 17 [c] 1 [d] 1 [e] 6 12 [2C.] A uniform, horizontal meter stick with length L and mass M is attached at one end to a pivot point P. What must be the magnitude of the vertical force applied to the other end of the stick to prevent it from moving? [a] 2 [b] 2 [c] [d] [e] 2 [2D.] A satellite with mass M is flying on a circular orbit with linear speed. What is the total energy of the satellite (assume that the gravitational potential energy is zero at infinity). [a] [b] [c] [d] [e] [2E.] A disk with radius R has mass per unit area that depends on the radius as for 0, with positive and constant. What is the mass of the disk? [a] [b] [c] [d] ln [e] 2 4

5 5

6 [3.] A non-ideal spring, when compressed or extended, exerts a force equal to:, where is the spring constant. Such non-ideal spring is placed vertically and compressed a distance L. A mass M is placed on the spring which is then released. Assume the spring is strong enough to push the mass in the air. a) Find the work done by the spring to get back to the uncompressed position when it is released. b) Find the speed of the mass M when the spring is back to its uncompressed length. (hint: the spring s is not the only force) c) Is the force of this non-ideal spring conservative? Explain. Express you answer in terms of, L, M, and g. Check the units/dimensions for each answer

7 7

8 [4.] A block with mass is attached to a massless string which is wrapped around a flywheel with mass M, radius R, and moment of inertia with respect to the center of mass (see figure). The string pulls without slipping on the flywheel as the block moves down vertically. a) Find the acceleration of the block (vector). b) Find the magnitude of the tension in the string. c) Find the time it takes the block to move a distance L (assume it starts from rest). Write your results in terms of, M, R, L, and g. Check the units/dimensions for each answer

9 9

10 [5.] A point particle with mass M moves along a straight line under the influence of a net force that is a function of time, given by:, where is positive and constant. a) If the particle starts from rest, find how long it will take it to cover a distance L. b) Find the speed of the particle after it has traveled a distance L. c) Find the work done on the particle by the net force over the distance L. Write your result in terms of M,, and L. Check the units/dimensions of each answer

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12 [6.] Two masses, and are placed in deep space and their position is fixed as shown in the figure. a) Find the net force on mass. b) Find the net force on mass. c) Find the potential energy of the two masses (assume that the potential energy is zero at infinity). Write your result in terms of,, a, b, and G. Check the units/dimensions of each answer

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14 [7.] A cylinder with mass m, radius a, and moment of inertia with respect to the center of mass, rolls without slipping around a loop with radius R as shown in the figure. a) What is the minimum speed of the center of mass at point C ( ) for the cylinder to move around the loop without falling off? b) What is the total kinetic energy of the cylinder at point C in the case of minimum speed? c) What is the minimum speed of the center of mass necessary at point B ( ) for the cylinder to move around the loop without falling off at the top (point C)? Write your results in terms of a, R, m, and g. Check the units/dimensions for each answer

15 15

16 EQUATION SHEET (Make sure to start all problems from these equations) Vectors: 2D:, ; tan ; cos, sin. cos ; sin + R.H.R. for direction Linear motion: Relative velocity: Newton s Laws: Examples of forces: ; ; ; ; ; / / / ; / / 0 0; ; gravity: ; ; spring: ; friction:, 0, Work: ; ; Power: Work-Energy Theorem: ; conservative forces: in general: or ΔΔ examples: Momentum and impulse: Center of mass: Circular Motion: Uniform circular motion: ; ; ; ; ; ; ; ; Non-uniform circular motion: ; Rolling without slipping: Moment of inertia:, or ; Torque: Angular momentum:, or Work and energy: Periodic motion: ; ; ; 2; SHM: cos ; cos 16

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