1. Physics 211 Second Sample Exam Fall 2004 Professors Aaron Dominguez and Gregory Snow Please print your name _______________________________________________________________ (Last name) (First name) Important: Please circle your lecture section: Section 150; 9:30 -- 10:45 am Section 250; 11:00 -- 12:15 pm Please read these instructions carefully before beginning. This is a closed-book exam. You may, however, refer to two 3"  5" cards and you may use a calculator. You may not share either of these. On partial credit problems, you must show your work, and partial credit may be assigned if the work is clear and neat. Multiple choice option: On the multiple choice problems, you may exercise the following option. As usual, if you circle one and only one of the possible answers, you will receive full credit for the problem if your choice is correct. However, you may opt to circle two answers -- if one of these is the correct answer, you will receive half-credit for the problem. Note: If you circle two answers, you forfeit the chance to get full credit for the problem. Possibly useful information:

2. 2 Problem 1 – Partial Credit and Multiple Choice (15 points.) In the system shown, the ropes turn the pulley wheels without slipping, and the pulleys turn on frictionless pivots, but they are massive. Each pulley wheel is a uniform disk of mass 4.0 kg and radius 25.0 cm. The system is released from rest, and mass M = 10.0 kg falls while the two masses m = 2.0 kg rise. A) With what speed is M moving when it has fallen 1.0 meter? (10 points.) Hint: This problem is best worked using conservation of energy. Speed = _______________________________________ m/s. B) Which set of statements relating the tensions T 1, T 2, T 3, T 4 is true? (5 points.) (Circle one answer, or two for the multiple choice option.) a) T 1 = T 2 = T 3 = T 4 b) T 1 > T 2, T 2 = T 3, T 3 < T 4, T 1 = T 4 c) T 1 T 4, T 1 = T 4 d) T 1 > T 2 > T 3 > T 4 e) T 1 < T 2 < T 3 < T 4 f) T 1 = 0, T 2 = T 3, T 4 = 0 M m m T1T1 T2T2 T3T3 T4T4..

3. 3 Problem 2 – Partial Credit (18 points.) 45 o F 20 cm Pivot point A uniform rod of length L = 1.0 m and mass m = 3.0 kg is free to rotate in a horizontal plane about a frictionless pivot point located 20.0 cm from one end, as shown. A horizontal force F = 4.0 N applied to the rod at its center begins to rotate the rod from rest. F is always directed perpendicular to the rod as it turns counterclockwise. A) What is the moment of inertia of the rod about the pivot point? (6 points.) Moment of inertia = _______________________________ kg m 2. B) What is the angular acceleration of the rod? (6 points.) Angular acceleration = _____________________________ rad/s 2. C) Starting from rest, how long does it take the rod to rotate through 45 o ? (6 points.) Time = __________________________________________ s.

4. 4 Problem 3 – Partial Credit (16 points.) vivi m1m1 m1m1 m2m2 m2m2 v top Before After A bullet of mass m 1 = 500.0 g is fired horizontally with an initial speed v i = 30.0 m/s at a block of mass m 2 = 1.0 kg which is suspended from a string of length L = 1.0 m as shown. The two masses stick together after the collision and swing around the pivot point in a vertical circle. A) With what speed are the masses moving when they reach the top of the circle? (10 points.) Speed = ____________________________________ m/s. B) What is the tension in the string in this vertical position? (6 points.) Tension = ___________________________________ N. L

5. 5 Problem 4 – Multiple choice (10 points.) r v cm  Covers distance d A ball of radius r = 40.0 cm rolls without slipping on a horizontal surface with a constant linear speed v cm = 1.50 m/s. A) What is the angular velocity of the ball in radians/second? (3 points.) a) 0.375 b) 0.6 c) 1.5 d) 3.75 e) 6.0 f) 60.0 B) Through how many revolutions has the ball turned when it has traveled a horizontal distance of d = 60.0 meters? (4 points.) a) 15.5 b) 23.9 c) 31.4 d) 40.0 e) 60.0 f) 89.7 C) What is the linear (tangential) speed (in m/s) of the point P when it is at the top of the ball? (3 points.) a) 0.0 b) 0.5 c) 1.0 d) 1.5 e) 2.5 f) 3.0 P (Diagram not to scale)

6. 6 Problems 5 (5 points) and 6 (5 points) – Multiple Choice Problem 5. The block shown (M = 2.0 kg) is released from rest at a position where the spring is compressed a distance of 0.50 m from its relaxed length. The spring constant k = 100.0 N/m. After release, the block slides to the right on the frictionless horizontal surface, detaches from the spring, and flies off the end of the table. With what speed does the block hit the floor, a vertical distance 1.2 m below? (Hint: Using conservation of energy to relate the block's starting and ending positions, this problem can be solved with one line of algebra.) a) 3.5 m/s b) 4.0 m/s c) 5.0 m/s d) 6.0 m/s e) 7.5 m/s f) 10.0 m/s Problem 6. A 2.0 kg mass traveling to the right with speed 4.0 m/s collides head on with a 3.0 kg mass traveling to the left with speed 6.0 m/s. After the collision, the two bodies stick together. The percentage kinetic energy loss in the collision, i.e. (K i – K f )/K i, is a) 53% b) 68% c) 72% d) 86% e) 91% f) 97% relaxed position M M 0.5 m 1.2 m k

7. 7 Problem 7 – Partial Credit (10 points.) Ice Man Sled 10 m A 70 kg man is standing on the extreme left end of a 10 m long, 200 kg “sled” which is free to slide left and right without friction on a frozen pond. He is holding a block of ice with a mass of 30 kg. The man walks to the extreme right end of the sled, sets the block down at the end of the sled, and walks back to his original position. How far (distance and direction) has the sled moved from its original position when the man has returned to the left end? Distance moved = _______________________ m, Direction (left or right) ________________________ Problem 8 – Multiple Choice (5 points.) A ball rotates in a circle of radius 50 cm. It’s angular position , measured with respect to the positive x-axis, is given by the function  (t) = 6t 3 – t 2, where t is in seconds and  is in radians. What is the magnitude of the angular acceleration of the ball (in rad/s 2 ) at time t = 2 seconds? a) 35 b) 44 c) 68 d) 70 e) 72 f) 84

8. 8 Problem 9 – Partial Credit (16 points.) R M m v0v0 m vfvf A m = 10.0 kg block slides on a frictionless table with initial velocity v 0 = 2.0 m/s, approaching a slot in the table where there is a cylinder at rest (mass M = 5.0 kg, radius R = 0.5 m) which is free to rotate about an axis through its center. A) Before the block reaches the slot, what is the angular momentum of the block with respect to the axis through the center of the cylinder? (6 points.) Angular momentum = _______________________________ kg m 2 /s. B) As the block passes over the slot in the table, it comes in contact with the cylinder. There is friction between the cylinder and the block, so the cylinder begins to turn clockwise until the block rolls without slipping across the cylinder. (This means the tangential speed of the rim is the same as the linear speed of the block.) What is the final velocity, v f, of the block after it has passed completely over the slot? (10 points.) Final velocity = ________________________________m/s. END OF EXAM