Celebration #2: Energy, Momentum, and Rotations

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Joy Marsh
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1 Physics 4A Fall 2013 Name Lab Celebration #2: Energy, Momentum, and Rotations Multiple Choice Questions (2 points each) 1) An object is rotating counter-clockwise in a circular path with increasing speed. Its total acceleration at the top of the path points: a) toward the center of the circular path (vector 1) b) in a direction tangent to the circular path (vector 2) c) outward (vector 3) d) none of the above 2) A cart on an air track is moving at 0.5 m/s when the air is suddenly turned off. The cart comes to rest after traveling 1 m. The experiment is repeated, but now the cart is moving at 1 m/s when the air is turned off. How far does the cart travel before coming to rest? a) 1 m b) 2 m c) 3 m d) 4 m e) 5 m 3) Two cylinders of the same size and mass roll down an incline. Cylinder A has most of its weight concentrated at the rim, while cylinder B has most of its weight concentrated at the center. Which reaches the bottom of the incline first? a) Cylinder A b) Cylinder B c) They tie 4) Car One is traveling due north and Car Two is traveling due east. After the collision shown, Car One rebounds due south. Which of the numbered arrows is the only one that can represent the final direction of Car Two? a) 1 b) 2 c) 3 d) 4 e) 5

2 Short Answer Questions (4 points each) 1) When an object s kinetic energy is increasing, must its potential energy be decreasing? Explain your answer. 2) When walking on a balance beam, it is easier to balance yourself with your arms outstretched. Why? 3) You are going to knock over a gigantic bowling pin at a fair by throwing a ball at it. You have a choice between two balls, one that collides elastically and another that collides inelastically. Which do you choose and why?

3 4) As a spherical shell rolls smoothly across a level surface, it has both translational kinetic energy and rotational kinetic energy. What percentage of the shell s total kinetic energy is rotational kinetic energy? 5) At the instant a 2.50 kg object is at position r = (3.50 m) iˆ (2.00 m) kˆ, it is subject to a force F = (7.25 N) ˆj+ (4.00 N) kˆ. What is the torque on the object from this force?

Problems (12 points each) 1) In the figure below, a roller coaster crosses the first hill of height h = 85 m with a speed v = 15.0 m/s. Ignore air resistance and any other frictional forces.

4 Problems (12 points each) 1) In the figure below, a roller coaster crosses the first hill of height h = 85 m with a speed v = 15.0 m/s. Ignore air resistance and any other frictional forces. a) What is the speed of the coaster at point A? b) At what height will the speed of the coaster be 31.0 m/s? c) How high will the coaster go on the last hill (beyond point B), which is too high for it to cross? d) Would your answer to part b increase, decrease, or remain the same if we did not ignore frictional forces? Explain your answer.

5 2) A collision occurs between a 2.00 kg particle traveling with velocity v ˆ ˆ 1 = ( 4.00 m/ s) i (5.00 m/ s) j and a 4.00 kg particle whose initial velocity is not known. After the collision, the two particles are observed to stick together and move off with a velocity of v = (2.67 m/ s) iˆ (3.00 m/ s) ˆj. What is the initial speed of the 4.00 kg particle? f

3) A square metal plate 0.180 m on each side is pivoted about an axis through point O at its center and perpendicular to the plate (see the figure below).

6 3) A square metal plate m on each side is pivoted about an axis through point O at its center and perpendicular to the plate (see the figure below). The square plate has a rotational inertia of kg m 2 about this axis. The magnitudes of the three forces acting on the plate are F 1 = 18.0 N, F 2 = 26.0 N, and F 3 = 14.0 N. a) Calculate the magnitude of the net torque about point O. Note: if you could not get part a, assume a net torque of 3.0 N m to answer parts b and c. b) Assuming that the metal plate is initially at rest and that the net torque on the plate does not change as it rotates, through how many revolutions will the plate have turned when it reaches an angular speed of 25.0 rad/s? c) What is the magnitude of the total acceleration of a point on a corner of the plate when it is rotating at 25.0 rad/s?

7 4) A 0.50 kg ball is dropped from rest from a height of 2.00 m above a wooden floor. The ball bounces off the floor and rebounds to a height of 1.50 m. a) What is the speed of the ball immediately before and immediately after impact with the floor? b) What is the magnitude and direction of the impulse exerted by the floor on the ball? c) If the ball is in contact with the floor for 10 ms, what is the magnitude and direction of the average force that the floor exerts on the ball?

5) The figure below shows two masses, M 1 = 2.50 kg and M 2 = 3.25 kg, connected by a massless rope that passes over a pulley (disk) of mass M = 2.0 kg and radius R = 15 cm.

8 5) The figure below shows two masses, M 1 = 2.50 kg and M 2 = 3.25 kg, connected by a massless rope that passes over a pulley (disk) of mass M = 2.0 kg and radius R = 15 cm. The coefficient of kinetic friction between the horizontal surface and mass M 1 is μ k = 0.35; mass M 2 hangs freely. When the system is released from rest, what are (a) the acceleration of each mass, (b) the tension in the horizontal section of rope, and (c) the tension in the vertical section of rope?

9 6) A bullet with a mass of 65 g is traveling horizontally at 325 m/s when it hits a 2.50 kg wooden block that is initially at rest. The bullet becomes imbedded in the block and together they slide across the floor. If the coefficient of kinetic friction between the block and the floor is 0.45, how far will the block (and bullet) slide before coming to rest?

F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26

F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26 Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,