Celebration #2: Energy, Momentum, and Rotations

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Calvin Nickolas Anthony
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1 Physics 4A Fall 2014 Name Lab: morning afternoon Celebration #2: Energy, Momentum, and Rotations Multiple Choice Questions (2 points each) 1) Consider a solid disk with an axis of rotation through the center (perpendicular to the diagram). Two holes are cut out near the center and the material is placed near the rim. Which has the larger I? a) I A > I B c) I A < I B c) I A = I B 2) An object moves in a circle at constant speed. The work done by the centripetal force is zero because: a) the displacement for each revolution is zero b) the average force for each revolution is zero c) there is no friction d) the magnitude of the acceleration is zero e) none of the above 3) In the overhead view of the figure below, five forces of the same magnitude act on a square plate that can rotate about point P, at the center of one of the edges. Which force results in the greatest magnitude torque? a) Force 1 b) Force 2 c) Force 3 d) Force 4 e) Force 5 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) The figure below shows three rocks that are launched from the same level with the same speed. One is launched straight upward, one is launched at an angle, and one is launched along a frictionless incline. Ignoring air resistance, rank the rocks according to their speed when they reach the dashed line, greatest first. 2) Is it possible for a stationary object that is struck by a moving object to have a larger final momentum than the initial momentum of the incoming object? Explain. 3) At the instant a 2.50 kg object is at position r= (2.75 mi ) ˆ (5.50 mk ) ˆ, it is subject to a force F= (4.25 N) ˆj+ (8.00 Nk ) ˆ. What is the torque on the object from this force?

3 4) As a solid sphere 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) The figure below is a graph of the angular velocity versus time for a rotating disk. For a point on the rim of the disk, rank the four instants a, b, c, and d according to the magnitude of (a) the tangential acceleration and (b) the radial acceleration, greatest first.

4 Problems (12 points each) 1) A new event has been proposed for the next Winter Olympics. As seen in the figure below, an athlete will sprint 100 m, starting from rest, then leap on a 20.0 kg bobsled. The person and bobsled will then slide down a 50.0 m long ice-covered (frictionless) ramp, sloped at 20.0, and into a spring with a carefully calibrated spring constant of N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40.0 kg, has been training for this event. She can reach a maximum speed of 12.0 m/s in the 100 m dash. (a) How far will Lisa compress the spring? (b) The Olympic committee has very exact specifications about the shape and angle of the ramp. Is this necessary? What factors about the ramp are important?

5 2) The figure below shows a collision between three balls of clay. The three hit simultaneously and stick together. What is the velocity (magnitude and direction) of the resulting blob of clay?

6 3) Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 12.5 s to speed up from rest to its top angular speed of 1.00 rotation every 1.30 s. Assume the angular acceleration is constant and the astronaut is strapped into a seat 6.0 m from the axis. What is the astronaut s total acceleration (in m/s 2 ) when the centrifuge is rotating at top speed?

7 4) A pendulum consisting of a thin rod with mass M and length L is free to rotate about an axis perpendicular to the page (see the figure below). It is released from rest from a horizontal position. Find the linear speed of a point at the end of the pendulum (opposite the pivot point) when the pendulum is at its lowest point.

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 uniform thin rod of mass g and length 1.00 m is pivoted about its center and initially at rest. A 3.00 g bullet is shot through the rod midway between the pivot and one end (see the figure below). The bullet approaches at m/s and leaves at m/s. With what angular speed is the stick spinning after the collision?

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry