AP Free Response Question
2010 C2
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A bowling ball of mass 6.0 kg is released from rest from the top of a slanted roof that is 4.0 meters long and angled at 30º, as shown above. The ball rolls along the roof without slipping. The rotational inertia of a sphere of mass M and radius R about its center of mass is
.
(a) On the figure below, draw and label the forces (not components) acting on the ball at their points of application as it rolls along the roof.
(b) Calculate the force due to friction acting on the ball as it rolls along the roof. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).
(c) Calculate the linear speed of the center of mass of the ball when it reaches the bottom edge of the roof.
(d) A wagon containing a box is at rest on the ground below the roof so that the ball falls a vertical distance of 3.0 meters and lands and sticks in the center of the box. The total mass of the wagon and the box is 12 kg. Calculate the horizontal speed of the wagon immediately after the ball lands in it.
Topic Formulas
Description
Published Formula
angular displacement
angular momentum
angular velocity
center of mass
centripetal acceleration
elastic potential energy
friction
gravitational force (vector)
gravitational potential energy
gravitational potential energy
Hooke's Law
impulse
impulse
kinetic energy
linear momentum
linear velocity and angular velocity
moment of inertia
net torque
Newton's 2nd Law
Newton's Law of Universal Gravitation
period and frequency
period of a simple pendulum
period of a spring
potential energy
power
power
power (dot product)
rate of change of momentum
rate of change of work
rotational kinetic energy
torque
torque
uniform acceleration - displacement and instantaneous velocity
uniform acceleration - instantaneous position
uniform acceleration - instantaneous velocity
work
work (dot product)
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Properties of Friction
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Rolling and Slipping
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