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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.

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