/5)MR2s. You are building a display for a children\'s science museum in which a

Question

/5)MR2s. You are building a display for a children's science museum in which a uniform, solid sphere of radius 0.078 m starts at rest at the top of a ''hill'' and rolls, without slipping, down a track and around a loop-the-loop of radius R = 1.3 m. You have already determined that the ball has to be moving at a speed no less than 3.46 m/s at the top of the loop in order to make it around the loop without falling. What is the minimum height of the ''hill'' in order to ensure that this happens? Note: The moment of inertia of a uniform, solid sphere (mass M and radius R s) about its center is (2

Explanation / Answer

1/2v^2 (bottom) x (mass + (Inertia/radius^2)) = mgh (PE)

But lets leave above.

Using the basis of 2/5mr^2 = solid ball inertia, then 0.7v^2 = gh (simplified)

Velocity top = 3.46 m/s

velocity at bottom = 0.7v^2 top + gh = 0.7 x 3.46^2 + (9.8 x 2.6) = 33.860

33.860/0.7 = v^2 = 48.371, sq-root = v = 6.954 m/s (bottom)

0.7v^2 = gh



33.860/g = h

33.860/9.8 = 3.455 m (answer)

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