In Fig. 8-35, a small block of mass m = 0.048 kg canslide along the frictionless

Question

In Fig. 8-35, a small block of mass m = 0.048 kg canslide along the frictionless loop-the-loop, with loop radiusR = 11 cm. The block is released from rest at pointP, at height h = 9R above the bottom ofthe loop. How much work does the gravitational force do on theblock as the block travels from point P to(a) point Q and (b) thetop of the loop? If the gravitational potential energy of theblock-Earth system is taken to be zero at the bottom of the loop,what is that potential energy when the block is(c) at point P, (d) atpoint Q, and (e) at the top of theloop?

Fig. 8-35
Problem 8.

Explanation / Answer

How much work does the gravitational force do on the block asthe block travels from point P to (a)point Q W= Pe max - PeQ = mgh - mgR =11mgR - mgR W= 10mgR and (b) the top of the loop? similarly W= Pe max - Pe2R = 11mgR -2mgR W= 9 mgR If the gravitational potential energy of the block-Earthsystem is taken to be zero at the bottom of the loop, what is thatpotential energy when the block is (c) at point P,   Pe max= Pe P = mgh=11mgR (d) at point Q, and Pe Q = mgR= mgR (e) at the top of the loop? Pe top = 2mgR Just plug and play.

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