p08_006.pdf

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Chapter 8 - 8.6
6. We use Eq. 7-12 for W g and Eq. 8-9 for U .
(a) The displacement between the initial point and Q has a vertical component of h
−
R downward
d =4 mgR .
(b) The displacement between the initial point and the top of the loop has a vertical component of
h
−
2 R downward (same direction as F g ), so (with h =5 R )weobtain W g = F g ·
d =3 mgR .
(c) With y = h =5 R , we find U =5 mgR at P .
(d) With y = R , we find U = mgR at Q .
(e) With y =2 R , we find U =2 mgR at the top of the loop.
(f) The newinformation ( v i
= 0) is not involved in any of the preceding computations; the above
results are unchanged.
(same direction as F g ), so (with h =5 R )weobtain W g = F g ·

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