You drop a 1.80 kg book to a friend who stands on the ground at distance D = 15.
ID: 1442721 • Letter: Y
Question
You drop a 1.80 kg book to a friend who stands on the ground at distance D = 15.0 m below. If your friend's outstretched hands are at distance d = 1.80 m above the ground (see the figure), (a) how much work Wg does the gravitational force do on the book as it drops to her hands? (b) What is the change U in the gravitational potential energy of the book-Earth system during the drop? If the gravitational potential energy U of that system is taken to be zero at ground level, what is U (c) when the book is released and (d) when it reaches her hands? Now take U to be 100 J at ground level and again find (e) Wg, (f ) U, (g) U at the release point, and (h) U at her hands.
Explanation / Answer
a) Wg = m*g*(D-d)
= 1.8*9.8*(15-1.8)
= 232.8 J
b) delta_U = -Wg
= -232.8 J
c) Ui = m*g*D
= 1.8*9.8*15
= 264.6 J
d) Uf = m*g*d
= 1.8*9.8*1.8
= 31.8 J
e)
Wg = m*g*(D-d)
= 1.8*9.8*(15-1.8)
= 232.8 J
delta_U = -Wg
= -232.8 J
Ui = 100 + m*g*D
= 100 + 1.8*9.8*15
= 364.6 J
Uf = 100 + m*g*d
= 100 + 1.8*9.8*1.8
= 131.8 J
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