You drop a 2.50 kg book to a friend who stands on the ground at distance D = 13.

Question

You drop a 2.50 kg book to a friend who stands on the ground at distance D = 13.0 m below. If your friend's outstretched hands are at distance d = 1.50 m above the ground (see the figure), how much work W_g does the gravitational force do on the book as it drops to her hands? What is the change Delta 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 when the book is released and when it reaches her hands? Now take U to be 100 J at ground level and again find W_g, Delta U, U at the release point, and U at her hands.

Explanation / Answer

a)
W = m*g*h
= m*g*(D-d)
= 2.5*9.8*(13-1.5)
=281.75 J

b)
delta U = - work done
= -281.75 J

c)
U = m*g*D
= 2.5*9.8*13
=318.5 J

d)
U= m*g*d
= 2.5*9.8*1.5
=36.75 J

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