You drop a 2.30 kg book to a friend who stands on the ground at distance D = 13.

Question

You drop a 2.30 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 = 1.70 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

As given in the question,

m = 2.3 kg, D = 13 m and d = 1.7 m

(a) Work done by the gravitational force do on the book as it drops to her hands,

Wg =  m*g*(D - d)  = (2.3)*(9.8)*(13 - 1.7) = 254.7 J

(b) The change U in the gravitational potential energy of the book-Earth system during the drop,

  U  =  Wg  =  254.7 J

If the gravitational potential energy U of that system is taken to be zero at ground level:

(c) The gravitational potential energy of system when the book is released,

  U  = m*g*D  = (2.3)*(9.8)*(13) = 293.02 J

(d) The gravitational potential energy of system when it reaches her hands,

  U  = m*g*d  = (2.3)*(9.8)*(1.7) = 38.32 J

Now take U to be 100 J at ground level and again repeating the above problems:

(e) Work done by the gravitational force do on the book as it drops to her hands,

  Wg  =  m*g*(D - d)  = (2.3)*(9.8)*(13 - 1.7) = 254.7 J

(f) The change U in the gravitational potential energy of the book-Earth system during the drop,

  U  =  Wg  =  254.7 J

(g) The gravitational potential energy of system when the book is released,

  U  = 100 + m*g*D  = 100 + (2.3)*(9.8)*(13) = 393.02 J

(h) The gravitational potential energy of system when it reaches her hands,

  U  = 100 + m*g*d  = 100 + (2.3)*(9.8)*(1.7) = 138.32 J

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