A 0.29-kg stone is held 1.2 m above the top edge of a water well and then dropped into it. The well has a depth of 4.5 m.(a) Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone−Earth system before the stone is released? J (b) Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone−Earth system when it reaches the bottom of the well? J (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?

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Asked Nov 22, 2019
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A 0.29-kg stone is held 1.2 m above the top edge of a water well and then dropped into it. The well has a depth of 4.5 m.

(a) Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone−Earth system before the stone is released?
J

(b) Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone−Earth system when it reaches the bottom of the well?
J

(c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?
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Expert Answer

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Step 1

Consider a stone(mass m) is held at height h from the surface of the water well and depth of the well is denoted by H.

m 0.29 kg
h 1.2 m
H 4.5 m
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m 0.29 kg h 1.2 m H 4.5 m

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Step 2

(a) Take the reference at the surface of the well. Write the expression of potential energy and plug the suitable values to determine the stone-Earth system potential energy(U1) when it is at height h from the surface of the water level.

U mgh
-(0.29 kg)(9.81 m/s )(1.2 m)
= 3.41 J
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U mgh -(0.29 kg)(9.81 m/s )(1.2 m) = 3.41 J

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Step 3

(b) Similarly, write the expression of potential energy and plug the suitable values to determine the stone-Earth system ...

U, mg (-H)
= (0.29 kg) (9.81 m/s(-4.5 m)
=-12.80 J
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U, mg (-H) = (0.29 kg) (9.81 m/s(-4.5 m) =-12.80 J

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