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Question

Does the Earth do any work on the Moon as the Moon moves in its orbit?

Solution

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If the net work done on a particle is zero, the forces acting on it are balanced, meaning that the net force exerted on the particle is also zero. Applying Newton's Second Law gives

Fnet=ma=0\begin{aligned} \vec{F}_{\text{net}}=m\vec{a}=0 \end{aligned}

a=0\boxed{\vec{a}=0}

Since the particle doesn't accelerate, there is no change in the magnitude or direction of its velocity, i.e., the particle moves at a constant speed,

v=const.\boxed{v=\text{const.}}

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