A crate is pulled across a horizontal, frictionless floor by a rope. At the same time, the crate pulls back on the rope, in accord with Newton's third law. Does the work done on the crate by the rope then equal zero?

Explanation:

If force F is applied on the crate , it will move with acceleration

a = F / m as no other force is acting on it .

This force is applied on the crate . work done by rope on crate  will be positive and equal to F x d where d is displacement .

The reaction force will apply on hand through rope. So work will also be done on hand by crate . This work will be negative as displacement in hand is opposite to direction of force on it.

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