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You do more work on the empty wheelbarrow, the first case.

The work of a given force on an object equals the product of the force (more precisely, the component of the force in the direction of the motion of the object) and the distance traveled by the object.

In the first case, the force on the empty wheelbarrow, however small, is non-zero, and the distance traveled by the wheelbarrow is non-zero. So the work done is non-zero.

In the second case, the force applied to the wheelbarrow is large, but the wheelbarrow does not move, so it travels zero distance. This means the work, which is force times distance, is zero.

**Therefore, you do more work in the first case.**

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