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Show that a force that does no work must...

Show that a force that does no work must be a velocity dependent force.

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To show that a force that does no work must be a velocity-dependent force, we can follow these steps: ### Step 1: Understand the Work Done by a Force The work done \( W \) by a force \( \mathbf{F} \) acting on an object that moves through a displacement \( \mathbf{d} \) is given by the equation: \[ W = \mathbf{F} \cdot \mathbf{d} \] This can also be expressed in terms of the velocity \( \mathbf{v} \) and time \( dt \): ...
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