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  • Show that a force that does no Work must be a velocity-dependent force.

Show that a force that does no Work must be a velocity-dependent force.

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To prove that a force with doing no works must be a velocity-dependent force, it is necessary to assume that zero work is done by the force. As given in the following equation:

dW=\overrightarrow{F}.\overrightarrow{dl}=0

We can write \overrightarrow{dl}=\overrightarrow{v}dt, \text{but}dt \neq 0

\Rightarrow \overrightarrow{F}.\overrightarrow{v}dt=0\\ \Rightarrow \overrightarrow{F}.\overrightarrow{v}=0

So, it is proven that the force F is dependent on the velocity, it implies there is a 90° angle between F and v. So if the velocity changes its direction, simultaneously the direction of the force will also change.

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infoexpert24

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