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Question
Show that a force that does no work must be a velocity dependent force.
Solution
To show that a force that does no work must be a velocity-dependent force, then we have to assume that work done by force is zero. As shown by the equation below:
`dW = vecF * vec(dl) = 0`
We can write, `vec(dl) = vecv dl`, but `dt ≠ 0`
⇒ `vecF * vecv dt = 0`
⇒ `vecF * vecv = 0`
So we can say that force F must be velocity dependent, this implies that angle between F and v is 90°. If the direction of velocity changes, then direction of force will also change.
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