Question

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

Answer 1

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.