Question

Show that a force that does not work must be a velocity dependent force

Answer 1

Force doesn't work . Means , work done = 0 by acting of force .
Let force is $\bold{\overrightarrow{F}}$, displacement due to force act on body is $\bold{\overrightarrow{dl}}$ .
So, W = $\bold{\overrightarrow{F}}.\bold{\overrightarrow{dl}}$
we also know, $\overrightarrow{dl}=\overrightarrow{v}.dt$
⇒W = $\overrightarrow{F}\overrightarrow{v}.dt=0$ , but dt ≠ 0
so, $\overrightarrow{F}.\overrightarrow{v}=0$,
It is possible only when Force is perpendicular upon velocity . hence, force is dependent upon velocity. If velocity change the direction then force should be change the direction in such a way that angle is maintained at 90° .