Show that a force that does no work must be a velocity-dependent force.
Hint: The force and the velocity should always be perpendicular to each other.
Step1: Let no work is done by a force, so we have,
dW = F.dl = 0
F.vdt = 0 (Since. dl = vdt and dt 0)
F.v = 0
Step 2: Thus, F must be velocity dependent which implies that angle between F and v is 90. If v changes (direction), then (directions) F should also change so that the above condition is satisfied.
