The document discusses how increasing the speed of a bar from a constant speed v to 2v would affect the applied force and power input. Doubling the speed from v to 2v would double the applied force from Fapp to 2Fapp and quadruple the power input from P to 4P, as power is proportional to the square of velocity. Therefore, the new force and power input would be 2F and 4P.

1. In Figure 31.10, a given applied force of magnitude Fapp results in a constant speed v and a
power input P. Imagine that the force is increased so that the constant speed of the bar is doubled
to 2v. Under these conditions, the new force and the new power input are which of the
following? O 2F and 4P O 4F and 4P O 4F and 4P O 2F and 2P RE s- B b) Figure 31.10
Solution
the equation for for force acting on the rod is
F= m dv/dt
since force depend on the velocity of the bar, if we increase speed , force also doubles
P = Fv = BIL* v
= B^2 l^2 v^2/R
if we increase velocity
Pnew = B^2 l^2 (2v)^2/R
= 4 *B^2 l^2 v^2/R
= 4p
so, first option is correct answer
2F and 4P is the correct answer