Question

Sand drops from a stationary hopper At a rate dm/dt onto a conveyor belt moving with velocity v, show that the power required to keep the belt moving at v is 2dk/dt

Answer 1

dm/dt=2                      f=2*0.2=0.4

u=0.2

Answer 2

Since,

dk/dt=1/2m2v.dv/dt.....(i)

And power=f.v

F.ext =-ru

=-(dm/dt)×(-v)

=Vdm/dt

Now ,..

P=F.ext.v...i.e

=Vdm/dt.v

=mdv²/dt

=m2v.dv/dt. .....from (i)

Hence ,

P=2dk/dt