Question

A particle of mass m moves under the influence of the force f= a (sin wt b + cos t

Answer 1

Keeping in view that; a particle of mass m moves under the influence of force F =a( sinwt i^ +coswt j^) where a ,w are constants and t is time . the particle is initially at rest atthe origin .

The instantaneous power given to the particle is zero.

F = ma

F/m = a

integral adt = v

F/m = a/m (sinwt i^ +coswt j^)

integrate to obtain v

v = a/wm (-coswt i^ +sinwt j^)

Power = F.v

=a( sinwt i^ +coswt j^) .a/wm (-coswt i^ +sinwt j^)

= (a^2/wm)(-sinwtcoswt+coswtsinwt) = 0