Question

What is the power required to give a body of a
mass 'm' a forward acceleration 'a' when it is
moving with velocity 'V' up a frictionless track
inclined at an angle 'O' to the horizontal?​

Answer 1

Answer:

Power = Work done / time = Force x velocity

The track is frictionless, so no frictional force acts on the mass.

If the track was horizontal, the power required to give the mass m a forward acceleration a when it is moving with velocity v is given by

Power = Force x velocity = (ma) x v = mav

But in this case, the track is inclined at an angle O to the horizontal. The component of the weight of the mass (against motion) along the track is mg sin O. Therefore, a force is required to keep the mass stationary (from moving down along the inclined track). This force should be equal in magnitude to the component of the weight so that the resultant acceleration (when considering only the component of the weight and this force) is zero.

This force would result in a power of mg sin O x v = mgv sin O.

So total power = mav + mgv sinO