Work done in non-inertial frames

Question

In which of the following cases will the work done by a weightlifter be maximum?

  • Stationary frame
  • Rotating frame
  • Accelerating upwards
  • Accelerating downwards

Solution

In lifting the weight, the weight-lifter will have to work against the net downward force acting on the mass, !!m!! in lifting it through a height !!h!!.

Case a: In the stationary reference frame, the net downward force acting on the mass is !!mg!!. Therefore work done will be

!!W_1 = mg * h!!

Case b: In the rotating frame, the pseudo force is acting horizontally outward and has no contribution in the net vertical force. Therefore, the net downward force is still !!mg!! and the work done in lifting the mass will be

!!W_2 = mg * h!!

Case c: In a lift accelerating upwards, the pseudo force acts downwards. Therefore, the net downward force is !!m * (g+a)!! and the work done will be

!!W_3 = m * (g+a) * h!!

Case d: In a lift accelerating downwards, the pseudo force acts upwards. Therefore, the net downward force is !!m * (g-a)!! and the work done will be

!!W_4 = m * (g-a) * h!!

Therefore, the net downward force is maximum in the case of a lift accelerating upwards, and the weight-lifter will have to do the maximum work in this case.

Get it on Google Play