Question

An escalator is moving down with the constant speed and a person on it moves such that he remains at rest with respect to ground. Choose correct statements with respect to ground frame.

• A. Work done by person is zero
• B. Work done by escalator on the person is zero
• C. Work done by gravity on person is zero
• D. Work done by escalator on person is negative

Answer 1

Answer: (B), (C)

Work done by escalator on the person is zero, Work done by gravity on person is zero

Answer 2

Since the person remains at rest with respect to the ground, their displacement relative to the ground is zero. Work done is given by $W = \vec{F} \cdot \Delta \vec{r}$. If the displacement $\Delta \vec{r}$ is zero, then the work done by any force (escalator, gravity, etc.) on the person is zero.

For the person to be at rest with respect to the ground while on a moving escalator, they must be moving relative to the escalator. Specifically, they must be walking up the escalator at a speed equal to the escalator's downward speed. This means the person exerts a force on the escalator steps in the direction of motion of the escalator, thus doing positive work on the escalator. Therefore, the work done by the person is not zero.