The weight of a person in a lift accelerating upwards

Question

Accepted Answer

When a lift accelerates upwards, the apparent weight of a person inside the lift increases. This phenomenon can be explained using the concepts of physics, specifically Newton's laws of motion and the concept of apparent weight.

1. **Explanation for Option 2 (Correct Answer):**
   - When a lift accelerates upwards, the person inside experiences an additional force due to the acceleration of the lift. The apparent weight of a person is the normal force exerted by the floor of the lift on the person. This normal force is what a weighing scale would measure as the person's weight.
   - The apparent weight can be calculated using the formula: $ W' = m(g + a) $, where $ W' $ is the apparent weight, $ m $ is the mass of the person, $ g $ is the acceleration due to gravity, and $ a $ is the acceleration of the lift.
   - Since the lift is accelerating upwards, $ a $ is positive, which means $ g + a $ is greater than $ g $ alone. Therefore, the apparent weight $ W' $ is greater than the actual weight $ mg $, leading to an increase in the apparent weight.

2. **Explanation for why other options are incorrect:**

- **Option 1 (is zero):**
     - The weight of a person cannot be zero unless the lift is in free fall, which is not the case when it is accelerating upwards. In free fall, the lift and the person inside would be accelerating downwards at the same rate as gravity, making the apparent weight zero. However, this scenario does not apply to an upward-accelerating lift.

- **Option 3 (decreases):**
     - The apparent weight decreases only when the lift is accelerating downwards or if it is moving upwards but decelerating. In the case of upward acceleration, the additional force due to the lift's acceleration adds to the gravitational force, increasing the apparent weight rather than decreasing it.

- **Option 4 (remains constant):**
     - The apparent weight remains constant only when the lift is moving at a constant velocity (either upwards or downwards) or is stationary. In these cases, there is no additional acceleration affecting the apparent weight. However, since the lift is accelerating upwards, the apparent weight does not remain constant.

In conclusion, when a lift accelerates upwards, the apparent weight of a person inside the lift increases due to the additional force from the lift's acceleration, making Option 2 the correct answer.