A man of 60kg mass is in a lift. Find the apparent weight of the man when the lift is moving (a) up with uniform acceleration `4ms^(-2)` (b) down with uniform acceleration of `2ms^(-2)` (`g=10ms^(-2))`

Answer

To find the apparent weight of a man in a lift under different conditions, we can use the following steps:

### Given:
- Mass of the man (m) = 60 kg
- Acceleration due to gravity (g) = 10 m/s²

### Part (a): Lift moving up with uniform acceleration of 4 m/s²

1. **Identify the forces acting on the man**:
- The gravitational force acting downward: \( F_g = m \cdot g = 60 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 600 \, \text{N} \)
- The lift is accelerating upward, which means the apparent weight will be greater than the actual weight.

2. **Calculate the apparent weight**:
- The apparent weight (W') when the lift is moving up is given by:
\[ W' = m \cdot (g + a) \]
- Where \( a \) is the acceleration of the lift (4 m/s²).
- Substitute the values:
\[ W' = 60 \, \text{kg} \cdot (10 \, \text{m/s}^2 + 4 \, \text{m/s}^2) = 60 \, \text{kg} \cdot 14 \, \text{m/s}^2 \]
- Calculate:
\[ W' = 840 \, \text{N} \]

### Part (b): Lift moving down with uniform acceleration of 2 m/s²

1. **Identify the forces acting on the man**:
- The gravitational force acting downward remains the same: \( F_g = 600 \, \text{N} \)
- The lift is accelerating downward, which means the apparent weight will be less than the actual weight.

2. **Calculate the apparent weight**:
- The apparent weight (W') when the lift is moving down is given by:
\[ W' = m \cdot (g - a) \]
- Where \( a \) is the acceleration of the lift (2 m/s²).
- Substitute the values:
\[ W' = 60 \, \text{kg} \cdot (10 \, \text{m/s}^2 - 2 \, \text{m/s}^2) = 60 \, \text{kg} \cdot 8 \, \text{m/s}^2 \]
- Calculate:
\[ W' = 480 \, \text{N} \]

### Final Answers:
- (a) Apparent weight when the lift moves up: **840 N**
- (b) Apparent weight when the lift moves down: **480 N**