A man of mass 60 kg climbed down using an elevator . The elevator had an acceleration of `4ms^(-2)` . If the acceleration due to gravity is `10 ms ^(-2)` , the man's apparent weight on his way down is

Options

A. 60 N
B. 240 N
C. 360 N
D. 840 N

Answer

To find the man's apparent weight while he is descending in the elevator, we can follow these steps:

### Step 1: Identify the Forces Acting on the Man
When the man is in the elevator, two main forces act on him:
1. The gravitational force (weight) acting downward, which is given by \( W = mg \).
2. The normal force (apparent weight) acting upward from the elevator floor.

### Step 2: Calculate the Weight of the Man
The weight of the man can be calculated using the formula:
\[ W = mg \]
where:
- \( m = 60 \, \text{kg} \) (mass of the man)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ W = 60 \, \text{kg} \times 10 \, \text{m/s}^2 = 600 \, \text{N} \]

### Step 3: Consider the Acceleration of the Elevator
The elevator is accelerating downward with an acceleration of \( a = 4 \, \text{m/s}^2 \). When the elevator accelerates downward, the apparent weight of the man will be less than his actual weight.

### Step 4: Apply Newton's Second Law
In the frame of reference of the elevator, the net force acting on the man can be expressed as:
\[ N - mg = -ma \]
where:
- \( N \) is the normal force (apparent weight),
- \( m \) is the mass of the man,
- \( g \) is the acceleration due to gravity,
- \( a \) is the acceleration of the elevator.

Rearranging the equation gives:
\[ N = mg - ma \]

### Step 5: Substitute the Values
Now, substituting the known values into the equation:
\[ N = mg - ma = m(g - a) \]
Substituting \( m = 60 \, \text{kg} \), \( g = 10 \, \text{m/s}^2 \), and \( a = 4 \, \text{m/s}^2 \):
\[ N = 60 \, \text{kg} \times (10 \, \text{m/s}^2 - 4 \, \text{m/s}^2) \]
\[ N = 60 \, \text{kg} \times 6 \, \text{m/s}^2 = 360 \, \text{N} \]

### Conclusion
The man's apparent weight while he is descending in the elevator is \( 360 \, \text{N} \).

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