A man weighing 60 kg is in a lift moving down with an acceleration of `1.8" ms"^(-2)`. The force exerted by the floor on him is

Options

A. (a)588 N
B. (b)480 N
C. (c)Zero
D. (d)696 N

Answer

To solve the problem step by step, we will calculate the force exerted by the floor on the man in the lift.

### Step 1: Identify the given values
- Weight of the man (m) = 60 kg
- Acceleration of the lift (a) = 1.8 m/s² (downward)
- Acceleration due to gravity (g) = 9.8 m/s² (approximately)

### Step 2: Understand the forces acting on the man
When the lift is moving downward with an acceleration, two forces are acting on the man:
1. The gravitational force (weight) acting downward, which is given by \( F_g = m \cdot g \).
2. The normal force (N) exerted by the floor of the lift acting upward.

### Step 3: Write the equation of motion
Since the lift is accelerating downward, we can apply Newton's second law. The net force acting on the man can be expressed as:
\[ N - F_g = -m \cdot a \]
Where:
- \( N \) is the normal force (force exerted by the floor on the man).
- \( F_g = m \cdot g \) is the weight of the man.
- \( a \) is the acceleration of the lift.

Rearranging the equation gives:
\[ N = F_g - m \cdot a \]

### Step 4: Calculate the gravitational force
Calculate the gravitational force acting on the man:
\[ F_g = m \cdot g = 60 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 588 \, \text{N} \]

### Step 5: Calculate the net force
Now, substitute the values into the equation for normal force:
\[ N = 588 \, \text{N} - (60 \, \text{kg} \cdot 1.8 \, \text{m/s}^2) \]
\[ N = 588 \, \text{N} - 108 \, \text{N} \]
\[ N = 480 \, \text{N} \]

### Step 6: Conclusion
The force exerted by the floor on the man is \( 480 \, \text{N} \).