Question

A carpenter of mass 50 kg is standing on a weighing machine placed in a lift of mass 20 kg. A light string is attached to the lift. The string passes over a smooth pulley and the other end is held by the carpenter as shown. When carpenter keeps the lift moving upward with constant velocity: (g = 10 m/s²)

• A. the reading of weighing machine is 15 kg
• B. the man applies a force of 350 N on the string
• C. net force on the man is 150 N
• D. Net force on the weighing machine is 150 N

Answer 1

Answer: (A), (B)

The correct options are (A) and (B).

Answer 2

To solve this problem, we need to analyze the forces acting on the carpenter and the lift separately.

1. Forces on the Carpenter:

The carpenter experiences the following forces:

• Weight ($W_c$): Downward force due to gravity, $W_c = 50g = 500$ N.
• Normal Reaction ($N$): Upward force from the weighing machine.
• Tension ($T$): Upward force from the rope.

Since the lift moves with constant velocity, the net force on the carpenter is zero:

$$N + T = 500 \text{ N}$$

2. Forces on the Lift:

The lift experiences the following forces:

• Weight ($W_l$): Downward force due to gravity, $W_l = 20g = 200$ N.
• Normal Reaction ($N$): Downward force exerted by the carpenter on the lift (equal and opposite to the normal reaction from the weighing machine).
• Tension ($T$): Upward force from the rope.

Since the lift moves with constant velocity, the net force on the lift is zero:

$$T = N + 200 \text{ N}$$

3. Solving for N and T:

Substitute the expression for $T$ from the lift's equation into the carpenter's equation:

$$N + (N + 200) = 500$$ $$2N = 300$$ $$N = 150 \text{ N}$$

Now, find $T$:

$$T = 150 + 200 = 350 \text{ N}$$

4. Interpretation:

• The weighing machine reads the normal reaction $N$, which is 150 N. Since $g = 10 \text{ m/s}^2$, this corresponds to a mass of 15 kg. Option (A) is correct.
• The carpenter applies a force equal to the tension $T$ on the string, which is 350 N. Option (B) is correct.
• The net force on the man is zero as he moves with constant velocity. Option (C) is incorrect.
• The net force on the weighing machine is zero. Option (D) is incorrect.