In a hypothetical situation where a man of mass M is inside a lift of mass m. Lift is connected to a pulley with one end of string attached to lift and man is holding the other end of string. What will be the force applied by man to stay in equilibrium?

Question

Answer

Understanding the Scenario
In this scenario, we have a man of mass M inside a lift of mass m. The lift is connected to a pulley, and the man is holding one end of the string attached to the lift. To analyze the forces involved, we need to consider the equilibrium conditions.
Forces Acting on the System
- Weight of the Man: The gravitational force acting on the man is Mg, where g is the acceleration due to gravity.
- Weight of the Lift: The gravitational force acting on the lift is mg.
- Tension in the String: The force applied by the man creates tension (T) in the string, which acts upward on the lift.
Equilibrium Condition
For the system to be in equilibrium, the total upward force must equal the total downward force. Therefore, we can set up the following equation:
- Total Downward Force: Mg + mg
- Total Upward Force: T
In equilibrium, these forces balance out, leading to the equation:
T = Mg + mg
Force Applied by the Man
Since the man is holding the string and creating tension, he must exert a force equal to the tension in the string. Thus, the force (F) applied by the man to stay in equilibrium is:
- F = T = Mg + mg
This indicates that the man must exert a force equal to the sum of his weight and the weight of the lift to prevent any movement.
Conclusion
To maintain equilibrium in this system, the man must pull on the string with a force equal to the combined weight of himself and the lift. This ensures that all forces are balanced, and the system remains stationary.

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