a man is of mass 60 kg is standing inside a lift of mass 30 kg .The lift is held with a wire passing through a pulley .there is a hole on the top of the lift and the wire is passed through that hole such that the other end of wire id in the hand of man inside the lift . how much force does he have to apply in order to make the lift remain at rest.

To determine the force that the man needs to apply to keep the lift at rest, we need to analyze the forces acting on both the man and the lift. This situation involves understanding the concepts of weight, tension, and equilibrium.

Understanding the Forces Involved

First, let's identify the weights of the man and the lift:

• The weight of the man (W_man) can be calculated using the formula: W = m × g, where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s²).
• The weight of the lift (W_lift) is similarly calculated.

Given:

• Mass of the man (m_man) = 60 kg
• Mass of the lift (m_lift) = 30 kg

Now, let's calculate the weights:

• W_man = 60 kg × 9.81 m/s² = 588.6 N
• W_lift = 30 kg × 9.81 m/s² = 294.3 N

Calculating Total Weight

The total weight acting downwards on the lift system (man + lift) is:

Total Weight (W_total) = W_man + W_lift = 588.6 N + 294.3 N = 882.9 N

Force Required to Maintain Equilibrium

For the lift to remain at rest, the upward force exerted by the man through the wire (tension, T) must equal the total weight acting downwards. Therefore, we can set up the equation:

T = W_total

Since the man is holding the wire, the force he applies (F_applied) must equal the tension in the wire:

F_applied = T = 882.9 N

Conclusion

Thus, the man needs to apply a force of approximately 882.9 N to keep the lift at rest. This force counteracts the gravitational pull on both himself and the lift, ensuring that the system remains in equilibrium.

This scenario illustrates the principles of static equilibrium, where the sum of forces acting on an object is zero when it is at rest. The man’s force effectively balances the weight of the lift and himself, allowing them to remain stationary.