How Does the Force on the Ceiling Change in Different Bosun's Chair Scenarios?

[IbadatPHY]

Homework Statement

A man sits on a bosun's chair that dangles from a massless rope, which runs over a massless pulley and back down to the man's hand.

mass of man and chair: 95kg

<---These are the ones that i could do.---->
1) With up force is the man suppose to pull go up at constant velocity?
2) With an upward acceleration of 1.3 m/s^2?
3) If another man below pulls on the rope from below, what force?
4) With an upward accell of 1.3 m/s^2?

Homework Equations

What is the magnitude of force on the ceiling from the pulley system in 1), 2), 3), 4) ?

The Attempt at a Solution

I can't visualize if there would be any force different, unless they would all be the same..

 

[Delphi51]

The force will depend on the acceleration because of F = ma.
Any other forces involved?
Looks rather tricky to me - better start with a free body diagram.

 

[kerimek]

I would approach this problem by first defining the system and identifying the forces acting on it. In this case, the system consists of the man, the bosun's chair, the rope, and the pulley. The forces acting on this system are the weight of the man and chair (mg), the normal force from the chair (N), the tension in the rope (T), and the force from the man pulling on the rope (F).

1) If the man is pulling on the rope with a force equal to his weight (mg), then the net force on the system is zero and the man will remain at a constant velocity. This is because the tension in the rope (T) is equal in magnitude and opposite in direction to the weight of the man and chair (mg).

2) If the man pulls on the rope with a force greater than his weight (mg), then the net force on the system is upward and the man will experience an upward acceleration. This is because the tension in the rope (T) will be greater than the weight of the man and chair (mg), resulting in a net force in the upward direction.

3) If another man pulls on the rope from below, the force he exerts on the rope will add to the tension in the rope (T). This will result in a greater net force on the system, causing the man to experience a greater upward acceleration.

4) If the man pulls on the rope with a force equal to his weight (mg) and there is an upward acceleration of 1.3 m/s^2, then the net force on the system must be greater than zero. This means that the tension in the rope (T) must be greater than the weight of the man and chair (mg).

To calculate the magnitude of the force on the ceiling from the pulley system in each of these scenarios, we can use Newton's second law (F=ma). The force on the ceiling will be equal in magnitude to the tension in the rope (T).

1) Since the man is pulling on the rope with a force equal to his weight (mg), the tension in the rope (T) will also be equal to his weight (mg). Therefore, the magnitude of the force on the ceiling will be 95kg x 9.8m/s^2 = 931 N.

2) If the man pulls on the rope with a force greater than his weight (mg),