What force must the man pull on the rope to rise with a constant velocity

In summary, the problem involves a man sitting in a bosun's chair attached to a massless rope and pulley system. He weighs 95kg and must pull on the rope with a force of 465.5N in order to rise with a constant velocity. The problem also demonstrates the mechanical advantage of using a pulley. In the second part, the man must pull with a force of 931N to rise with an upward acceleration of 1.3m/s^2. Lastly, the weight of the man and chair, along with the force applied, is the magnitude of the forces on the ceiling from the pulley system.
  • #1
suspenc3
402
0
Ok, I already posted this a few days ago but I am bringing it back because i don't quite understand

a man sits in a bosuns chair that dangles from a massless rope, which runs over a massless frictionless pulley, and back down to the mans hand. The combined mass of the man and the chair is 95Kg. with what force must the man pull on the rope to rise with a constant velocity

so..
T=-mg/2

T = 465.5N
this doesn't make sense because if he is to rise any amount, he would have to exert more force that gravity does..Wouldnt he?
 
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  • #2
suspenc3 said:
Wouldnt he?

No, the problem says that he is to move at constant velocity. That means that the net force that is applied to him must equal the total weight of the man and the chair exactly.
 
  • #3
Ok..confused now..does this mean that he must exert a force of 931N
Or was my original answer right?
 
  • #4
No, you were right at the beginning. The net force acting on the man + chair is 2T. The man only has to exert a force of T. The problem is supposed to show you the mechanical advantage of using a pulley.
 
  • #5
Ok, Thanks

So part B asks with what magnitude must the man pull on the rope if he is to rise with an upward acceleration of 1.3m/s^2
Any hints?
 
  • #6
Use Newton's second law.
 
  • #7
Now it says that the rope is extended to the ground where a co-worker is pulling on the rope
With what force magnitude must the co-worker pull on the rope to maintain a constant velocity?

now would the answer be 931N
 
  • #8
Yesiree. That's because the force applied to the chair + man is only T, whereas before it was 2T.
 
  • #9
Now it is asking for the magnitude of the forces on the ceiling from the pulley systems

Would this part just be the weight of the man+chair +the force applied?
 

1. What is meant by "constant velocity" in this scenario?

The term "constant velocity" means that the man is moving up the rope at a steady and unchanging speed. This means that the force he is exerting on the rope is equal to the force of gravity pulling him down, resulting in a balanced system.

2. How does the force of gravity affect the man's movement?

The force of gravity pulls the man down towards the ground. In order for him to rise with constant velocity, he must exert an equal force in the opposite direction on the rope to counteract the force of gravity. This creates a balanced system where the man can move up the rope at a steady pace.

3. Does the weight of the man affect the force he needs to exert on the rope?

Yes, the weight of the man does play a role in the amount of force he needs to exert on the rope to rise with a constant velocity. The heavier the man, the more force he will need to exert to counteract the force of gravity pulling him down.

4. How can we calculate the force the man needs to pull on the rope?

To calculate the force needed, we can use the formula F = ma, where F is the force, m is the mass of the man, and a is the acceleration, which in this case is 0 since the man is moving at a constant velocity. So, the force needed would be equal to the weight of the man, which is his mass multiplied by the acceleration due to gravity.

5. Why must the force on the rope be equal to the force of gravity for the man to rise with constant velocity?

In order for the man to rise with constant velocity, the forces acting on him must be balanced. This means that the force he exerts on the rope must be equal and opposite to the force of gravity pulling him down. If one of these forces is greater than the other, the man's movement will not be constant and he will either accelerate or decelerate.

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