Pulley Cable System (Conceptual)

In summary: You are not far off, but your explanation could be more clear. In summary, the minimum force F that allows the window washer to move upward is equal to one-third of the product of the window washer's mass and the acceleration due to gravity. This is found by understanding that the tension in the rope holding up the platform is 2T because of the pulley cable system and the rope also exerts a force on the man in an action-reaction pair. The solution can be written as F=Mg/3, which is just 3T=mg rearranged and with T=F. However, it is important to avoid the illusion that a pulley has magical force and to accurately represent the forces acting on the system.
  • #1
jzwiep
21
0

Homework Statement



A window washer of mass M is sitting on a platform suspended by a system of cables and pulleys as shown . He is pulling on the cable with a force of magnitude F. The cables and pulleys are ideal (massless and frictionless), and the platform has negligible mass.

http://session.masteringphysics.com/problemAsset/1010932/17/MFS_1l_18_001.jpg"

Find the magnitude of the minimum force F that allows the window washer to move upward.

Homework Equations



None that I'm aware of.

The Attempt at a Solution



Based on the F = Tension in the rope

The Tension in the rope holding up the platform is 2T because of the pulley cable system.

This is where I get lost. So the tension in the cable also acts back on the man (as an action-reaction pair)?

Here's a terribly drawn MS paint http://i.imgur.com/lDe6c.png" to better illustrate what I'm asking. Is it right? or even close?

Thanks.
 
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  • #2
Yes, if the man exerts a force T on the rope, the rope exerts a force T on the man. You are asked to find that force. Note that your picture is missing the rope which acts up on the pulley on the right, supporting that pulley from the ceiling. I am not sure how you arrived at 3T = mg, which is the correct solution given to you?
 
  • #3
Try to avoid the illusion a pulley has magical force.
 
  • #4
PhanthomJay said:
Yes, if the man exerts a force T on the rope, the rope exerts a force T on the man. You are asked to find that force. Note that your picture is missing the rope which acts up on the pulley on the right, supporting that pulley from the ceiling. I am not sure how you arrived at 3T = mg, which is the correct solution given to you?

The correct answer was: F=Mg/3

Which is just 3T=mg rearranged and with T=F

Am I really that far off?

Chronos said:
Try to avoid the illusion a pulley has magical force.

Could you be a little more specific please? I'm not really sure what you're saying. Which pulley did I create an imaginary force at?
 
  • #5
jzwiep said:
The correct answer was: F=Mg/3

Which is just 3T=mg rearranged and with T=F

Am I really that far off?
The answer is correct, I just wasn't sure if it was your answer or just the book's answer.
 

Related to Pulley Cable System (Conceptual)

1. How does a pulley cable system work?

A pulley cable system is a simple machine that consists of a wheel with a grooved rim and a rope or cable running through the groove. As the rope is pulled, the wheel rotates, allowing for the transfer of force and the lifting or lowering of an object. The number of pulleys used in the system can determine the amount of force needed and the direction of the force.

2. What are the advantages of using a pulley cable system?

One advantage of using a pulley cable system is that it allows for the transfer of force over a distance, making it easier to lift heavy objects. It also allows for the direction of the force to be changed, which can be useful in certain situations. Additionally, pulley cable systems are simple and easy to set up, making them a popular choice for lifting and moving objects.

3. Are there different types of pulley cable systems?

Yes, there are three main types of pulley cable systems: fixed, movable, and compound. A fixed pulley is stationary and only changes the direction of the force. A movable pulley is attached to the object being lifted and reduces the amount of force needed. A compound pulley combines both fixed and movable pulleys to increase the mechanical advantage and make lifting even easier.

4. What are some common uses of pulley cable systems?

Pulley cable systems have a variety of uses, including in construction for lifting heavy materials, in elevators for moving people between floors, and in cranes for lifting and moving large objects. They are also commonly used in sports equipment, such as weightlifting machines, and in everyday household items, such as blinds and curtains.

5. How do I calculate the mechanical advantage of a pulley cable system?

The mechanical advantage of a pulley cable system can be calculated by counting the number of ropes supporting the object being lifted. For a fixed pulley, the mechanical advantage is 1, for a movable pulley it is equal to the number of ropes, and for a compound pulley, it is equal to the number of ropes on the movable pulley multiplied by the number of ropes on the fixed pulley.

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