Work Done on Pulley System: 840J

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Homework Help Overview

The problem involves a pulley system with a mechanical advantage of 3, where a box weighing 420N is lifted 6m using a force of 140N applied over a distance of 18m. The discussion centers around calculating the work done in this scenario, considering the definitions and implications of work in a mechanical context.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the force applied, the distance moved by the box, and the calculation of work done. There are questions about the correct interpretation of forces involved, particularly regarding the force exerted on the box versus the force applied to the rope.

Discussion Status

Some participants have provided insights into the definitions of work and the forces at play in the pulley system. There is an ongoing exploration of how to correctly calculate work based on the forces involved and their respective distances. Multiple interpretations of the problem are being discussed, particularly regarding the distinction between the force applied to the rope and the force acting on the box.

Contextual Notes

Participants note the importance of specifying which force is being considered when discussing work, as well as the implications of mechanical advantage in the context of the problem. There is also a mention of ideal conditions, such as the absence of friction, which may affect the calculations.

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Homework Statement


The pulley system has a mechanical advantage of 3. You want to lift the box weighing 420N 6m above the ground. You pull 18m of rope with 140N of force. What is the work done? (Ignoring the angle)

Homework Equations


Work=force*distance

The Attempt at a Solution


I thought that since the box moved 6m, and you put in 140N of force, so 6* 140= 840J of work.
 
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V1NW3N said:

Homework Statement


The pulley system has a mechanical advantage of 3. You want to lift the box weighing 420N 6m above the ground. You pull 18m of rope with 140N of force. What is the work done? (Ignoring the angle)

Homework Equations


Work=force*distance

The Attempt at a Solution


I thought that since the box moved 6m, and you put in 140N of force, so 6* 140= 840J of work.
Welcome to the PF. :smile:

The work equals the change in gravitational potential energy. The pulley system does not change that.

The pulley just let's you use less force over a longer distance. Makes sense? What is your revised answer? :smile:
 
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V1NW3N said:
I thought that since the box moved 6m, and you put in 140N of force, so 6* 140= 840J of work.
No. The force of 140 N is exerted over a distance of 18 m. (The box moves 6 m, but the force on the box equals its weight, not 140 N.)
 
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V1NW3N said:

Homework Statement


The pulley system has a mechanical advantage of 3. You want to lift the box weighing 420N 6m above the ground. You pull 18m of rope with 140N of force. What is the work done? (Ignoring the angle)

Homework Equations


Work=force*distance

The Attempt at a Solution


I thought that since the box moved 6m, and you put in 140N of force, so 6* 140= 840J of work.
When asking work, it should be specified "work of what force on what body".
The 140 N force is applied on the rope. The work of that force multiplied by the displacement of the point of attack of the force gives the work of that force.
The mechanical advantage of the pulley system is 3, so the force experienced by the box is 420 N. That should be multiplied by the displacement of the box to get the work done on the box by the 420 N force.
If there is no friction, the pulleys are ideal, then these works are equal.
 
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thanks I got it now, the work is 2520N
 
V1NW3N said:
thanks I got it now, the work is 2520N

The unit of work is joule (J). N (Newton) is force.
 
Doc Al said:
No. The force of 140 N is exerted over a distance of 18 m. (The box moves 6 m, but the force on the box equals its weight, not 140 N.)
Well, the force on the box is equal its weight and the tension from the pulley system, in opposite direction. If it does not accelerate, the net force on the box is zero.
 
ehild said:
Well, the force on the box is equal its weight and the tension from the pulley system, in opposite direction. If it does not accelerate, the net force on the box is zero.
I meant the force that the pulley system exerts on the box, not the net force on the box. :smile: That's the force doing the work against gravity on the box, which is what we care about here.

Similarly, it's the force that the person exerts on the rope that matters, not the net force on the rope.
 

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