Work Done on Pulley System: 840J

[V1NW3N]

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.

 

[berkeman]

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.

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?

 

[Doc Al]

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.)

 

[ehild]

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.

 

[V1NW3N]

thanks I got it now, the work is 2520N

 

[ehild]

thanks I got it now, the work is 2520N

The unit of work is joule (J). N (Newton) is force.

 

[ehild]

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.

 

[Doc Al]

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. 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.