# Work with Pulleys: Questions & Answers

• mbrmbrg
In summary, Figure 7-48 shows a canister with mass m = 11 kg hanging from a pulley, with a force F being exerted on the free end of the cord. To lift the canister at a constant speed, the magnitude of F must be equal to the weight of the canister. To lift the canister by 1.9 cm, the free end of the cord must be pulled twice the distance. The work done on the canister by the applied force is equal to the product of F and the distance it is pulled. The work done on the canister by the gravitational force is not affected by the pulleys and remains equal to the product of the weight of the canister and the distance it
mbrmbrg
In Figure 7-48 (see attatched), a cord runs around two massless, frictionless pulleys. A canister with mass m = 11 kg hangs from one pulley, and you exert a force F on the free end of the cord:

(a) What must be the magnitude of F if you are to lift the canister at a constant speed?
(b) To lift the canister by 1.9 cm, how far must you pull the free end of the cord?
(c) During that lift, what is the work done on the canister by your force (via the cord)?
(d) What is the work done on the canister by the gravitational force on the canister?

I don't like pulleys. Can I just pretend that the applied force acts directly on the canister and points straight up? I'm fairly certain that's OK for parts (a) and (c), but I'm not so sure about part (b).

#### Attachments

• WebAssign 7.11 diagram.doc
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W-oah. I have the problem from WebAssign; I finally flipped through my textbook (Halliday, 7e) in the vague hope that the book would provide inspiration. It adds a helpful little line at the end of the problem: "(Hint: When a cord loops around a pulley as shown, it pulls on the pulley with a net force that is twice the tension in the cord.)"
Was I supposed to figure that out by myself?
And does that mean that I can indeed imagine the applied force as acting directly on the canister, but it points up and has twice the magnitude of the pulling-on-rope force?

BTW, my attatchment still says that it's pending approval, but I can download it no problem.

Last edited:
Hokey-dokey. I got it all right, and I even know how I got it all right. But I'm not quite sure why it all worked.

Take part (b): just multiply the distance by two. But why? How would I have figured that out other than looking in the back of the book and working backwards to figure out how they manipulated their numbers to get their answer?

For part (c), W=Fxcosphi=Fx*1. Why is x the distance you pull rather than the distance the can moves? Same for part (d)

## 1. What is a pulley?

A pulley is a simple machine that is used to lift or move objects by using a rope or cable that is wrapped around a wheel. It can change the direction or magnitude of a force, making it easier to move heavy objects.

## 2. How does a pulley work?

A pulley works by distributing the weight of an object evenly across multiple ropes or cables, allowing us to use less force to lift or move the object. The rope or cable is wrapped around a wheel, and as we pull on one end, the wheel turns and lifts the object on the other end.

## 3. What are the different types of pulleys?

There are three main types of pulleys: fixed, movable, and compound. Fixed pulleys are attached to a stationary object and only change the direction of the force. Movable pulleys are attached to the object being lifted and can increase the mechanical advantage. Compound pulleys use a combination of fixed and movable pulleys to increase the mechanical advantage even more.

## 4. What is mechanical advantage?

Mechanical advantage is a measure of how much a machine can multiply the input force to make a task easier. In the case of pulleys, it is the ratio of the output force (the weight of the object being lifted) to the input force (the force we apply to the rope or cable).

## 5. How can I calculate the mechanical advantage of a pulley system?

To calculate the mechanical advantage of a pulley system, divide the weight of the object being lifted by the amount of force you need to apply to the rope or cable. For example, if you are lifting a 100-pound object with a system that requires you to pull with 25 pounds of force, the mechanical advantage would be 100/25 = 4. This means that the pulley system is making the task four times easier.

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