# A question regarding efficiency of pulleys

• Nikola Tesla
In summary, the efficiency of a pulley system is the ratio of useful work to input work, but it will always be less than one due to friction. The more pulleys involved, the more friction and lower the efficiency. Mechanical advantage, on the other hand, is the ratio of output force to input force and is the main purpose of using a pulley. The mechanical advantage can be calculated by counting the number of ropes in the system. However, friction and deformation of the rope can also affect the efficiency of the pulley system. Overall, a system with good bearings can be very efficient.
Nikola Tesla
Does a pulley have more efficiency if it has just one of those cirgular thingies

or more

http://www.kirkwood.k12.mo.us/parent_student/khs/BartinJ/four_pulley.gif

An explanation would be helpful as well.

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Do you mean efficiency or mechanical advantage? The efficiency of a simple machine is the ratio of useful work to input work; real machines always have an efficiency less than one due to friction. You always lose some energy. (I would imagine that the more pulleys involved, the more friction and thus the lower the efficiency.)

Mechanical advantage is something different. It's the ratio of output force to input force. The entire point of using a pulley (in addition to changing the direction of the force) is to multiply the force. In your first example, the single pulley has a mechanical advantage of 2: If you pull with a force of 10N, the pulley exerts a force of 20N on the attached load. In your second example, the mechanical advantage is 4.

Doc Al said:
Do you mean efficiency or mechanical advantage? The efficiency of a simple machine is the ratio of useful work to input work; real machines always have an efficiency less than one due to friction. You always lose some energy. (I would imagine that the more pulleys involved, the more friction and thus the lower the efficiency.)

Mechanical advantage is something different. It's the ratio of output force to input force. The entire point of using a pulley (in addition to changing the direction of the force) is to multiply the force. In your first example, the single pulley has a mechanical advantage of 2: If you pull with a force of 10N, the pulley exerts a force of 20N on the attached load. In your second example, the mechanical advantage is 4.

I am talking about percent efficency of output work over input work. So, are you sure that the less pulleys involved, the better efficiency? Also, let's exclude friction.

I'm not talking about Mechanical advantage, though. However, is there a way of knowing how to calculate the mechanical advantage by looking at the pulley system? I'm sort of able to do it by figuring out how many ropes the object is using, but I do not think it's a proper way of doing it. Thanks for the help.

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Nikola Tesla said:
I am talking about percent efficency of output work over input work. So, are you sure that the less pulleys involved, the better efficiency? Also, let's exclude friction.
You can't exclude friction, which is the cause of the less than perfect efficiency. Without friction, the efficiency will equal 1.

I'm not talking about Mechanical advantage, though. However, is there a way of knowing how to calculate the mechanical advantage by looking at the pulley system? I'm sort of able to do it by figuring out how many ropes the object is using, but I do not think it's a proper way of doing it. Thanks for the help.
That's how I do it, just count the ropes. Ignoring friction (and the mass of the rope), the tension is the same throughout the rope.

Doc Al said:
You can't exclude friction, which is the cause of the less than perfect efficiency. Without friction, the efficiency will equal 1.

Hmm, I see. Thanks for taking the time to answer.

Doc Al,

"...Without friction, the efficiency will equal 1."

Don't forget deformation of the rope. With good bearings, it could be the major cause for less than perfect efficiency.

jdavel said:
Don't forget deformation of the rope. With good bearings, it could be the major cause for less than perfect efficiency.
Interesting. I'll have to think about that. It's not obvious to me how rope deformation affects things.

Doc Al,

Well, don't think too long!

After rethinking, I'm not sure it would make much difference. If the rope has a low k, then some work would go into pulling it tight before anything starts to move. But once the the tension in the rope becomes sufficient to lift the load, no more energy would be lost to stretching of the rope. It would still have to bend as it goes over the pulleys, but that probably doesn't amount to much.

Come to think of it, a system of pulleys with good bearings is probably pretty darn efficient!

My thoughts exactly.

## 1. How do pulleys affect the efficiency of a system?

Pulleys can increase or decrease the efficiency of a system depending on how they are used. When a pulley is used to change the direction of a force, it can increase the efficiency of the system by reducing the amount of force needed to lift an object. However, if the pulley is used to lift an object directly, it can decrease efficiency by adding friction and requiring more force.

## 2. What factors affect the efficiency of pulleys?

The efficiency of pulleys can be affected by several factors, including the number of pulleys used, the type of pulley (fixed, movable, or compound), the angle of the pulley system, and the amount of friction present in the system. Additionally, the weight and size of the objects being lifted and the strength and direction of the force applied can also impact the efficiency of pulleys.

## 3. How can the efficiency of a pulley system be calculated?

The efficiency of a pulley system can be calculated by dividing the output work (the weight being lifted) by the input work (the force applied). This calculation will give a decimal value, which can then be multiplied by 100 to get the efficiency percentage. For example, if a 100-pound weight is being lifted with a force of 50 pounds, the efficiency would be 50% (100/50 = 0.5 x 100 = 50%).

## 4. Are there any disadvantages to using pulleys?

While pulleys can be very useful in increasing the efficiency of a system, there are some potential disadvantages. Pulleys can add complexity to a system and require more maintenance, especially if they have moving parts. Additionally, if the pulleys are not set up correctly or are not strong enough for the weight being lifted, they can break or fail.

## 5. How can the efficiency of pulleys be improved?

The efficiency of pulleys can be improved by using high-quality, well-maintained pulleys with low friction. Additionally, using the correct number and type of pulleys for the job can also increase efficiency. Properly adjusting the angle of the pulley system and distributing the weight evenly can also improve efficiency. Regularly inspecting and maintaining the pulleys can also help to maintain their efficiency over time.

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