Why does adding more pulleys increase the force on a block?

[anony123]

Hello,
First of all, I'm new to this forum and to not know whether this thread is in the right place or not. If not, feel free to replace it.

I'm in my first year of university, studying industrial engineering. On a test I got the following image:

The red square is a block with a specific mass, the grey lines are a string, the circle with an 'M' inside is a motor that rolls up the string, and the other red circles are pulleys.

for the test,we had to calculate the power of the motor on the block after a specific amount of seconds. The power of the motor, the mass of block and the coefficients of friction between the block and the ground were given, and we were allowed to neglect the friction between the string and the pulleys. (also, the block cannot rotatate or something, you can view it as one "particle")

I'm not going to ask you guys to solve this problem, but I just have a question about it:
The motor will give the block a specific force with a direction towards the motor, but if the motor would be directly connected to the blok, without any pulleys (see image below), would the force on the block be the same, will it be larger, or smaller?

On the answer of my test, the force would be larger with 2 pulleys than it would be when the motor is directly connected to the block, so the more pulleys, the stronger the force of the block towards the motor. But I don't really understand why, isn't that a little bit illogical? because if that would be true, we could, in theory, connect 1000 pulleys to the block, and then we could move a very heavy block with just a tiny weak motor, because the more pulleys, the stronger the force. That's a little bit strange, no?

Thanks in advance.

Anthony

 

[Student100]

The entire purpose of a pulley is create some sort of mechanic advantage.

On the answer of my test, the force would be larger with 2 pulleys than it would be when the motor is directly connected to the block, so the more pulleys, the stronger the force of the block towards the motor. But I don't really understand why, isn't that a little bit illogical? because if that would be true, we could, in theory, connect 1000 pulleys to the block, and then we could move a very heavy block with just a tiny weak motor, because the more pulleys, the stronger the force. That's a little bit strange, no?

You could, but you would be doing an equivalent amount of work on the block either way to move it a certain distance.

To try to come to terms with this, why don't you use the block example above and look at the forces and work required to move the block.

 

[anony123]

Thank you for your answer.

if the force on the block, when the motor is directly connected to the block, be for example 1 Newton. How much mould the force be on the block be when there are 2 pulleys then? How much larger would it be?

Anyway, it still doesn't feel right for me. So this means that I would be able to move an entire house with just the motor of my ceiling fan, as long as I use enough pulleys?

 

[Student100]

Thank you for your answer.

if the force on the block, when the motor is directly connected to the block, be for example 1 Newton. How much mould the force be on the block be when there are 2 pulleys then? How much larger would it be?

You tell me.

Anyway, it still doesn't feel right for me. So this means that I would be able to move an entire house with just the motor of my ceiling fan, as long as I use enough pulleys?

You could move your house with ideal pulleys and a tiny motor. In the real world, pulleys aren't ideal and at some point the advantage of another pulley is outweighed by the loses (frictional, heat, whathaveyou).

 

[gneill]

Moderator note: Since this is a fairly general topic (mechanical advantage and pulleys) and not really a specific homework problem, I'm moving the thread to General Physics.

Edit: Heh. @jedishrfu beat me to it!

 

[anony123]

You tell me.

I think you will have a force three times as big, because your motor will have to do 3 times more rotations to move the block the same distance as if there would be no pulleys, but I'm not really sure abut this.

 

[Nugatory]

I think you will have a force three times as big, because your motor will have to do 3 times more rotations to move the block the same distance as if there would be no pulleys, but I'm not really sure abut this.

That's one way of coming at the answer. Another way is draw a diagram with all the forces (force of each length of rope on whatever is at each end, force of the pulley supports on the pulleys, force of the motor on the rope, force of the ground on the motor) and work out the net force on the pulleys, block and motor. The motor and the pulley fixed to the ground are not moving, so you know the net force on them must be zero.

 

[ZapperZ]

I think you will have a force three times as big, because your motor will have to do 3 times more rotations to move the block the same distance as if there would be no pulleys, but I'm not really sure abut this.

You may not believe it, but you know all about this already. Just look at the similar situation for a fulcrum-lever system:

Here, you can already see that a smaller force can be applied to lift a heavy object.

The trade-off here is that you apply this smaller force over a larger distance, so that the total work done by the heavy weight is the SAME as the total work done by the force lifting it. It is not the "force" that has to be "conserved", but rather the total energy in the form of work done.

This is no different than the pulley system. You can apply a smaller force, but you have to apply it through a longer distance than the object you're lifting.

Zz.

 

[anony123]

Thank you all very much for your answers, now I have a better understanding of problems like this!

 

[malemdk]

Archimedes said if he could a lever so long, he would lift earth!
The lever he had asked might be lights years length !

 

[lychette]

The entire purpose of a pulley is create some sort of mechanic advantage.
You could, but you would be doing an equivalent amount of work on the block either way to move it a certain distance.

To try to come to terms with this, why don't you use the block example above and look at the forces and work required to move the block.

I think the ONLY purpose of a pulley is to change the direction of a force...it cannot change the VALUE of a force. What do you think ?

 

[Student100]

I think the ONLY purpose of a pulley is to change the direction of a force...it cannot change the VALUE of a force. What do you think ?

Pulleys can both change the direction of force and decrease the amount of force required to be applied to move some object.

Example, if you lift a bucket with 100 Newtons of force over one second a distance x, with a pulley system set up appropriately you could now say, move that same bucket a distance x in four seconds with an applied per second force of 25 Newtons. In the end you've moved the object the same distance x and applied the same force over that distance. The work remains the same. The pulley enabled you to have an easier time going about it though.

A pulley is just a lever incognito, like ZapperZ post points out.

 

[A.T.]

I think the ONLY purpose of a pulley is to change the direction of a force...it cannot change the VALUE of a force.

It's not about "a force", but about the relationship between two forces doing work. A pulley make the direction and magnitude of them different.

 

[lychette]

It's not about "a force", but about the relationship between two forces doing work. A pulley make the direction and magnitude of them different.

In relation to a pulley can you clear up what is meant by the 'two' forces doing work and how a pulley changes the magnitude of 'them' (the two forces)

 

[sophiecentaur]

Problems like this one, where there is a Motor involved. needed to be treated carefully and the results don't necessarily translate to reality. Motors often have performance which differ when stalled and when running. The motor would be running at a different speed in the two cases (with and without pulleys) and that could well mean that the available force was different. To be on the safe side and to get realistic results, it would be better to do the calculation with the motor replaced with a Force meter, providing a specified, constant force. Then you could add the motor, making sure that it will actually do what's required.
The efficiency of such systems has already been mentioned above and can be very relevant.

 

[A.T.]

In relation to a pulley can you clear up what is meant by the 'two' forces doing work and how a pulley changes the magnitude of 'them' (the two forces)

You have an input force and an output force. Pulleys/gears/levers allow these two forces to be different in magnitude.

 

[sophiecentaur]

In relation to a pulley can you clear up what is meant by the 'two' forces doing work and how a pulley changes the magnitude of 'them' (the two forces)

Have you done any reading around of this topic? There are dozens if sites with diagrams and discussions - and there are many textbooks (on line and paper).
The input force 'does work on' the pulley block and the pulley block 'does work' on the output load.

 

[lychette]

Have you done any reading around of this topic? There are dozens if sites with diagrams and discussions - and there are many textbooks (on line and paper).
The input force 'does work on' the pulley block and the pulley block 'does work' on the output load.

I think we have a problem understanding the difference between a pulley and a pulley block!
Your original statement referred to a pulley, in this statement you refer to a pulley block.
The difference is significant !
I am very familiar with textbook analysis of single pulleys and pulley blocks consisting of several pulleys, with precise use of the terms the analysis is very straight forward

 

[A.T.]

I am very familiar with textbook analysis of single pulleys...

Then you should already now how to get more force out than you put in, with a single pulley.

 

[lychette]

Then you should already now how to get more force out than you put in, with a single pulley.

Correct
I prefer to talk about tension in the string/rope rather than "force put in" and the load rather than the "force out".
I know how to exert a force on a load of 10N, 20N, 30N, 40N...etc by applying a tension of 10N using pulley blocks. The purpose of the pulleys in the blocks is simply to change the direction of the tension...not to change the tension.
This could become silly so I prefer to make no more posts to this thread.

 

[jack action]

I think we have a problem understanding the difference between a pulley and a pulley block!
Your original statement referred to a pulley, in this statement you refer to a pulley block.
The difference is significant !
I am very familiar with textbook analysis of single pulleys and pulley blocks consisting of several pulleys, with precise use of the terms the analysis is very straight forward

What works with pulley blocks also work with single pulleys; It's only a matter of disposition.

In relation to a pulley can you clear up what is meant by the 'two' forces doing work and how a pulley changes the magnitude of 'them' (the two forces)

Example:

If the 2 red blocks have the same weight, then $F_1 = 2F_2$. Just a single pulley in both cases.

 

[sophiecentaur]

Your original statement referred to a pulley, in this statement you refer to a pulley block.
The difference is significant !

Well yes. There a many different ways of getting mechanical advantage but it all boils down to force or distance multiplication. U used the term Pulley Block because the force on the load is only in one place. The original diagram shows more than one force acting on the load - probably a less common arrangement. (except in problems!)