Pulley system

[chiddler]

I have an extremely weak understanding of pulley systems like this one:

The simple algorithm that seems to work for me is to count the number of pulleys that is in the system and divide the weight of the mass by that number. Here, 60 N / 4 = 15 N force required to pull it up.

but i want a real understanding. This seems simple, judging by how little text there is explaining it.

To start somewhere: Each rope pulls upwards, right? But if you count the number of vertical ropes, there are 5 of them. So why isn't it mg/5?

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[milski]

The mass is hanging from only 4 of these vertical ropes, thus divide by 4, not by 5. Or you can imagine the leftmost rope being pulled to the left - it would work the same way.

 

[chiddler]

The mass is hanging from only 4 of these vertical ropes, thus divide by 4, not by 5. Or you can imagine the leftmost rope being pulled to the left - it would work the same way.

So is it as simple as counting the ropes pulling the mass up given that they are attached to the mass?

 

[milski]

So is it as simple as counting the ropes pulling the mass up given that they are attached to the mass?

I'd be very careful about a generalization like that. It will be true for a simple system where you just weave the rope through the pulleys like your example. But can be made more complicated with ropes attached to the center of the pulley.

 

[chiddler]

I'd be very careful about a generalization like that. It will be true for a simple system where you just weave the rope through the pulleys like your example. But can be made more complicated with ropes attached to the center of the pulley.

i'm trying to visualize what you mean by that. can you please be more descriptive with the different pulley system? how would you solve that?

 

[milski]

Something like this:

You'll have to consider the two ropes separately. First in the same way as in your example, the long rope will be pulling down on the leftmost pulley with 6g/4 N. Then from that pulley you have two ropes going up, so it will be half of that - 6g/8 N for the final answer.

I was really brief but if I'm not making any sense, let me know.

 

[chiddler]

i understood.

thanks for your help!