Pulley Carrying Capacity: Can It Handle 150 lbs?

[NekotoKoara]

Ok, so I just started researching about pulleys. Fascinating simple machines. I had a question about their carrying capacity (don't know if that's the technical word for it but work with me here). Let's say we have a two pulley system. One fixed on the ceiling, one moveable on attached to the thing being lifted and one end of the rope being attached to the ceiling. Let's say the moveable pulley is built to handle 200 pounds of force. The object being lifted is 150 pounds. When the object is suspended in midair it exerts 150 pounds of force downwards on the pulley and the two rope segments combined pull up on it with 150 pounds of force. I'm struggling to understand if it is going to be able to hold the weight or not. I want to say yes because its only 150 pounds and the pulley can hold up to 200. But at the same time it feels like magnitude of both forces pulling upward and downward would equal 300 pounds and cause the pulley to malfunction and/or break. Can someone help me have a better intuition on this scenario? With Newton's laws it always seems like a slow progression towards understanding them, 2 steps forward and 1 step back. lol

 

[Nidum]

Do a simple drawing of the pulleys and ropes and mark in the forces that you think are acting . Post the result here for us to see .

 

[russ_watters]

The object being lifted is 150 pounds. When the object is suspended in midair it exerts 150 pounds of force downwards on the pulley and the two rope segments combined pull up on it with 150 pounds of force. I'm struggling to understand if it is going to be able to hold the weight or not. I want to say yes because its only 150 pounds and the pulley can hold up to 200. But at the same time it feels like magnitude of both forces pulling upward and downward would equal 300 pounds and cause the pulley to malfunction and/or break. Can someone help me have a better intuition on this scenario? With Newton's laws it always seems like a slow progression towards understanding them, 2 steps forward and 1 step back. lol

Newton's third law says that all forces always come in pairs. Does that help?

 

[NekotoKoara]

Do a simple drawing of the pulleys and ropes and mark in the forces that you think are acting . Post the result here for us to see .

 

[russ_watters]

What does this diagram tell you?

 

[NekotoKoara]

What does this diagram tell you?

It tells me that the moveable pulley has 150 pounds of force pulling it down by the weight of the object and the the ropes are pulling up on it with a combined total of 150 pounds force which is why it is not accelerating. But I guess what I don't know is when a pulley is made and its tested to withstand 200 pounds of force are they adding up to magnitudes of both forces and saying it can handle 100 pounds of force pulling down on it and 100 pounds of force pulling up on it? Or are they saying it can hold a 200 pounds weight which implies it can handle the 200 pounds of force that is pulled in the opposite direction when it is suspended? I feel like I am making this way more complicated than it has to be.

 

[russ_watters]

I feel like I am making this way more complicated than it has to be.

You are, but don't worry, it is a common problem.
You drew vectors pointing in opposite directions, acting at a point. What is the sum of two vectors of equal magnitude and pointing in opposite directions?
[Edit; made a mess...]

Consider you weigh 150 pounds and are standing on a bathroom scale. Does it display 300 pounds? Or worse, 600 pounds?

 

[NekotoKoara]

You are, but don't worry, it is a common problem. There are two issues now:
1. You drew vectors pointing in opposite directions, acting at a point. What is the sum of two vectors of equal magnitude and pointing in opposite directions?

2. A free body diagram typically shows the forces acting on an object. You drew the forces acting on and by each object. You showed too many forces (though still instructive...).

Consider you weigh 150 pounds and are standing on a bathroom scale. Does it display 300 pounds? Or worse, 600 pounds?

1. 0
2. Point taken. But with a free body diagram wouldn't forces on the pulley just be 150 pounds upward and 150 pounds downward? Which then yes they would add up to zero. But if you had rope that was able to handle a ton and you attached a weight to the pulley that was a ton, the pulley would break even though the net forces on it added up to zero.

I understand your question about the scale, of course it would read 150 pounds. Which makes me think then of course its that the pulley would be able to handle an object that weighs 200 pounds.

It's just a little frustrating because I feel on one hand I get it and on the other hand I feel like I don't understand it at all.

 

[russ_watters]

1. 0

Since you aren't quite getting there, I'll be more descriptive (we generally try to push instead of pull...):

Since those forces sum to 0, not 300, they must be telling you something totally different from what you are thinking. All summing to zero tells you is that the object isn't accelerating (in static situations, forces sum to zero).

The bathroom scale (analog type) is really just a needle connected to a spring. The spring is compressed by equal and opposite forces from both sides. A compression force (and a tension force) is basically one force that acts in two different directions at once.

The wiki on tension shows a ball supported by a rope. At each point is a pair of forces and on each object is a pair of forces, all summing to zero. Then, zoomed in on the rope is individual little elements of forces pulling apart. The tension is one number to represent the forces pulling in opposite directions.
https://en.wikipedia.org/wiki/Tension_(physics)

2. Point taken. But with a free body diagram wouldn't forces on the pulley just be 150 pounds upward and 150 pounds downward? Which then yes they would add up to zero.

...yeah, I made a bit of a mess there and deleted that objection, but you'd already seen it. I was thinking at first that you were showing the force on the pulley and the force on the bearing. I was misunderstanding your issue slightly -- though in the end, it is basically the same problem.

But if you had rope that was able to handle a ton and you attached a weight to the pulley that was a ton, the pulley would break even though the net forces on it added up to zero.

Right. What matters is that the failure force (maybe it's a tension, but it hasn't been defined) is one number that manifests as a pair of forces.

 

[NekotoKoara]

Since you aren't quite getting there, I'll be more descriptive (we generally try to push instead of pull...):

Was there a physics pun in there somewhere? ;-) I appreciate your patience and your attempt to work the answer out of me. Seems what I need to do is a bit more research on tension and delve more into the physics of statics. I've just begun looking into this area and I think I was pushing my brain just a bit further than it was able to handle with the info it had available to it. You've given me a lot to think about and I hope I will continue to improve my intuition with these types of things. Thanks!