# Calculating actual weight lifted on a pulley weight machine

Hi,
I have a pin-loaded pulley weight home gym machine. There are 9 weight plates that are 10 lbs each, so for each exercise the maximum weight that can be done is 90 lbs. However, there is a chart in the manual that shows the weight resistance for various exercises based on how many plates are used. For most exercises, the resistance is listed as being substantially more than the weight lifted based simply on the plates.

I'm trying to understand if there is any way to calculate what would be more of a true weight that is being lifted, and I thought this seemed like a physics matter. In other words, would it be closer to the weight lifted from the plates, or from what the resistance chart shows? What confuses me is that (for example), with all 9 plates being used, the chest press is listed as being 215 lbs of resistance. It feels like more than 90 lbs to me, but not quite 215. But yet, the leg press is listed as 275 lbs of resistance for 9 plates. From my experience with using a pin loaded leg press at another gym, what I have on my machine seems like 90 lbs to me.

I can provide images of the machine if that would help.

Thanks

phinds
Gold Member
2021 Award
Have you taken mechanical advantage into account? If you press on a leg exerciser, for example, and the weights are attached near a pivot point, that's going to be one resistance weight but if the weight were attached much further from the pivot point, it would be a much larger resistance weight.

Have you taken mechanical advantage into account? If you press on a leg exerciser, for example, and the weights are attached near a pivot point, that's going to be one resistance weight but if the weight were attached much further from the pivot point, it would be a much larger resistance weight.
When it comes to the differences between the chest and leg press, that would make sense then. If I understand what you mean, the leg press is pushed farther away from the weights than the chest press.

phinds
Gold Member
2021 Award
When it comes to the differences between the chest and leg press, that would make sense then. If I understand what you mean, the leg press is pushed farther away from the weights than the chest press.
That's a very vague statement and is not necessarily the reason. Do you understand mechanical advantage?

That's a very vague statement and is not necessarily the reason. Do you understand mechanical advantage?
I don't think so then.

phinds
Gold Member
2021 Award
OK, hold on, I'll draw a pic for you Point D pivots freely. The meaningful pivot point is either A or B. Whichever one is the pivot point is fixed (and the other one doesn't exist). Point C pulls a rope that goes a pulley and lifts the weights.

If A is the pivot point then your feet have to press 500 lbs to lifts weights of 100 lbs because for every unit of distance your foot moves, the weights move 5 times that much. If B is the pivot point, your feet have to press 20 lbs to lifts weights of 100 lbs because for every foot your foot moves, the weights only move 1/5th of that distance.

The weights could be 10 feet farther away and it would make no difference at all, except that the rope pulled by point C would have to be 10 feet longer. That's why I said your statment "leg press is pushed farther away from the weights" was vague.

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Thanks for the explanation; I think I got it. So, it's really all about the length of the rope in relation to where the pivot point is located. That answers the question of the differences in weight resistance between exercises.

Now with my other question of how much weight is actually being lifted for a given exercise, this was my understanding of the situation. In the case of using 9 weight plates (90 lbs) for the chest press, it requires 215 pounds of force to move that weight. But the pulley system reduces that amount. What I'm still not sure about is by how much?

I was reading more about pulleys from this article. In the case of the weight machine, it looks to me as though at least 4 pulleys are moving. For a given exercise on the machine, the weight is being lifted the same distance, so I thought the only variable at play would be the number of pulleys. But I didn't think it seemed right that the force required in this case is only 54 pounds (215/4). Am I missing something?

phinds
Gold Member
2021 Award
Thanks for the explanation; I think I got it. So, it's really all about the length of the rope in relation to where the pivot point is located. That answers the question of the differences in weight resistance between exercises.
No, it absolutely is NOT about the length of the rope. It is about the ration of the length of the rigid bar on each side of the pivot point. The length of the rope is irrelevant AS I SAID.

Now with my other question of how much weight is actually being lifted for a given exercise, this was my understanding of the situation. In the case of using 9 weight plates (90 lbs) for the chest press, it requires 215 pounds of force to move that weight. But the pulley system reduces that amount. What I'm still not sure about is by how much?
No idea without an exactly dimensioned diagram of the machine

I was reading more about pulleys from this article. In the case of the weight machine, it looks to me as though at least 4 pulleys are moving. For a given exercise on the machine, the weight is being lifted the same distance, so I thought the only variable at play would be the number of pulleys. But I didn't think it seemed right that the force required in this case is only 54 pounds (215/4). Am I missing something?
I'll have to look at that tomorrow. I'm off to bed.

No, it absolutely is NOT about the length of the rope. It is about the ration of the length of the rigid bar on each side of the pivot point. The length of the rope is irrelevant AS I SAID.

No idea without an exactly dimensioned diagram of the machine

I'll have to look at that tomorrow. I'm off to bed.
Ok. When it comes to the length of the bar, yes, I misread that previous statement. Now I'm clear on that.

Thanks for looking into the other part.

phinds
Gold Member
2021 Award
I was reading more about pulleys from this article. In the case of the weight machine, it looks to me as though at least 4 pulleys are moving. For a given exercise on the machine, the weight is being lifted the same distance, so I thought the only variable at play would be the number of pulleys. But I didn't think it seemed right that the force required in this case is only 54 pounds (215/4). Am I missing something?
Yes, what you are missing is that the weight is NOT being pulled through the same distance. To lift the weight 1 foot, for example (in the top image in the link provided) the operator has to pull the chain WAY more than 1 foot. How much is a function of the mechanical advantage. With a single pulley with a rope tossed over it, the mechanical advantage is 1:1. With a pulley added below the first one, the advantage is 2:1, which means the operator has to pull the rope twice as far as he wants the weight to rise. And so forth ...

It's not the number of pulleys per se since a single pully can have multiple paths, it's the number of paths up and down.

Yes, what you are missing is that the weight is NOT being pulled through the same distance. To lift the weight 1 foot, for example (in the top image in the link provided) the operator has to pull the chain WAY more than 1 foot. How much is a function of the mechanical advantage. With a single pulley with a rope tossed over it, the mechanical advantage is 1:1. With a pulley added below the first one, the advantage is 2:1, which means the operator has to pull the rope twice as far as he wants the weight to rise. And so forth ...

It's not the number of pulleys per se since a single pully can have multiple paths, it's the number of paths up and down.
Ok. So is it correct to say that if the manual specifies 215 lbs of resistance to move 90 lbs, that assumes a fixed distance (like lifting the weights 1 foot)? And if the weights are lifted (for example) 10 inches, it could be something like 200 lbs of resistance? And if 15 inches, closer to 240 lbs?

So then to answer my original question, is it true then that I just need to figure out how many up and down paths the rope is pulled on, and then divide the listed resistance weight by that number?

phinds
Gold Member
2021 Award
Ok. So is it correct to say that if the manual specifies 215 lbs of resistance to move 90 lbs, that assumes a fixed distance
Jeez, I really seem to be doing a crappy job of explaining this. NO, it would NOT assume a fixed distance it would assume a distance ratio of whatever the resistance weight is divided by the actual weight. So if 215lbs is the resistance and 90 lbs is the actual weight, then you are having to move your body part only 90/215 feet for every foot the weights move so that the resistance weight seems like (215/90)*90lbs = 215 lbs.

I think I have explained this every way I know how so I would recommend that if you need further help, someone else should provide it.

Jeez, I really seem to be doing a crappy job of explaining this. NO, it would NOT assume a fixed distance it would assume a distance ratio of whatever the resistance weight is divided by the actual weight. So if 215lbs is the resistance and 90 lbs is the actual weight, then you are having to move your body part only 90/215 feet for every foot the weights move so that the resistance weight seems like (215/90)*90lbs = 215 lbs.

I think I have explained this every way I know how so I would recommend that if you need further help, someone else should provide it.
Sorry, I think it's just that I have a hard time with physics. I attempted an engineering physics class in college and ended up dropping it.

I think I have enough of an understanding to figure out exactly how much weight is being lifted by the person. I did some more reading and it looks like I need to figure out what distance the weights are moving vs how far my hands/feet move for a given exercise.

EDIT: I think I have now solved this. I got measurements done for the chest press and the weights moved 18 inches while the bar moved 15 inches. So that's a ratio of 5/6, so from my understanding that means it took 108 lbs to move the 90 lb weight. Based on the total resistance required, I can see that this works out to a 2:1 mechanical advantage with how they designed the pulley system.

Thanks again for the help.

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