NationStates Jolt Archive

I need help with this conundrum. Why is the tension acting on each end of a rope hanging over a pulley the same? One load hangs from each end, and the mass of the two loads are unequal.

EDIT For more clarification:

A 400 kg gorilla is on one end of the rope, a 350 kg sandbag is on the other side of the rope. The rope goes over a pulley . Why is the tension on both sides the same?

Possibly got something to do with the modulus of elasticity of the rope. That can't change regardless of the mass on either end, and so the tension is the same throughout.

Besides, if the tension changed depending on the mass hanging at each end, then the rope wouldn't be pulled down by the heavier mass, which is obviously what would happen.

Take two peniciliin...and leave the peas.

I'd imagine the heavier load would have to be a certain size bigger to be the center of tension?! :confused: Perhaps twice the smaller load?!

Possibly got something to do with the modulus of elasticity of the rope. That can't change regardless of the mass on either end, and so the tension is the same throughout.
i don't think the tension is dependent on the modulus of elasticiy. Tension is only dependent on mass of load. The tension caused by a 1 kg object on a stiff rope is the same as the tension of a 1 kg object on a rubber band. i'm not exactly sure though, I wish i were smarter :mp5: :mp5: :mp5:

I'd imagine the heavier load would have to be a certain size bigger to be the center of tension?! :confused: Perhaps twice the smaller load?!
My homework problem gives that the correct outcome is that the tensions acting on each end of the rope are the same no matter what the mass difference is, I am asked to explain why.

For more clarification:

A 400 kg gorilla is on one end of the rope, a 350 kg sandbag is on the other side of the rope. The rope goes over a pulley . Why is the tension on both sides the same?

i don't think the tension is dependent on the modulus of elasticiy. Tension is only dependent on mass of load. The tension caused by a 1 kg object on a stiff rope is the same as the tension of a 1 kg object on a rubber band. i'm not exactly sure though, I wish i were smarter :mp5: :mp5: :mp5:


My homework problem gives that the correct outcome is that the tensions acting on each end of the rope are the same no matter what the mass difference is, I am asked to explain why.

I'm sorry. I can't help you there.

i don't think the tension is dependent on the modulus of elasticiy. Tension is only dependent on mass of load. The tension caused by a 1 kg object on a stiff rope is the same as the tension of a 1 kg object on a rubber band. i'm not exactly sure though, I wish i were smarter :mp5: :mp5: :mp5:

Er...Hooke's law?

Because it's ONE piece of rope...therefore it has the same tension throughout. I'm sure theres a better way to explain that, but I've just woken up.

Need any more clarification then just ask...I'll go make myself some coffee and wake up :p

My best guess would be that the tension of the rope is equal to the sum of the two masses. Particularly if both gorilla and sandbag are hanging freely.

Because it's ONE piece of rope...therefore it has the same tension throughout. I'm sure theres a better way to explain that, but I've just woken up.

Need any more clarification then just ask...I'll go make myself some coffee and wake up :p
That makes sense to me. I'm not sure how pulling tension is measured, but I would think it would be 750 kg total. Pulling on the rope at both ends with a combined force of 750 kg should have the same effect as pulling on one end with a force of 750 kg when the other is fixed. The fact that there's a pully in the middle shouldn't make any difference. But hey, I don't really know; I've never even taken physics.

Because it's ONE piece of rope...therefore it has the same tension throughout. I'm sure theres a better way to explain that, but I've just woken up.

It is pretty good.

Suppose there was no sandbag. Then there would be no tension - the gorilla just pulls the rope and gets it. The concept tension requires both sides to be connected to something.
(yes, this is a simplification)

My best guess would be that the tension of the rope is equal to the sum of the two masses. Particularly if both gorilla and sandbag are hanging freely.
Oh yeah, if the gorilla is on the ground, it doesn't really matter what his mass is so long as it's enough to keep the sandbag in the air. Then you've only got 350 kg of tension, I think.

It is pretty good.

Suppose there was no sandbag. Then there would be no tension - the gorilla just pulls the rope and gets it. The concept tension requires both sides to be connected to something.
(yes, this is a simplification)
but how do you define when "something" is acceptably heavy? When the 400 kg gorilla is counterbalanced by a 1 kg piece of rock I'd imagine that the gorilla would just pull the rope down and it wouldn't be taut. is the tension 401 kg?

Er...Hooke's law?
Tension = ma, where m is mass of load and a is acceleration of load... the modulus does not appear in this equation, therefore tension is independent of modulus. Hooke's law has to do with the string's reaction to the tension. A rope and rubber band will have the same tension if 1 kg masses are hung from both, but the rope will not deform as much as the rubber band.

The weight of the loads is equal to the tension of the pulley. This tension is same all along the rope.When the pulley is in equlibrium, the rope is pulled down with a force equal in magnitude to the tension of the rope. :)


I think that's right!!!

Isn't tension measured in newtons? (I did a level maths and physics but I'll be damned if I can remember a word of it)

http://physics.about.com/cs/freebodydiagrams/a/191003_2.htm <--I remember this website helped me with maths/physics, so Antebellum South - try having a nosey round on there.

alright i have to get this done quick so i wrote in your explanation of uniform tension through the rope. thanks for the help everyone!!!!

Imagine your rope as horizontal. With one end fixed. Now pull on the other end with a force (Newtons). Unless the rope moves, and we have said it is fixed there must be an equal and opposite force to the force you just applied. This force is the tension in the rope. There is no difference in theis force at any point along the rope. Now imagine the rope is not fixed but has a given resistence. 350 kgms-1. You pull with a force of 350 kg kgms-1 no movement, and therefore a tension in the rope of 350kgms-1 If you now pull with a force of 400 kgms-1 the rope moves. the tension in the rope remains at its limit of resistence at 350kgms-1

Now swap the image to one of the rope hung over a pulley. Assume that the pully is frictionless (normal assumption for this type of problem). You have a force applied to each end of the rope these are applied by the masses of the object.. These forces offset, with the lower one defining the tension in the whole rope.

I thought tension was reliant on mass - so, as T = mg (mass x gravity), I'd have thought since the mass differs on either side of the pulley, the tension would be different. However, the load distribution may come into effect - perhaps something is negated because the tension is being distributed across a central axis. I dunno, I never covered questions like this.

Now swap the image to one of the rope hung over a pulley. Assume that the pully is frictionless (normal assumption for this type of problem). You have a force applied to each end of the rope these are applied by the masses of the object.. These forces offset, with the lower one defining the tension in the whole rope.
AAhhhhhh, that makes sense.

F U C K. we just went over this in class, i did not calculate the tension correctly... the correct formula in this case is

Tension = 2 * m1g * m2g / (m1g + m2g ) :eek:

where m1 is mass of gorilla in kg, m2 is mass of sandbags in kg, g is 9.8 ms-2

final tension is 3659 kgms-2

This class truly rapes me

It's been a long while since I've been in any physics classes, so I can't answer with any sort of formula or rule, but based on logical thinking, it seems to me that Battery Charger's assessment is correct (as is everyone else who said something along these lines)...

This problem really doesn't have anything to do with the pulley itself... The pulley is just a way to set up the situation (and throw a bit of obfuscation into the mix)...

The real situation we have here is simply that a rope is being pulled in opposite directions by two forces... Here's where the pulley comes into play... It's simply a turning point that can make those opposing forces go in seemingly the same direction (I.E. down)...

But again, that doesn't matter, all that matters is that you've got is a 350kg force pulling on one end of the rope, and a 400kg force pulling on the other... So, the tension on the rope's entirety is simply the combination of the two...

[Edit:]
Hmmm, apparently I'm a bit off in this assumption, based on the latest post...

I can't really see why there'd be a difference between a pulley system and a linear application of the same forces, but hey, I'm not in physics class...lol

It's been a long while since I've been in any physics classes, so I can't answer with any sort of formula or rule, but based on logical thinking, it seems to me that Battery Charger's assessment is correct (as is everyone else who said something along these lines)...

This problem really doesn't have anything to do with the pulley itself... The pulley is just a way to set up the situation (and throw a bit of obfuscation into the mix)...

The real situation we have here is simply that a rope is being pulled in opposite directions by two forces... Here's where the pulley comes into play... It's simply a turning point that can make those opposing forces go in seemingly the same direction (I.E. down)...

But again, that doesn't matter, all that matters is that you've got is a 350kg force pulling on one end of the rope, and a 400kg force pulling on the other... So, the tension on the rope's entirety is simply the combination of the two...

[Edit:]
Hmmm, apparently I'm a bit off in this assumption, based on the latest post...

I can't really see why there'd be a difference between a pulley system and a linear application of the same forces, but hey, I'm not in physics class...lol
yeah i thought battery charger and every one else's reasoning was correct. most of the people in my class had similar reasoning too. everyone is right that tension is uniform throughout the rope, but the method of calculation is not as obvious as it appears. everyone in the class tried to explain the calculation using what we thought was 'real world logic'. but the teacher ripped that apart with some manipulation of algebra. next time when i use 'real world logic' i have to keep in mind if it fits with the laws of physics. i completely flunked this homework assignment

Imagine your rope as horizontal. With one end fixed. Now pull on the other end with a force (Newtons). Unless the rope moves, and we have said it is fixed there must be an equal and opposite force to the force you just applied. This force is the tension in the rope. There is no difference in theis force at any point along the rope. Now imagine the rope is not fixed but has a given resistence. 350 kgms-1. You pull with a force of 350 kg kgms-1 no movement, and therefore a tension in the rope of 350kgms-1 If you now pull with a force of 400 kgms-1 the rope moves. the tension in the rope remains at its limit of resistence at 350kgms-1

Now swap the image to one of the rope hung over a pulley. Assume that the pully is frictionless (normal assumption for this type of problem). You have a force applied to each end of the rope these are applied by the masses of the object.. These forces offset, with the lower one defining the tension in the whole rope.
apparently the linear model can be analogous to the pulley model only if on one side of the linear rope there is a force of 3920 kgms-2 (400 kg with acceleration equal to g) and on the opposite side there is a force of 3420 kgms-2 (350 kg with acceleration equal to g). in this case the tension can be calculated with that annoying formula just like with the pully, resulting in tension of 3659 kgms-2

well to the question you asked orignally I would have thought it was because the pulley was frictionless.

I need help with this conundrum. Why is the tension acting on each end of a rope hanging over a pulley the same? One load hangs from each end, and the mass of the two loads are unequal.

EDIT For more clarification:

A 400 kg gorilla is on one end of the rope, a 350 kg sandbag is on the other side of the rope. The rope goes over a pulley . Why is the tension on both sides the same?


you my good friend are a moron. in the above situation the gorrila would experiance a resultant force of 50gN meaning it would fall and probably hit the ground. Fact is the system is not in equilibrium so it doesnt apply

There are 400kg N pulling the rope in one direction and 350kg N pulling the rope in the opposite direction. That makes a total of 50g N pulling the rope in the gorilla's direction. The gorilla and the sandbag are both accelerating in the gorilla's direction and their total mass is 750 kg, so their acceleration is 50g / 750 = 1g/15.

The tension in the rope on the gorilla's side changes its acceleration from 1g to 1g/15. That's a difference of 14g/15. Multiplying the mass by the difference in acceleration gives a tension of 400 * 14g/15 = 1120g/3 N.

The tension in the rope on the sandbag's side changes its acceleration from 1g to -1g/15. That's a difference of 16g/15. Multiplying the mass by the difference in acceleration gives a tension of 350 * 16g/15 = 1120g/3 N.

1120 * 9.8 / 3 = 3659.

You don't need a formula if you know the earlier principles

If you learn to draw decent free-body-diagrams, all your problems will be solved. Kinematics is painfully easy with this tool: just look at the object. and vectorially add up the arrows attached to it. simple. Now, F=ma, and you're off to the races.

i like the one rope idea,
another cheap nonscientific or mathematical way around it is that the sand and ape are supported by something

There are 400kg N pulling the rope in one direction and 350kg N pulling the rope in the opposite direction. That makes a total of 50g N pulling the rope in the gorilla's direction. The gorilla and the sandbag are both accelerating in the gorilla's direction and their total mass is 750 kg, so their acceleration is 50g / 750 = 1g/15.

The tension in the rope on the gorilla's side changes its acceleration from 1g to 1g/15. That's a difference of 14g/15. Multiplying the mass by the difference in acceleration gives a tension of 400 * 14g/15 = 1120g/3 N.

The tension in the rope on the sandbag's side changes its acceleration from 1g to -1g/15. That's a difference of 16g/15. Multiplying the mass by the difference in acceleration gives a tension of 350 * 16g/15 = 1120g/3 N.

1120 * 9.8 / 3 = 3659.
wow either that was a lot of BS or you are extremely intelligent