Is Tension in Equilibrium Achievable with Two Connected Blocks?

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SUMMARY

The discussion centers on the equilibrium of two blocks of equal mass connected by a cord and pulley system, with one block hanging off a cliff. It is established that the blocks will not be in equilibrium if friction is absent, as the hanging block will exert a downward force, causing the top block to slide off the cliff. The key takeaway is that without friction, the forces acting on the blocks are unbalanced, leading to motion. The analysis highlights the importance of considering the entire system and the role of static friction in determining whether the blocks can remain stationary.

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Hi, according to my understanding of tension, if I had two blocks of equal masses connected by a cord and a pulley (one on a cliff and the other hanging off a cliff), would they be in equilibrium? The block hanging would pull the cord down by mg, and then the cord will pull the block on top, and then by Newton's third law, the block will pull back equally.. Is this right? thank you
 
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holezch said:
Hi, according to my understanding of tension, if I had two blocks of equal masses connected by a cord and a pulley (one on a cliff and the other hanging off a cliff), would they be in equilibrium? The block hanging would pull the cord down by mg, and then the cord will pull the block on top, and then by Newton's third law, the block will pull back equally.. Is this right? thank you

They would only be in equilibrium if the block on the cliff can resist the forward pull (from the pulley) through friction. Otherwise the block on the cliff would slide forward.
 
thanks for the reply, I'm assuming that there is no friction. Could you tell me what went wrong with my "analysis"?

mg pulls on cord from the bottom, cord pulls on top mass by mg but by Newton's third, it pulls back on the cord by mg? So the force applied to the top mass would've been mg but it's mg - mg because of the reaction force..?

thanks
 
I don't understand where the pulley comes into this system. Please elaborate.
 
http://www.physics247.com/physics-homework-help/008.jpg

I found a picture of something that is visually like my scenario, only in my case, all the masses are equal

thanks
 
Ahh I understand now, and yes, without friction and assuming the pulley is ideal, the block on the cliff would slide off. This is because what the block hanging off the cliff is doing is applying a tension force to the rope, which is causing the rope to apply a force on the block on the cliff. Without friction, the forces are unbalanced, which means the block would move and fall off the cliff.

A situation where the two blocks would be in equilibrium is if the cliff was removed, and both blocks were hanging; with the pulley in the middle of the rope.

Hope this helps.
 
Thanks, yes but wouldn't the block on the cliff pull back on the cord with the same force?
 
oops, I don't mean equilibrium I guess, I mean that the hanging block won't fall down

thanks
 
008.jpg

The mass on top has a net force acting to the right, due to the tension in the rope. With no friction, that is the only horizontal force acting on that mass, therefore it must accelerate to the right.
 
  • #10
holezch said:
Thanks, yes but wouldn't the block on the cliff pull back on the cord with the same force?

Yes, and that force pulling back on the rope is friction; the force resultant from the contact of the cliff to the block, that resists motion.

So, in a friction-less situation, the block will fall.

In situation with friction, the block might or might not fall; depending on the coefficient of static friction.
http://upload.wikimedia.org/wikipedia/commons/4/4f/Friction_alt.svg
This is a pretty good picture of a free body diagram of something similar to your problem. Just imagine that your rope is tied to the left side of the block, that contact would give you your 'F' force, the force that is trying to move the block. The friction force then is parallel to the surface the block is placed on, and resists movement. That is the F_{f} force.
There is no internal force of the block that resists movement, it is friction.
 
  • #11
thanks for the replies guys, RedBelly89 , I guess I wasn't talking about the top block, I'm really asking if the dangling block will move down? (I don't think so, since by Newton's third law, the top block pulls back on the rope by the same force)

and KrisOhn, I was talking about the reaction force, by Newton's third law, as the cord pulls the top block, the top block will pull the cord.. so will the dangling block move?
it seems impossible that the dangling block won't move as the top one does.. but applying Newton's laws seems to suggest this to me..

thanks guys
 
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  • #12
holezch said:
will the dangling block move?

If one block moves, the other will since they`re joined by a rope.

And yes, the reaction force from the dangling block`s weight is essentially force `F` in the diagram I linked to. And the `top block pulling the cord` force is friction.

As for whether the block moves or not, I cannot say, it is dependent on the coefficient of static friction for that surface.

I`m not sure how to explain it much simpler than that.
 
  • #13
KrisOhn said:
If one block moves, the other will since they`re joined by a rope.

And yes, the reaction force from the dangling block`s weight is essentially force `F` in the diagram I linked to. And the `top block pulling the cord` force is friction.

As for whether the block moves or not, I cannot say, it is dependent on the coefficient of static friction for that surface.

I`m not sure how to explain it much simpler than that.

thanks, I'm downloading an svg viewer so I can view your picture.

But the top block will pull the cord even if there is no friction, isn't that true?? it exerts a reaction force on the cord?

the cord pulls down the block, so the block pulls the cord up. :S
 
  • #14
holezch said:
thanks, I'm downloading an svg viewer so I can view your picture.

But the top block will pull the cord even if there is no friction, isn't that true?? it exerts a reaction force on the cord?

SVG viewer? I've never heard of those, I just open those files in my browser, always have, its the first picture on the wiki page for friction if you want an easier option...

I'm going to use an analogy, explaining this should not be so difficult. Let's say you're skiing, you tie a rope to a rock that is the same mass as you, and then kick the rock off the side of a cliff. You hold onto the rope. When the rope becomes taught, there is a force exerted on your hands by the rope, this is similar to the force exerted by the rope on the block. And since you are on skis, the coefficient of static friction is low enough that you will start to slide, and acceleration will occur.
 
  • #15
KrisOhn said:
SVG viewer? I've never heard of those, I just open those files in my browser, always have, its the first picture on the wiki page for friction if you want an easier option...

I'm going to use an analogy, explaining this should not be so difficult. Let's say you're skiing, you tie a rope to a rock that is the same mass as you, and then kick the rock off the side of a cliff. You hold onto the rope. When the rope becomes taught, there is a force exerted on your hands by the rope, this is similar to the force exerted by the rope on the block. And since you are on skis, the coefficient of static friction is low enough that you will start to slide, and acceleration will occur.

I know what you're trying to say about friction, there must be a force applied onto THE BLOCK so if the block is not to move towards the cliff.. But I'm still confused about Newton's third law! So, the dangling block pulls the cord by mg.. mg pulls the top block so that it moves horizontally.. but for every action there is an opposite but equal reaction.. so the top block exerts a reaction force of mg onto the rope.. so the block is exerting an equal force onto the rope.. what happens to the dangling block? the dangling block exerts mg down on the cord, and the top block exerts a force up onto the cord in the other direction.. so in a free body diagram of the bottom block, shouldn't there be a force T pulling it up?
thanks
 
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  • #16
holezch said:
So, the dangling block pulls the cord by mg.. mg pulls the top block so that it moves horizontally.. but for every action there is an opposite but equal reaction.. so the top block exerts a reaction force of mg onto the rope.. so the block is exerting an equal force onto the rope..

The friction force is top block's reaction force.
 
  • #17
You're assuming that the whole system is in free fall. It's not. Consider the system of two masses. The net force on the system is just the weight of the hanging block (mg). But the total mass of the system is 2m. So the acceleration of the system is g/2. Now, with what force much *each* block be pulled on in order to accelerate at g/2? The answer is that each block has a net force of mg/2 on it. Since the hanging block has a force of mg acting on it downward, there must therefore be an upward force of mg/2 acting on it (in order to get the required net downward force). That result tells you what the tension in the rope is. It's totally consistent as well, because if the rope is pulling with mg/2 at one end, then it is pulling with force mg/2 at the other end as well (explaining the acceleration of the block on the surface).

Newton's Third Law is certainly true. The force with which the hanging block pulls down on the rope is certainly the same as the force with which the the rope pulls up on the hanging block.
 
  • #18
cepheid said:
You're assuming that the whole system is in free fall. It's not. Consider the system of two masses. The net force on the system is just the weight of the hanging block (mg). But the total mass of the system is 2m. So the acceleration of the system is g/2. Now, with what force much *each* block be pulled on in order to accelerate at g/2? The answer is that each block has a net force of mg/2 on it. Since the hanging block has a force of mg acting on it downward, there must therefore be an upward force of mg/2 acting on it (in order to get the required net downward force). That result tells you what the tension in the rope is. It's totally consistent as well, because if the rope is pulling with mg/2 at one end, then it is pulling with force mg/2 at the other end as well (explaining the acceleration of the block on the surface).

Newton's Third Law is certainly true. The force with which the hanging block pulls down on the rope is certainly the same as the force with which the the rope pulls up on the hanging block.

okay, thanks a lot, I think it's clear to me now - I wasn't considering the system as a whole.. it's interesting to see that I've made an incorrect assumption without even knowing it, could you tell me where in my "argument" my assumption that the whole system is in free fall occurs? Is it when I said that the bottom block pulls the cord down by mg as the top one pulls it up by mg? so if the system were in free fall, would it still not be an equilibrium?

EDIT: ah yeah, that does make sense, in the free fall version, there are 2 forces moving the system, the weight of the bottom one and the weight of the top one, so the total force of the system is 2mg.. then it's analogous to what you just explained just now.. :)

thanks, I really appreciate it.
 
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  • #19
KrisOhn said:
The friction force is top block's reaction force.

that's not Newton's third law, the force of friction will have its own action-reaction pair, as the tension has its own action-reaction pair.. they are only caused by single forces themselves
 
  • #20
holezch said:
that's not Newton's third law, the force of friction will have its own action-reaction pair, as the tension has its own action-reaction pair.. they are only caused by single forces themselves

It simplifies things a bit, but I see problems with my statement of that. Disregard it :(
 

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