Does Newton's third law apply to Atwood's machine?

In summary, the Atwood's machine with two masses, m1 and m2, accelerates in the direction of the heavier mass, m2, due to the application of Newton's second law. This may seem to contradict Newton's third law, but this is because the tension in the string is not equal to the weight of the masses. The tension in the string is equal on both sides of the pulley and does not counteract the force of gravity on each block, as the system is accelerating. Instead, the tension balances with the gravitational force to produce the net acceleration of the system.
  • #1
Syrus
214
0

Homework Statement



Consider Atwood's machine with two masses, m1 and m2 with m1 less than m2. Now, according to application of Newton's third law, the system accelerates in the direction of the heavier mass (here, m2). This, however, seems to contradict Newton's third law, which implies that the interaction between the block and the rope are equal and opposite. That is, the tension of the string should counteract the force of gravity on each block. Obviously, though, there is a fallacy someplace in my argument. Does anyone mind pointing it out?

Homework Equations


The Attempt at a Solution

 
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  • #2
Going by my applied maths textbook and having a quick look at a diagram for an attwood machine. It appears that the force acting on the pulley is eqivilent to 2 times the force of tension in the string over it.

I'll do a quick diagram to show why.
 
  • #3
Syrus said:

Homework Statement



Consider Atwood's machine with two masses, m1 and m2 with m1 less than m2. Now, according to application of Newton's [strike]third[/strike] second law, the system accelerates in the direction of the heavier mass (here, m2).
I think you mean that the center of mass of the system accelerates, with respect to the ground, in the direction of the net force, which is down
This, however, seems to contradict Newton's third law, which implies that the interaction between the block and the rope are equal and opposite.
this is correct regarding Newton 3, but there is no contradiction.
That is, the tension of the string should counteract the force of gravity on each block. Obviously, though, there is a fallacy someplace in my argument. Does anyone mind pointing it out?
the string tension does not counteract the force of gravity. That would be true only if the system is not accelerating. Newton 3 says that if the block exerts a force on the string equal to 'A', then the string exerts an equal and opposite force on the block with a magnitude of 'A'. 'A' is generally not equal to the block's weight.



Homework Equations





The Attempt at a Solution

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  • #4
Heres my quick diagram.

attachment.php?attachmentid=44588&stc=1&d=1330631460.png


Then consider the pulley and only the forces acting directly on it.

attachment.php?attachmentid=44589&stc=1&d=1330631460.png
 

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  • #5
rollcast, it sounds like you're atttesting to Newton's third law holding for the pulley itself and the rope. I perhaps should have made it more clear that i was interested in the third law interaction between the rope and each mass (i.e. that the interactions between the rope and each mass would cancel out and hence the net acceleration should be zero).
 
  • #6
Syrus said:
rollcast, it sounds like you're atttesting to Newton's third law holding for the pulley itself and the rope. I perhaps should have made it more clear that i was interested in the third law interaction between the rope and each mass (i.e. that the interactions between the rope and each mass would cancel out and hence the net acceleration should be zero).

I thought you meant the pulley when you said block as in a pulley block.
 
  • #7
Syrus said:
rollcast, it sounds like you're atttesting to Newton's third law holding for the pulley itself and the rope. I perhaps should have made it more clear that i was interested in the third law interaction between the rope and each mass (i.e. that the interactions between the rope and each mass would cancel out and hence the net acceleration should be zero).

well Syrus, you can still see by his diagram that all of the tension in that set-up cancels out, thus we are left with only the weights, and they are unbalanced
 
  • #8
Shishkabob,

I guess where my confusion arises is in figuring why the tensions are equal when (it seems) they should not be (due to the fact that the blocks are not identical in mass and hence, by N3, the tension force applied to each mass should counteract the gravitational force- whence rendering no acceleration).

A previous remark addressed this issue by stating that the downward force of the mass was not, in fact, equal to the gravitational force acting on it, but i am still failing to grasp why this is so.
 
  • #9
I'm pretty sure it's the weight of the heavier block minus the weight of the less massive block.

Imagine the blocks laid out flat on the ground with the ropes connecting them. Block one has a force acting on it equal to its weight, and the other block has a force acting on it equal to its weight

or even imagine it like two guys pulling on it in opposite directions. One guy pulls with a constant force that is larger than the other guy, which direction does the whole rope-two guy system move?
 
  • #10
Syrus said:
A previous remark addressed this issue by stating that the downward force of the mass was not, in fact, equal to the gravitational force acting on it, but i am still failing to grasp why this is so.
You should apply Newton's 2nd Law to the masses. Let's look at the heavier one, in a free body diagram. Let's say it has a mass of 20 kg, or a weight of 200 N. Newton 2 says that

[itex]F_{net} = ma [/itex], and since the net force is 200 N down and T Newtons up, then

[itex] 200 - T = ma [/itex]

Now since the system is accelerating and not at rest, then the acceleration is greater than 0, and thus, T must be less than the gravitational force of 200 N.

The tension of a string wrapped around a frictionless and massless ideal pulley is always the same on both sides of the pulley.

Newton 3 holds for all cases of accelerating or non accelerating bodies. In this case, the rope exerts a force of T upward on the 20 kg mass, so the mass exerts an opposite force of T downward on the rope. T is not equal to 200 N. Newton 3 refers to equal and opposite forces on different objects. Newton 2 applies to forces on the same object.
 
Last edited:

Related to Does Newton's third law apply to Atwood's machine?

1. How does Newton's third law apply to Atwood's machine?

According to Newton's third law, for every action there is an equal and opposite reaction. In the case of Atwood's machine, the two masses suspended by a pulley are exerting equal and opposite forces on each other. The heavier mass exerts a greater downward force, causing the lighter mass to accelerate upwards.

2. What is the relationship between Newton's third law and Atwood's machine?

Newton's third law states that forces always occur in pairs. In Atwood's machine, the two masses experience equal and opposite forces, and these forces are what cause the system to move and accelerate.

3. Does Newton's third law only apply to Atwood's machine?

No, Newton's third law applies to all objects and systems in motion. It is a fundamental law of physics that can be observed in everyday situations, not just in Atwood's machine.

4. Can Newton's third law be seen in Atwood's machine?

Yes, the equal and opposite forces between the two masses in Atwood's machine can be visually observed as the heavier mass accelerates downwards and the lighter mass accelerates upwards.

5. How does understanding Newton's third law help to explain Atwood's machine?

By understanding Newton's third law, we can see that the forces exerted by the masses in Atwood's machine are equal and opposite, and this helps us to explain why the system moves and accelerates in the way it does. It also allows us to make predictions about the behavior of the system based on the known forces acting on it.

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