What is the relationship between tension and net force in Atwood machines?

[JeweliaHeart]

Hello. I am learning about tension in Atwood machines( ideal pulley, frictionless mass, etc.) and I am having trouble grasping the concept of tension.

I thought that the tension in a rope should be equal to the net force on both masses. That way the forces are balanced out and the masses are at some sort of equilibrium (rest).

But my text is saying:

For a system where m2> m1

Fnet= T- m1g= m1a

Fnet= m2g -T=m2a

These net forces are not assumed to be equal to each other thought, but why not?
They should be equal to one another or at least there should be some balancing force opposite but equal in magnitude to the sum of these net forces, right? Otherwise, there will be a net acceleration in one direction and the system will not be at rest. *scratches head*

 

[Doc Al]

These net forces are not assumed to be equal to each other thought, but why not?
They should be equal to one another or at least there should be some balancing force opposite but equal in magnitude to the sum of these net forces, right? Otherwise, there will be a net acceleration in one direction and the system will not be at rest. *scratches head*

Why would you think an Atwood's Machine with unequal masses would be in equilibrium? Of course there is a net acceleration! And the net force on each mass must be different. (However the acceleration of each mass would be the same magnitude.)

 

[JeweliaHeart]

Are you saying that the masses are moving? I imagined them being stationary, being held by the rope, one mass at a higher height than the other, and the tension in the rope being created by the forces on opposing sides.

 

[dreamLord]

Yes, the masses are moving. The heavier mass moves down, and the lighter mass up, both by the same amount which is why their acceleration is the same.

 

[JeweliaHeart]

But don't they eventually come to a resting point in the air or do they both eventually reach to the ground, the heavier one leading the lighter one?

 

[Doc Al]

Are you saying that the masses are moving?

If the masses are unequal, then they will accelerate. So sure they are moving!

I imagined them being stationary, being held by the rope, one mass at a higher height than the other, and the tension in the rope being created by the forces on opposing sides.

The only time the masses would be stationary, is if the masses were equal (and started from rest).

The best way to find the tension, under any circumstance, is to apply Newton's 2nd law to each mass separately, just like your book advises. You'll get two equations which will allow you to solve for the two unknowns: the tension in the rope and the acceleration of the masses.

 

[Doc Al]

But don't they eventually come to a resting point in the air or do they both eventually reach to the ground, the heavier one leading the lighter one?

They do not come to rest; the acceleration remains constant until one of them hits something. The heavier one falls while the lighter one rises--sooner or later one of them will smack into something.

 

[swooshfactory]

The Atwood machine connects two masses by a pulley (the pulley is assumed to be massless and frictionless; these are assumptions that make the pulley ignorable except that when one mass goes up the other goes down.) The only way the two unequal masses in this situation would come to rest is if one hits and stays on the ground.

 

[JeweliaHeart]

Okay. Thanks so much. I understand the net acceleration part now.
There is net acceleration and they will both eventually reach the ground, right, b/c there is no friction on the pulley to stop them, right?

 

[JeweliaHeart]

Oops. Sorry, for repeating question. Didn't see the answers above.