Why Does an Atwood's Machine Behave as It Does?

[Leilei]

Okay, I had to do a problem concerning the Atwoods machine over the weekend. I'm not doing very well in Physics right now, and I don't have any friends in that class, so I thankfully found this place. I have already tried thinking about these problems...

1. If two objects of equal mass are suspended from either end of a string passing over a light pulley (an Atwood's machine), what lind of motion do you expect to occur? Why?

I said that if the two objects of equal masss are suspended over a light pulley, the objects will move only until they are both at wqual distances from the ground. Then they will not move at all.

But the part I'm stuck on is -- why? Why does this occur? How can I explain this correctly?

2. For an Atwood's machine, how would you expect the acceleration to change if you:

- Move mass from one side to the other, keeping the total mass constant?

I'm not sure if this is correct: I said, the acceleration would increase. The mass of one side is gerater than the mass of the other, meaning the heaver side has a greater weight force (mg) acting upon it equating to a greater accelearation.

- How about if you gradually increase the mass of both sides, keeping the difference in mass constant?
I said the acceleration will remain the same because ratio of masses are equal. I am not sure if this is correct either.

3. Why do the two masses have the same acceleration?
I said the two masses have the same acceleration because the tension throughout the string is equal. The combined mass pulls each other at the same rate becauseb oth have the same foreces acting upon them.

I'm not sure at all if any of my answers are correct. What I need the most help on is #1. If somebody could help me, I would appreciate it very much.

 

[HallsofIvy]

Please do not post the same question on two different forums.

 

[M98Ranger]

Hi there,

First of all, don't worry, it's completely normal to struggle with physics and it's great that you're seeking help! Let's go through your answers and see if we can clarify things for you.

1. Your answer is correct! The reason why the objects will eventually stop moving is because they reach a state of equilibrium where the tension in the string is equal on both sides, meaning the forces on both sides are balanced. This is also known as the "principle of moments" or "principle of balanced forces". In simpler terms, the objects will stop moving because there is no net force acting on them.

2. Your answer for the first part is correct. When you move mass from one side to the other, the heavier side will have a greater weight force and thus a greater acceleration. For the second part, your answer is not quite correct. The acceleration will actually decrease as the total mass increases, because the weight force (mg) is also increasing. This means that the net force and thus the acceleration, which is directly proportional to the net force, will decrease.

3. Your answer is correct! The reason why the two masses have the same acceleration is because they are connected by the same string and thus experience the same tension force. This tension force is what causes the acceleration, and since it is equal on both sides, the acceleration will also be equal.

I hope this helps clarify things for you. Keep practicing and seeking help when needed, and you'll do great in your physics class!