What are the forces on the center of mass?

[eprparadox]

Homework Statement

[/B]
A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from rest the heavier object moves downward and the lighter object moves upward with the same magnitude acceleration. Which of the following statements is true for the system consisting of the two masses?

A. The center of mass remains at rest.
B. The net external force is zero.
C. The velocity of the center of mass is a constant.
D. The acceleration of the center of mass is g, downward.
E. None of the above statements are true.

Homework Equations

The Attempt at a Solution

The answer is E for this question, but I'm stuck on justifying choice B.

In particular, I want to be able to draw out the forces on this system of two masses. I don't know how to account for the tension in the rope on both sides and gravity.

I think I have trouble in general when talking about "system" like this and drawing out the forces. Any thoughts on how to draw out this force diagram?

 

[PeroK]

I'm not sure what exactly your problem is. The tension in the string has to be calculated, but as the pulley is frictionless the tension must be the same on both sides. That said, you don't really need to consider the tension to rule out option B.

Can you see a simple argument to rule out option B? Why do you think the external force might be zero? What would happen to the system if it were?

 

[eprparadox]

Hey @PeroK thanks for the response.

If the external forces are zero, then the center of mass can't accelerate. But intuitively, this doesn't make sense because there is an external force due to the gravitational acceleration downward.

But then that has me asking what other forces are acting on the center of mass that are preventing it from just simply falling with acceleration of $g$ downward?

Thanks again

 

[Suyash Singh]

approach all problems one by one and see if they are true
I am no expert so correct me if i am wrong
A)Hint: masses are moving with same acceleration
B)Hint:Draw diagram and use formulas
C)Hint:same as A
D)Hint:same as A

As an example i will tell you this
If we throw a particle in parabolic path and it breaks into 2 or more pieces the center of mass will continue to travel along the same path.

 

[PeroK]

Hey @PeroK thanks for the response.

If the external forces are zero, then the center of mass can't accelerate. But intuitively, this doesn't make sense because there is an external force due to the gravitational acceleration downward.

But then that has me asking what other forces are acting on the center of mass that are preventing it from just simply falling with acceleration of $g$ downward?

Thanks again

Okay, if you approach the problem that way, then you need to look at the other forces (tension).

But, if you look at the problem differently ...

Hint: you don't need to calculate the acceleration of the centre of mass; you just need to know that it is accelerating.

 

[Dr Dr news]

You might start by locating the center of mass and following it in time and space.

 

[PeroK]

As an example i will tell you this
If we throw a particle in parabolic path and it breaks into 2 or more pieces the center of mass will continue to travel along the same path.

Which isn't very helpful.

 

[Dr Dr news]

You know the driving force and the total mass being accelerated.