Tension from two carts & hanging object on pulley

[Huski]

Homework Statement

Hi. My problem (from my picture) is which string (A or B) has more tension when the 50g object accelerates down and both carts move left. The pulley and string can be considered massless and frictionless.

Homework Equations

Fnet = m*a

The Attempt at a Solution

My thinking is string B has more tension than string A once they're accelerating left. I think this the reason because according to Newton's 2nd Law, F=ma, the string in between the carts has more force since the objects between it (carts 1 & 2) have a bigger mass than the what the two objects string A is in between (hanging mass and cart 1).

 

[haruspex]

Homework Statement

Hi. My problem (from my picture) is which string (A or B) has more tension when the 50g object accelerates down and both carts move left. The pulley and string can be considered massless and frictionless.

Homework Equations

Fnet = m*a

The Attempt at a Solution

My thinking is string B has more tension than string A once they're accelerating left. I think this the reason because according to Newton's 2nd Law, F=ma, the string in between the carts has more force since the objects between it (carts 1 & 2) have a bigger mass than the what the two objects string A is in between (hanging mass and cart 1).

F=ma relates the net force acting on an object, the mass of the object, and the resulting acceleration of the object.
What is the net force on B? What is the net force on A?

 

[Huski]

There are no numerical values if that's what you're wondering. I believe the net force on object 2 is greater than object 1.

 

[haruspex]

There are no numerical values

You don't need them. Let the tensions in the strings be T₁ and T₂, the masses be m and the acceleration a. Write the ΣF=ma equation for each cart.

I believe the net force on object 2 is greater than object 1.

But they have the same masses and acceleration, so how can that be?

 

[Huski]

But they have the same masses and acceleration, so how can that be?

Ok, so looking at my FBD, tension T₂ on cart 1 wants to pull right while T₂ on cart 2 wants to pull left. The tension for T₁ shows that it's pulling left and the hanging mass has T₁ point up, but pointing up shouldn't effect anything because the pulley is frictionless. So maybe then the tensions are the same for both strings if this is the case?

 

[Huski]

No forget what I said, if the object accelerates left, the tension has to be stronger in string A.

 

[haruspex]

No forget what I said, if the object accelerates left, the tension has to be stronger in string A.

Yes. That string has to have enough tension to accelerate both carts, whereas string B is only accelerating one.

 

[Huski]

That makes sense. Thank you!