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## Homework Statement

I am stuck on this problem:

So the question is asking for F

_{21}, F

_{12}, F

_{32}, and F

_{23}. (That's the force by 2 on 1).

The mass of m

_{2}is variable.

There are four cases where I need to solve for the forces: when m

_{2}has mass of 3kg, 0.3kg, 0.03kg, and 0kg.

The mass of m

_{1}= 2.5kg, the mass of

_{3}= 3.5kg.

Also assume that friction is neglected.

I am confused on how to resolved the tension force in a system with numerous objects.

The T is constant, 3N. imagine there's a person pulling on the string with a constant force of 3N.

I know the acceleration of all three carts in each case should be the same.

But how do I solve for the tension force in the strings between the carts?

## Homework Equations

F=ma

Newton's 3rd Law

Pretty sure that's all I really need here.

## The Attempt at a Solution

[/B]Ok, so I drew free-body-diagrams for each case. I know T is always equal to 3N. The weight force and normal force of all three carts aren't taken into account.

Should the tension force in the strings be constant?

Suppose I were to do case 1 with m

_{2}= 3kg:

T=3N

F

_{net}= 3N

3 = (m

_{1}+m

_{2}+m

_{3})a

a = 3/(2.5+3+3.5) = 0.33 m/s/s (for the whole system, so each cart has the same acceleration)

Going from left to right, solving for F

_{23}, would the force m

_{2}on m

_{3}be equal to (m

_{2}+m

_{1})0.33?

Then would F

_{32}be equal in magnitude but in the opposite direction of F

_{23}because of Newton's 3rd Law?

I'm not sure what to include or exclude when I'm calculating a force within a specific part of a system.

Any pointers would be very helpful. Thanks.