How Is Tension Calculated in an Atwood Machine with Equal Masses?

[darealprince]

Homework Statement

In an atwood machine which is a pulley with two wieghts attached to it (m1 and m2), m1= m2, how much tension is found on the string? I thought that it would be zero tension on the string but that appeared to be wrong. How would you solve it?

The Attempt at a Solution

 

[akfortyseven]

Well first of all, you should acknowledge that the system has no acceleration. A pulley with equal masses will have no acceleration. Also, if the masses are equal, you no longer need the subscripts. Just label both of them "m."

You can either do the drawing the free body diagrams or figure out the sum of the forces. Let's start out with the sum of the forces.

The formula for the sum of the forces (if you don't already know) is netForce=mass*acceleration. Since there is no acceleration, mass*acceleration would equal zero since acceleration is zero.

Now let's draw the free body diagrams. For m1 and m2, there are two forces acting upon it: tension of the string "T" and the force of gravity acting upon the mass. Since you know the net force is zero, the tension of the string and the force of gravity on the mass is equal. If you don't already know, force of gravity = mass*gravity. So for both masses, the net force would look like this: Tension - mass*gravity=zero or Tension=mass*gravity (T=mg).

 

[darealprince]

I recalculated the tension and i got 2mg since the masses were the same but it was wrong. So since the masses are the same would it just be g? or 2g?

 

[akfortyseven]

I recalculated the tension and i got 2mg since the masses were the same but it was wrong. So since the masses are the same would it just be g? or 2g?

Ok. If you do the net force for each mass, both of them turn out to be T=mg. All you need to do is plug in the things you know since the equation is already solved for tension, the value you're trying to find. Tension = mg. It would just be g.

Does that clear it up? I'm not sure if I explained it well.