Fletcher’s Trolley (Hanging Mass Problem)

1. The problem statement, all variables and given/known data
A 1.20kg object is placed on a smoothe level table and is attached to a hanging mass using a light string over frictionless pulley in a Fletcher’s trolley arrangement. The 1.20kg object accelerates along the table at 2.31m/s^2 while the hanging object accelerates down at the same rate. Determine the

a. Mass of the hanging object

b. tension in the string

3. The attempt at a solution

I drew 2 FBDs with the forces acting on each individual mass.

We know that Fapp = Fg2 = T

What I can’t figure out is a formula that rearranges the variables to find m2

For example, I know that a = F/∑m

But we don’t know what ∑m is.

We could relate Fapp to Fg2, but to do that we’d need to know m2

We can relate T to Fapp or Fg2, but we’d need to know m2…

You can see my dilemma. I’ve tried a good 10 different formulas, and now I’m just spitballing. I have no idea how I am supposed to create a formula that tells us m2 without knowing F

Please help.

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