Tensions over a pulley, 3 objects connected with 2 strings

[gmorrill]

Homework Statement

The string connecting the m₁ and the m₂ passes over a light frictionless pulley. Given m₁ = 6.51kg, m₂ = 7.48kg, m₃ = 9.75kg. The acceleration of gravity is 9.8 m/s².

1) Find the downward acceleration of m₂ mass. Answer in units of m/s²

2) Find the tension in the string connecting the m₁ and m₂ masses. Answer in units of N.

3) Find the tension in the string connecting the m₂ and the m₃ masses. Answer in units of N.

Picture is embedded in PDF, but easy to describe:
A single pulley hanging from ceiling, on the right side of the pulley the string goes down to connect to m₁. On the left side of the pulley the string goes down to connect to m₂. Then a string connects m₂ to m₃ below it.

I've already solved #1 and #2, I'm stuck on #3.

Homework Equations

a = [(m₁ - m₂) / (m₁ + m₂)] * g
T = [(2m₁ * m₂) / (m₁ + m₂)] * g
derived in class

The Attempt at a Solution

I extended those formulas to 3 masses (instead of just 2) to calculate the acceleration 4.42527 m/s² and T₁ = 92.6065 N.

I've tried drawing force diagrams and adding the components to find T₂ several ways, but I'm getting confused.

This is a practice homework where we're given the answers - then our real homework is through UT and uses the same problems with different numbers; so I know my answers to 1 and 2 are correct, and #3 I'm not getting the correct answer. The answer is supposed to be 52.4036 N.

 

[Delphi51]

Consider the forces on m3. There is m3*g down and the Tension up. Use
sum of forces = ma

 

[gmorrill]

Heh, figures it's way simpler than I was trying. I was trying to add the Tension of the first string over the pulley along with the weight of m1, then subtracting the weight of m2 and m3.

Many thanks!