Atwood Machine, two masses + two pulleys (w/ mass)

[destrow111]

Homework Statement

An Atwood machine is constructed using two
wheels (with the masses concentrated at the
rims). The left wheel (m1) has a mass of 2.1 kg and
radius 21.44 cm. The right wheel (m2) has a mass
of 2.8 kg and radius 33.94 cm. The hanging
mass on the left (m3) is 1.53 kg and on the right (m4)
1.13 kg.

Homework Equations

Sum of Torque1= (m3)g(r1) - T(r1) = (m1)(r1)a
Sum of Torque2= T(r2) - (m4)g(r2) = (m2)(r2)a

The Attempt at a Solution

used subsitution to solve for a...
a = ((m3)g - (m4)g) / ((m1) + (m2))

 

[tiny-tim]

welcome to pf!

hi destrow111! welcome to pf!

(try using the X₂ icon just above the Reply box )

Sum of Torque1= (m3)g(r1) - T(r1) = (m1)(r1)a
Sum of Torque2= T(r2) - (m4)g(r2) = (m2)(r2)a

i'm not sure what the set-up is, but looking at those two equations, if T is an unknown, then you need to eliminate T …

how would you do that? ​

 

[destrow111]

I actually figured it out!

there were actually three different tensions so i added sum of forces equations for each of the masses then subsituted a couple times until acceleration was the only unknown!

ended up being a = (g(m₃ - m₄)) / (m₁ + m₂ + m₃ + m₄)