Question

An Atwood machine is constructed using two

wheels (with the masses concentrated at the
rims). The left wheel has a mass of 2.5 kg and
radius 22.2 cm. The right wheel has a mass
of 2.7 kg and radius 27.49 cm. The hanging
mass on the left is 1.59 kg and on the right
1.24 kg
m
mz
What is the acceleration of the system?
The acceleration of gravity is 9.8 m/s.
Answer in units of m/s.

Answer 1

Left:
2*g-TL=2*aL
aL=α*0.231
therefore
TL=2*(g-α*0.231)

Right:

TR-1.4*g=4*aR
aR=α*0.272
therefore
TR=1.4*(g+α*0.272)

Wheels:
TL*0.231-TR*0.272=
(2*0.231^2+2.3*0.272^2)*α

combine and solve for α