Question

An Atwood machine is constructed using a hoop with spokes of negligible mass. The 2.3 kg mass of the pulley is concentrated on its rim, which is a distance 23.5 cm from the axle. The mass on the right is 1 kg and on the left is 1.65 kg. The acceleration of gravity is 9.8 m/s^2. What is the magnitude of the linear acceleration a of the hanging masses?

Answer 1

let

M = 2.3 kg,
r = 23.5 cm = 0.235 m

m1 = 1.65 kg
m2 = 1 kg

let a is the acceleration of the blocks

T1 and T2 are the tensions in the string.

T1 = m1*g - m1*a

T2 = m2*g + m2*a

Net Torque acting on pulley, Tnet = T1*r - T2*r

I*alfa = (T1-T2)*r

I*a/r = (T1-T2)*r

I*a = (T1 - T2)*r^2

M*r^2*a = (T1-T2)*r^2

M*a = T1 - T2

M*a = m1*g - m1*a - (m2*g + m2*a)

a*(m1 + m2 + M) = (m1-m2)*g

a = (m1 - m2)*g/(m1 + m2 + M)

= (1.65 - 1)*9.8/(1.65 + 1 + 2.3)

= 1.29 m/s^2