Question

# An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes...

An Atwood's machine consists of two masses, m1 and m2, connected by a string that passes over a pulley. If the pulley has radius and moment of inertia 1/2 MR^2 about its axle. Determine the acceleration if masses m1 and m2. Compare the situation in which moment of inertia is ignored

let tension in string connecting the mass m2 is T2 and tension in string connecting to mass m1 is T1.

let acceleration of the system be a m/s^2.

assume m2> m1

writing force equation for m2:

m2*g-T2=m2*a

==>T2+m2*a=m2*g....(1)

writing force equation for the pulley:

torque=moment of inertia*angular acceleration

==>T2*R-T1*R=0.5*M*R^2*(a/R)=0.5*M*a*R

==>T2-T1=0.5*M*a....(2)

writing force equation for mass m1:

T1-m1*g=m1*a

==>T1-m1*a=m1*g...(3)

from equation 1, T2=m2*g-m2*a

from equation 2, T1=m1*g+m1*a

using these in equation 2:

m2*g-m1*g-m2*a-m1*a=0.5*M*a

==>(m2-m1)*g=(0.5*M+m1+m2)*a

==>a=(m2-m1)*g/(ma+m2+0.5*M)

when moment of inertia is ingored,

acceleration becomes (m2-m1)*g/(m1+m2)

so acceleration in case of pulley with moment of inertia is lesser.

#### Earn Coins

Coins can be redeemed for fabulous gifts.