Question

An Atwood machine consists of two masses, mA = 65 kg and mB = 75 kg , connected by a massless inelastic cord that passes over a pulley free to rotate. The pulley is a solid cylinder of radius R = 0.45 m and mass 6.0 kg. Determine the acceleration of each mass

Answer 1

let

m = 6 kg, R = 0.45 m

let a is the acceleration of blocks and alfa is the angular acceleration of the pulley.

let TA and TB are the tensions in the strings connected to block A and B respectively.

net force acting on B, FnetB = mB*g - TB

mB*a = mB*g - TB

TB = mB*g - mB*a ------(1)

similarly, TA = mA*g + mA*a ----(2)

net torque acting on pulley, (TB - TA)*R = I*alfa

(mB*g - mB*a - mA*g - mA*a)*R = (1/2)*m*R^2*a/R

(mB - mA)*g = (m/2 + mA + mB)*a

a = (mB - mA)*g/(m/2 + mA + mB)

= (75 - 65)*9.8/(6/2 + 65 + 75)

= 0.685 m/s^2