This is a common physics problem and it mentioned in several textbooks.
45. An Atwood machine (shown in figure below) 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 kg. (a) Determine the acceleration of each mass. (b) What % error would be made if the moment of inertia of the pulley is ignored? [Hint: the tensions FTA and FTB aare not equal]
Analyze the problem:
It is an Atwood typical problem but here the pulley’s mass is not ignored and the tensions forces are different for the same cord. Having the pulley’s mass ignored and the tension being the same for the single cord simplify the problem, so here we have to approach the problem in different way but using the same methods (Newton’s laws!).
What are the given information?
- Block A mass, mA = 65 Kg
- Block B mass, mB=75 Kg
- Pulley mass, M=6 kg
- Pulley Radius, R=0.45 m
What are needed information?
- Acceleration of both blocks.
- Percentage error of the two cases (the pulley’s moment of inertia is ignored and the pulley’s moment of inertia is not ignored).
- Finding the acceleration of the two blocks:
2. Finding the percentage error: