Non ideal pulley with two masses

[Voitonic]

Hi,

So I have a problem with a question upon reviewing a past physics final.

Two boxes are connected by a massless, unstretchable rope that passes over a non-ideal pulley. The radius and mass of the pulley are R = 0.100m and M = 1.75 kg. As the pulley turns, friction at the axle exerts a constant torque of magnitude of 0.480 Nm. The moment of inertia of the pulley is 1/2MR². Box B1 has a mass m₁=3.98 kg and its initial location is 0.850 m above the floor. Box B2 has a mass of m₂= 2.01 kg and its initial location is at the floor. After the boxes are released from rest, B1 descends to the floor, while B2 is lifted.

I'm trying to solve for the tension between each section of rope and the pulley as well as finding the acceleration of each box.

Any help would be appreciated,
Thanks!

 

[K^2]

It's rather straight forward.

m₁, m₂ - the two masses.
a₁, a₂ - corresponding accelerations.
T₁, T₂ - corresponding tensions.
α - angular acceleration of the pulley.
I, R - relevant properties of the pulley.
τ_f - friction torque.

Consider m₁ descending, m₂ rising as positive direction.

$$m_1 a_1 = m_1 g - T_1$$

$$m_2 a_2 = T_2 - m_2 g$$

$$I \alpha = T_1 R - T_2 R - \tau_f$$

$$a_1 = a_2 = \alpha R$$

Rest is just algebra.

P.S. When solving a problem like this, just write out equations of motion for every degree of freedom you have, then add any available constraints.

 

[Voitonic]

Thanks for the help.

You're right, after looking at it again the question is pretty straight forward. I guess I just need to learn how to organize my thoughts better.