Masses Over a Uniform Cylindrical Pulley

[Cdh0127]

ηϖ1. Homework Statement

Homework Equations

I=½MR²
PE=mgh

The Attempt at a Solution

The first thing that jumped out at me was "uniform cylinder" so I went ahead and calculated the moment of inertia for the cylinder and got I=½(4.4)(.4)² = .352 and held onto that.

Then, I calculated the forces due to gravity of each mass that is pulling down on the string.
F_mb = 48kg×9.8m/s² = 470.4N
I'm not sure if I do the same for m_a because it's resting on the table, so is there a force pulling on the string creating tension?

But the next thing I did was find the gravitational potential energy of m_b:
PE = mgh = 48kg×9.8m/s²×2.5m = 1176 J.

I'm not sure if torque is needed, but I went ahead and calculated it anyways:

T=F×r = 470.4N×.4m = 188.16

And that is all I can think to do. I'm not sure how the radius, inertia, mass, and other properties of the pulley affect the masses A and B that move up and down via the string over that pulley.

Could I take the 1176 J of potential energy and set it equal to ½mv²? But what mass would I use? Mass of the system (A + B)? Solve for V? That seems too simple for this section, because we are learning about angular kinematics, torque...etc. I think I'm missing something.

Thank you for your time and advice!

 

[BvU]

Hi there,

The hint in the exercise is pretty clear: use energy considerations. So list off all the energies (my clue: there's more than you mentioned so far, but you are thinking in the right direction) at t=0 at at t = bump.

Extra tip: does the $\bf I$ you calculated have any influence ? (Imagine a huge R0 to decide)