Finding pulley mass in Atwood's machine using energy conservation

[Tanahagae]

Homework Statement

The two masses (m₁ = 5.2 kg and m₂ = 2.6 kg) in the Atwood's machine shown in The Figure are released from rest, with m₁ at a height of 0.79 m above the floor. When m₁ hits the ground its speed is 1.7 m/s.

Assuming that the pulley is a uniform disk with a radius of 12 cm, outline a strategy that allows you to find the mass of the pulley.

Determine the pulley's mass.

Homework Equations

Rotational Kinetic Energy: K + (1/2)Iw²
Conservation of Energy: K_i + U_i = K_f + U_f

The Attempt at a Solution

I am more or less stumped on this problem. Information that is known is that v₀ = 1.7 m/s and v_f = 0. The E_i = mgh (I think since the system starts at rest and m₁ has Gravitation Potential Energy). E_f = (1/2)mv² + (1/2)Iw². All this is speculation since I am grasping at a way to solve this problem.

Also, from looking at other related problems people tend to find acceleration through the Kinematics v² - v₀²/2(x - x₀). However, I am not sure how to apply the acceleration of m₁, all I know is that it translates through the pulley system.

Another possible acceleration I found was a = [(m1 - m2)/(m1 + m2)]g. This formula brought up a different acceleration than the previous, but once again I am not certain how to apply it.

Reassurance that I am on the right route, and a hint would be greatly appreciated.

 

[Buttons840]

What is the question? Your problem is nothing but stated facts, and there is no question. Literally, not a single question mark.

 

[Tanahagae]

Thank you for bringing that to my attention. I have spent so much time belaboring the issue through my mind that I completely forgot to actually spell out the question.

Although, no question marks does not mean there exist no questions.