Calculating Tension Using Work Energy Theorem

[JHLee]

Hi, I have a homework and I kind of stuck on it. Here is the question:

A 17 kg object on a rough ramp (coefficient of friction = 0.35N, ramp's angle = 25 degrees) is connected to a vertically hanging object via a pulley with I = 23 kg m^2 and the radius is 0.25m. The hanging object had weight 971N. The hanging object dropped 7 meters. Find the tension on the 17 kg object using work energy theorem.

So far I've found the actual weight of the hanging object which is approximately 99kg. The velocity 4.95m/s, the acceleration 1.75m/s^2, and angular velocity 19.8m/s.

When I use the Newton's Law of motion, I could find the tension of the 17kg object equal to 330N while for the 99kg equal to 796.75N so the angular acceleration would be approximately 5 m/s^2. But the thing is, I need to find the tension of the 17kg using the work energy theorem as well but I don't know how.

Please help me? Thanks!

 

[haruspex]

found the actual weight of the hanging object

Mass

angular velocity 19.8m/s.

Wrong units.

find the tension of the 17kg using the work energy theorem

The question is a bit strange. You had to work with forces and accelerations because of the residual velocity. But having found that, you have the KE, so you could write out the energy balance for the 17kg object to find the work done against friction.
Rather an artificial "use" of the theorem, though.