Work Energy Theorem of a spring

[theBEAST]

Homework Statement

The Attempt at a Solution

Is this correct? Is the change in potential energy U_final-U_initial?

My answer turns out to be a positive number, so intuitively does this mean that some of the kinetic energy went into potential and thus the final potential energy is greater than the initial?

 

[haruspex]

Looks fine, but several things bother me.
What is "k_g = 0.5m"?
Why are you told the initial speed of the disk?
Seems to me that the disk does not have enough KE to travel two revolutions down the slope, and it won't recoil that far either. But I cannot think of another interpretation of the question.

 

[theBEAST]

Looks fine, but several things bother me.
What is "k_g = 0.5m"?
Why are you told the initial speed of the disk?
Seems to me that the disk does not have enough KE to travel two revolutions down the slope, and it won't recoil that far either. But I cannot think of another interpretation of the question.

k_g is the radius of gyration, it would be used to solve for the total KE which is the sum of the rotational and translational motion. This is given to throw the students off I think :P

 

[haruspex]

k_g is the radius of gyration, it would be used to solve for the total KE which is the sum of the rotational and translational motion. This is given to throw the students off I think :P

OK, but that doesn't satisfy my last point. As far as I can see, the information given is inconsistent. It would not travel two whole revolutions, in either direction. (Would somebody check that?) Superfluous information is one thing, contradictory information quite another.

 

[Nickie]

Yes, that is correct. According to the Work-Energy Theorem, the change in potential energy (Ufinal-Uinitial) is equal to the work done on the spring, which is also equal to the change in kinetic energy. This means that some of the initial kinetic energy was converted into potential energy, resulting in a positive change in potential energy. This is often seen in the case of a spring, where compressing or stretching the spring stores potential energy that can be released as kinetic energy when the spring returns to its original position.