Rotational Motion Question with Work Energy Theorem

[Yosty22]

Homework Statement

A 392-N wheel comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill, it is rotating at 25.0rad/s. The radius of the wheel is .6m and its moment of inertia about its rotation axis is 0.800MR². Friction does work on the wheel as it rolls up the hill to a stop, a height h above the bottom of the hill; this work has absolute value 3500J. Calculate h

Homework Equations

Work Energy Theorem

The Attempt at a Solution

I tried to use the work-energy theorem but I feel like I am missing the velocity of the center of mass of the wheel. I set up my equation as:

U₁+K₁+W_other=U₂+K₂ where "W_other is the work done by friction, in this case 3500J in the direction opposite of motion. Also, U₁ cancels and I believe K₂ should cancel out.

Therefore, my equation is:

3500J+.5mv²+.5Iω²=mgh

It seems like I have 2 unknowns, h and v. Am I missing something?

 

[cepheid]

If you know omega, then you know v, because rolling without slipping means that every centimetre of distance moved by a point on the circumference of the wheel must correspond to the same number of centimetres of distance translated forward by the centre of mass of the wheel. Think about it and you'll see that if this weren't true, the wheel would have to be slipping.

 

[tiny-tim]

Hi Yosty22!

At the bottom of a hill, it is rotating at 25.0rad/s. The radius of the wheel is .6m …

It seems like I have 2 unknowns, h and v. Am I missing something?

you can find v (the initial speed) from the 25.0 rad/sec