Calculating Incline Distance for Rotational Motion

AI Thread Summary
To determine how far a hollow cylinder rolls up an incline of 15 degrees from an initial speed of 3.3 m/s, both translational and rotational kinetic energy must be considered. The initial kinetic energy is a combination of translational energy (1/2 mv^2) and rotational energy (1/2 Iω^2), where I is the moment of inertia and ω is the angular velocity. The discrepancy between the calculated distance of 0.56 meters and the book's answer of 4.3 meters suggests that the rotational aspect was not fully accounted for in the initial calculation. Properly applying energy conservation principles will yield the correct incline distance. Understanding the relationship between kinetic and potential energy is crucial in solving this problem accurately.
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A hollow cylinder(hoop) is rolling on a horizontal surface at v = 3.3 m/s when it reaches an incline of 15 degrees. how far up the incline will it go?

this was in the chapter about rotational motion but from my understanding of it, it can be solved just by taking the kinetic energy and having it equal the potential energy. when i did that the answer i got was 0.56 meters but the answer in the book is 4.3, I am guessing that what i did doesn't work. Anyone care to explain?
 
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Did you take into account both rotational and translational kinetic energy?
 
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