Calculating Incline Distance for Rotational Motion

[fizzzzzzzzzzzy]

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?

 

[hage567]

Did you take into account both rotational and translational kinetic energy?

 

[ogb p]

It is important to consider the conservation of energy in this situation. While it is true that the kinetic energy at the bottom of the incline will be equal to the potential energy at the top, there are other factors at play that need to be taken into account. The energy of the system is not just dependent on the rotational motion of the cylinder, but also the translational motion. When the cylinder reaches the incline, it will start to roll up the incline while also continuing to move forward. This means that the kinetic energy will not just be dependent on the rotational velocity, but also the linear velocity. Additionally, there may be friction present on the incline, which will also affect the energy of the system. Therefore, a more comprehensive approach, taking into account all of these factors, is needed to accurately calculate the distance the cylinder will travel up the incline. This may involve using equations for both rotational and translational motion, as well as considering the effects of friction.