Calculate the velocity of a cylinder as it leaves the top of a slope (using Energy)

[jisbon]

Homework Statement

Cylinder with mass 1.5kg and 0.1m radius roll without slipping up a slope of length 3m and height 1m. Cylinder has an initial translational velocity of 4m/s. Calculate velocity of the cylinder as it leaves the top of the slope.

Relevant Equations

Gain in GPE = Loss in translational KE + loss in rotational KE

I seem to be able to do this problem (at least from what I think, but my answer is still wrong according to the answer key, please do help check.)

Since:
Gain in GPE = Loss in translational KE + loss in rotational KE
##\left(m\cdot g\cdot h\right)=\left(\frac{1}{2}\left(m\right)\left(v_{f}^2\right)-\frac{1}{2}\left(m\right)\left(v_{i}^2\right)\right)+ \left(\frac{1}{2}\left(I\right)\left(\omega_{f}^2\right)-\frac{1}{2}\left(I\right)\left(\omega_{i}^2\right)\right)##
Whereby
##I = 0.5 (mr^2) = 0.5 (1.5*0.1^2)##
##\omega = v/r = 4/0.1##

##\left(1.5\cdot 9.8\cdot 1\right)=\left(\frac{1}{2}\left(1.5\right)\left(v_{f}^2\right)-\frac{1}{2}\left(1.5\right)\left(4^2\right)\right)+\left(\left(\frac{1}{2}\left(0.5\cdot \:1.5\cdot \:0.1^2\right)\left(\frac{v_{f}}{0.1}\right)^2\right)\:-\:\left(\frac{1}{2}\left(0.5\cdot 1.5\cdot 0.1^2\right)\left(\frac{4}{0.1}\right)^2\right)\right)##

Are the equations correct/did I miss something out? Thanks

 

[scottdave]

Since it does not slip, what happens to rotational speed in relation to translational speed? Ok, i think you took care of that. I'm on my phone so it's hard to read all of the symbols.

 

[scottdave]

I think I see it now. You really have what appears to be just an error of swapping the signs. Try writing it like this: (Total energy at beginning) = (Total energy at top) to see how that works, and if you spot the error.

 

[jisbon]

I think I see it now. You really have what appears to be just an error of swapping the signs. Try writing it like this: (Total energy at beginning) = (Total energy at top) to see how that works, and if you spot the error.

Solved the error. Thanks for your help. Will use your method in the future

 

[haruspex]

Solved the error. Thanks for your help. Will use your method in the future

Either method is fine. The problem was that your reference equation was in terms of loss of energy, but you turned that into final - initial, which would be a gain in energy.
It is generally safer to record reference equations in terms of gain.