# Conservation of Energy/Angular Momentum

1. Jan 10, 2007

### velvetymoogle

1. The problem statement, all variables and given/known data
Hi.
The problem is "A wooden block of mass m slides with an initial speed of vi up a straight incline that makes an angle of theta with the horizontal. If the incline is rough with a coefficient of kinetic friction uk, determine the maximum height it rises in terms of h found in part a (which was H = vi^2/2g)"

2. Relevant equations
conservation of energy
You can only use m (mass of block), vi (initial velocity), theta, and g (gravity)

3. The attempt at a solution
KE at the bottom = PE at the top + Work.
mgh + Fd = 1/2mv^2
h = [mvi^2 - ukmgcos(theta)d]/mg
Problem is, I don't know what d is and it can't be part of my final answer. I know it's the distance that the block travels up the ramp, but how do I figure that out?
Also, since it says in terms of h found in part a, does that mean I set everything equal to vi^2/2g?

How would I do this with a hoop with radius R?

2. Jan 10, 2007

### pmp!

So, you correctly applied the conservation of mechanical energy.
Could you right d as a function of h and $\theta$?

The hoop will have in the end not only linear velocity but also angular velocity. Apply again conservation of mechanical energy, but this time consider also the kinetic rotational energy. :tongue:

3. Jan 10, 2007

### velvetymoogle

Okay this is going to sound really confusing but am I on the right path for the block one?

I got to the point where gh = 1/2(vi)^2 - ukg(cot(theta))h
At this point, do I plug in what I got for H in part (a) since it wants it says "in terms of h found in part a"? What exactly are they asking me to do?

4. Jan 11, 2007

### velvetymoogle

Nevermind. I was being stupid and forgot they are two different H's