Conservation of energy

1. Apr 29, 2017

tennisgirl92

1. The problem statement, all variables and given/known data
A block of mass 10kg starts at the top of a frictionless track which forms a quarter circle with radius 10m. It is given an initial downward velocity of 10m/s. What is the velocity at the bottom of the track?

2. Relevant equations
KEtranslational, f+ KErotational, f+PEf=KEtranslational, i+KErotational, i+ PEf
KE, rotational=1/2Iw2
KE, translational=1/2mv2
PE=mgh
I=MR2
w=v/r
3. The attempt at a solution
I believe the initial equation would be set up like this.
1/2mvf2+ 1/2 MR2(V/R)2+mghf=1/2mvi2+1/2 MR2(V/R)2+mghi

which would then reduce to:
vf2=vi2+ghinitial

This does not seem like the likely way to do it because we are not given the height of the mass at the top. Should I be using the rotational and translational KE in the equation? At what point is it rotational and what point translational?

2. Apr 29, 2017

Mastermind01

Look carefully.

Why would it rotate? When does something rotate?

3. Apr 29, 2017

tennisgirl92

Would the radius be the initial height?

When it is rolling? I'm not exactly sure.

4. Apr 29, 2017

Mastermind01

That is correct.

Try and think intuitively if you don't know the physics behind it.

5. Apr 29, 2017

tennisgirl92

Ok, now I see how to do this. I obtained 17.2 m/s, which is correct. Thank you!

However, I still don't see how the radius could be equal to the height of the ramp. There is a picture provided that looks like a skateboard ramp, with a strict vertical height and then the inside being curved with a radius. The vertical height does not look equal to the radius, even though I know this is not to scale.

6. Apr 29, 2017

TomHart

Does the picture below look like the picture you have of the skateboard ramp? Is the quarter circle oriented like that?

7. Apr 29, 2017

tennisgirl92

yes, it is just like that, except flipped so that the curve is on the right and height on the left.

8. Apr 29, 2017

TomHart

So does it make sense to you that the radius = height?

9. Apr 29, 2017

tennisgirl92

Yes, I do see it now-my picture did not have the radius being pointed horizontally and vertically, just down the middle. Thank you for all your help!