# Time hollow cylinder spends on ramp

1. Dec 9, 2008

### cashmoney805

1. The problem statement, all variables and given/known data
A hollow cylinder (hoop) is rolling on a horizontal surface at speed v= 3.3 m/s when it reaches a 15 degree incline. (a) How far up the incline will it go? (b) How long will it be on the incline before it arrives back at the bottom?

2. Relevant equations
Energy conservation:
1/2 Iw^2 + 1/2mv^2 = mgh

v^2 = vo^2 +2ax
x=vot + .5at^2
v=vo+at

3. The attempt at a solution
I for this problem is (I think) 1/2 m (r1^2 + r2^2), but the r's cancel because w^2 = v^2/(r1^2 + r2^2)

So I believe the energy equation simplifies to .25v^2 + .5v^2 = gh

I solve and get h = .833 and so the length = .833/sin15 = 3.22
However, the book says the length is 4.29.

Also, after that I don't know where to go.

For time, I tried v=vo+at, for a I used 9.8sin 15 and t (up) I got 1.3s
However, the total t= 5.2 s

Thank you so much!

2. Dec 9, 2008

### Staff: Mentor

Careful. Treat this as a thin hoop--with a single radius. (You're using a formula for a thick hollow cylinder. You'd have to set r1 = r2 to use that one.)

You'll need to redo this, after fixing the above.

Careful--gravity is not the only force acting. A simpler way would be to figure out the average speed as it goes up the ramp.

3. Dec 9, 2008

### cashmoney805

What other force is acting on it?

Ok, I treated the hoop as a thin one and now my equation is:

v^2 = gh
h = 1.1 m, so length is 1.1/sin15 = 4.29m woo!

Now for t... I don't really know what to use anymore :/

4. Dec 9, 2008

### Staff: Mentor

Friction.

Good.

You know the distance. What's the average speed up the incline?

5. Dec 9, 2008

### cashmoney805

vo/2

Ah then do x/v = t. How do you know when to use average velocity though? I never seem to use that.