Time hollow cylinder spends on ramp

[cashmoney805]

Homework Statement

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?

Homework Equations

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

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

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!

 

[Doc Al]

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)

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.)

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

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

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

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.

 

[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 :/

 

[Doc Al]

What other force is acting on it?

Friction.

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!

Good.

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

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

 

[cashmoney805]

Friction.


Good.


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

vo/2

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