Cylinder Rolling Down an Inclined Plane

1. Mar 30, 2012

eagles12

1. The problem statement, all variables and given/known data

A 3.0kg solid cylinder (radius=.15m, length=.7m) is released from rest at a top of a ramp and allowed to roll without slipping. The ramp is .9m high and 5m long. Find the rotational and translational kinetic energy.

2. Relevant equations

krot=1/2Iw^2
Ktrans=1/2mv^2

3. The attempt at a solution

I already determined that the final kinetic energy is 26J

v=rw
v=(.15)w
Ktrans=1/2(3)(v^2)

2. Mar 30, 2012

eagles12

i set up
mgH=1/2mv^2+1/2Iw^2
and got
26=1/2(3)v^2+1/2(.1225)w^2
26=.03375w^2+.06125W^2
26=.095w^2
w=16.54
with this i got
Krot=16.76
but it is saying this is not correct

3. Mar 30, 2012

Saitama

Wrong moment of Inertia!!

4. Mar 30, 2012

eagles12

would it be 1/2 MR^2

5. Mar 30, 2012

Saitama

If i tell that, then i would solve your homework.
Think about it, how the cylinder will roll down (about which axis)?

6. Mar 30, 2012

eagles12

i got the rotational one and plugged in the w and r into v=rw
then squared v and multiplied by the mass
and divided by two, but i didn't get the right answer

7. Mar 30, 2012

ehild

The moment of inertia of the cylinder with respect to the axis through its centre is 1/2 MR^2. It is not 0.1225. How did you get that value?

(The in a plane motion of a rigid body is equivalent with a translation of its CM and rotation around the axis through the CM.)

ehild

8. Mar 30, 2012

Saitama

And can you tell us what value of g you used?
I don't get 26 neither by 10 nor 9.8.

9. Mar 31, 2012

eagles12

i used 9.8 and it has already told me that Kf=26 and Krot=8.8 are correct.
using this, i used v=rw to get v=3.399 and plugged that into 1/2mv^2
doing that i got 17 but it is saying this is incorrect.

10. Mar 31, 2012

lep11

Seriously...why 17J is not correct answer? If total energy is 26.486J and rotational energy is 8.8J then the kinetic energy will be 26.486J-8.8J=17.687J~18J. I was always taught to use the value 9.81m/s^2 and not to use rounded values like 26J in calculations.