Rotational Motion of a cylinder

AI Thread Summary
A hollow cylinder is rolling at 4.3 m/s when it encounters a 15-degree incline. The distance it travels up the incline is calculated to be 7.3 meters using conservation of energy principles. The discussion highlights the challenge of determining the time taken to ascend and descend the incline due to the cylinder's rotational motion. It suggests using kinematic equations to find the time for the ascent and then doubling it for the total time. The key focus is on calculating acceleration and applying the appropriate kinematic formulas.
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Homework Statement


A hollow cylinder (hoops) is rolling on a horizontal surface at speed v = 4.3 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



PE = KE + RE
SOH CAH TOA

w = v/r

I = mr^2


The Attempt at a Solution



A) I figured out letter A with conservation of Energy (yawn) distance = 7.3 m

B)I am not sure exactly how to solve this problem. If it was a non rotating cube i could do it very easilly =D. I am sure the fact that it is rotating though affects it somehow. For a cube I would use the Kinetics equations (y = -.5gt^2 + vt + y0) to solve for time. Could someone help me out thanks =D
 
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the time taken to go up the incline=the time taken to come down.
calculate time taken to go up sing simple kinamtic relations and then double it to get the desired result.

use velocity final=0
velocity[initial]=4.3 m/s
distance=7.3 m

now the important part is accln- i leave it to you to figure it out.
use =s=ut+1/2at^2
 

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