What is the speed of a cylinder rolling down a hill?

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Homework Help Overview

The problem involves a cylinder rolling without slipping down a hill, starting from a height h. The original poster attempts to determine the speed of the cylinder at the bottom, initially calculating it based on potential and kinetic energy without considering the rotational aspect of the motion.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the energy transformation from potential to kinetic energy, questioning the original poster's assumption that all potential energy converts to translational kinetic energy. Some participants highlight the need to account for rotational kinetic energy due to the cylinder's rolling motion.

Discussion Status

There is an ongoing exploration of the energy dynamics involved in the problem. Participants are questioning the assumptions made about the energy conversion and discussing the implications of the cylinder's moment of inertia. No consensus has been reached, but several productive lines of inquiry are being pursued.

Contextual Notes

Participants note that the cylinder's mass distribution and rotational motion are critical to understanding the problem. There is an emphasis on the forces acting on the cylinder and the role of kinetic energy in both translational and rotational forms.

zeralda21
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Homework Statement



A cylinder rolls without slipping down a hill. It is released from height h. What is its speed when it come down? The cylinder mass may be completely concentrated on the radius R, which is the radius of the cylinder.

http://i.imgur.com/Ge3x1nu.png

The Attempt at a Solution



The answer is supposed to be v=√(gh) but my calculations give;

At the top the potential energy is E=mgh and at the end(h=0) all energy has become kinetic energy since no friction/air drag is acting. Thus mgh=(1/2)mv^2 <--->v=√(2gh). Why is this wrong??
 
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The cylinder is not a point-mass - some of the kinetic energy is required to have it rolling.
 
mfb said:
The cylinder is not a point-mass - some of the kinetic energy is required to have it rolling.

I am trying but I am not following. The only acting force is the downward gravitational force mg and normal force from the ground. So if energy isn't the same at the top and bottom, where has it gone.

I also don't understand that kinetic energy is required to have it rolling. The kinetic energy at the top is zero and keeps increasing as h decreases(same rate inversely right?).
 
zeralda21 said:
I am trying but I am not following. The only acting force is the downward gravitational force mg and normal force from the ground. So if energy isn't the same at the top and bottom, where has it gone.

I also don't understand that kinetic energy is required to have it rolling. The kinetic energy at the top is zero and keeps increasing as h decreases(same rate inversely right?).

Garvity and Normal the only acting forces, then what makes the cyllinder roll?
HINT: There is one more force that you are missing, draw the diagram and you will get it!
 
Consider the moment of inertia of the cylinder
 

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