Loop the loop. Rotational problem

Click For Summary

Homework Help Overview

The problem involves the motion of a cylinder rolling down from a height to complete a loop-the-loop track. It examines the conditions under which a rolling object, as opposed to a sliding object, can successfully navigate the loop without losing contact, focusing on energy conservation principles and the relationship between potential and kinetic energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the energy requirements for a rolling object compared to a sliding object, questioning whether the height from which the rolling object must be released is greater, lesser, or the same. There are considerations of rotational and translational kinetic energy, as well as potential energy. Some participants express uncertainty about the correct radius to use in calculations related to rotational kinetic energy.

Discussion Status

Participants are actively engaging with the problem, exploring different aspects of energy conservation and the definitions of variables involved. Some guidance has been offered regarding the application of conservation of energy at different points in the loop, but there is still uncertainty regarding the specifics of the calculations and the definitions of terms.

Contextual Notes

There is a noted assumption that friction is sufficient for rolling without slipping, and participants are grappling with the implications of this assumption on the energy calculations. Additionally, there is confusion regarding the radius used in the equations, specifically whether it refers to the radius of the loop or the radius of the cylinder.

makeAwish
Messages
128
Reaction score
0

Homework Statement



In this problem you will consider the motion of a cylinder of radius Rcyl that is rolled from a certain height h so that it "loops the loop," that is, rolls around the track with a loop of radius Rloop shown in the figure without losing contact with the track.

Unless otherwise stated, assume that friction is sufficient that the cylinder rolls without slipping. The radius Rcyl of the cylinder is much smaller than the radius Rloop of the loop.

a) Compared to an object that does not roll, but instead slides without friction, should a rolling object be released from the same,a greater, or a lesser height in order just barely to complete the loop the loop?

b) Find the minimum height h that will allow a solid cylinder of mass m and radius Rcyl to loop the loop of radius Rloop.
Express h in terms of the radius Rloop of the loop.


Homework Equations



For part 1, the height is it greater becos the rolling object needs more potential energy to be converted to its translational and rotational kinetic energy and some to overcome friction, while the non rolling object only need potential energy to be converted to translational and rotational kinetic energy?

Both will have translational and rotational kinetic energy, am i right??

For part 2, I'm thinking of using conservation of energy. But for the rotational kinetic energy Kr = 1/2*I*w^2

The omega (w) = v/R

But i duno if R is radius of loop or radius of cylinder..


Pls help me.. Thanks!
 

Attachments

  • 20081124195416336315324138925005269.jpg
    20081124195416336315324138925005269.jpg
    6.3 KB · Views: 971
Physics news on Phys.org
Radius of cylinder
 
rl.bhat said:
Radius of cylinder

hmm. but why? cos i tot r is actually the radius of the circle of rotation which is the radius of loop..
 
Because when the cylinder rolls up the circular loop, it has rotational kinetic energy, translational KE and potential energy. Now apply the law of conservation of energy.
you can apply it at the bottom of the loop and at the top of the loop.
 
rl.bhat said:
Because when the cylinder rolls up the circular loop, it has rotational kinetic energy, translational KE and potential energy. Now apply the law of conservation of energy.
you can apply it at the bottom of the loop and at the top of the loop.


hmm i noe tat it has rotational kinetic energy, translational KE and potential energy.. but i still don't understand why r is not radius of loop, for v = r*w.. =x
 
Rotational KE is calculated when the body is rotating about an axis passing through it. And the axis of the loop is not passing through the cylinder.
 
rl.bhat said:
Rotational KE is calculated when the body is rotating about an axis passing through it. And the axis of the loop is not passing through the cylinder.

hmm.. i think i get it.. :) thanks! :)
 
hmm. how abt part one? is my thinking correct?
 

Similar threads

Loop problem with skier on ramp going into a loop-the-loop
  • · Replies 13 ·
Replies
13
Views
2K
Loop the Loop Problem Solution | N > 0, Energy Conservation Method
  • · Replies 8 ·
Replies
8
Views
4K
Starting height of marble rolling around a loop the loop
  • · Replies 12 ·
Replies
12
Views
13K
Determine energy required to stop rolling mass
  • · Replies 10 ·
Replies
10
Views
899
Kinetic Energy of a Cylinder Rolling Without Slipping
  • · Replies 21 ·
Replies
21
Views
5K
A cylinder rotating on a plane with friction and then moving across a frictionless plane to a collision
  • · Replies 1 ·
Replies
1
Views
1K
A cylinder of snow rolls down a hill gathering more snow -- calculate its speed
  • · Replies 39 ·
2
Replies
39
Views
4K
Radius of largest possible loop of an Airplane.
  • · Replies 4 ·
Replies
4
Views
2K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
  • · Replies 10 ·
Replies
10
Views
3K
A ball climbing a ramp while "rolling the wrong way"
  • · Replies 32 ·
2
Replies
32
Views
3K