Conservation of energy for a system

Click For Summary

Homework Help Overview

The problem involves a massless wheel with a mass and a uniform chain, exploring the conservation of energy and momentum in a rotating system. The objective is to determine the speed of the mass when it reaches a specific point after being set in motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using conservation of energy as a primary approach but express difficulty in framing the necessary equations. There are questions about the initial conditions and the application of conservation of momentum. Some participants seek clarification on the derivation of energy terms and the moment of inertia involved.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the validity of their equations. There is a focus on understanding the gravitational potential energy terms and their relevance to the problem setup. No consensus has been reached, and various interpretations are being explored.

Contextual Notes

Participants note the lack of initial velocity and the implications of the chain's length not being specified. There is uncertainty regarding the definitions and assumptions related to the moment of inertia and potential energy terms.

Arka420
Messages
28
Reaction score
0

Homework Statement


Figure shows a massless wheel of radius R on which at a point a mass m is fixed and a uniform chain of mass 2m is tied to it which passes over the rim of the wheel and half of its length is hanging on other side as shown in the figure. When a small clockwise jerk is given to the wheel, it starts rotating. Find the speed of the mass m when it reaches a point P directly opposite to its initial point.
xqhJzwE.png

Homework Equations


The equations for conservation of energy and momentum (both angular as well as linear)

The Attempt at a Solution

[/B]Conservation of energy is the first attempt,but I am facing one hell of a trouble framing the equations. Conservation of momentum? Well,I don't have the inital velocity.
 
Physics news on Phys.org
Arka420 said:
Conservation of energy is the first attempt,but I am facing one hell of a trouble framing the equations.
Then show your attempt please.
Arka420 said:
Conservation of momentum? Well,I don't have the inital velocity.
The initial velocity is negligible, but conservation of momentum doesn't help here.
 
mfb said:
The initial velocity is negligible, but conservation of momentum doesn't help here.
Hmm. Looks like all I have to do is conserve energy.
 
mfb said:
Then show your attempt please.
Is the equation 2mgl = mgl + 1/2mv^2 + 1/2Iw^2 (I is the moment of inertia about the center of the pulley wheel,while w is the angular velocity) by any chance?
 
Where do 2mgl and mgl come from?
Arka420 said:
(I is the moment of inertia about the center of the pulley wheel
The moment of inertia of what?
 
mfb said:
Where do 2mgl and mgl come from?
They are the gravitational potential energy terms. Seeing that the length of the chain is not given,we can say that (pi)R = half times the length (which is given in the question itself).
mfb said:
The moment of inertia of what?
The moment of inertia of the mass m about the center of the pulley?

Am I doing something wrong?
 
Arka420 said:
They are the gravitational potential energy terms.
Sure, but potential of what relative to what? They don't look right in the way you used them.
Arka420 said:
The moment of inertia of the mass m about the center of the pulley?
Okay.
Arka420 said:
Am I doing something wrong?
Yes, and it is unclear what because you don't explain how you got your formulas.
 

Similar threads

Replies
55
Views
6K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
10
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
Replies
7
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K