Conservation of moentum and a spring.

Click For Summary

Homework Help Overview

The discussion revolves around a problem involving the conservation of momentum and energy in a collision between two balls, one of which is attached to a spring. The original poster presents a scenario where a ball collides with another ball that has three times its mass, resulting in a spring compression and the need to find the spring constant.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of conservation of energy and momentum principles, questioning the correctness of the original poster's equations and assumptions. There are inquiries about the relationship between work and potential energy, as well as how to account for energy loss during the collision.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's approach and suggesting alternative considerations. There is an exploration of the correct equations to use, particularly regarding kinetic energy and the work done by the spring and friction. Multiple interpretations of the problem are being examined.

Contextual Notes

Participants note the presence of friction and energy loss during the collision, which complicates the application of conservation laws. The original poster's reliance on certain equations is questioned, and there is an emphasis on the need for clarity regarding the energy transformations involved.

JohnGG
Messages
4
Reaction score
0

Homework Statement


We got a ball moving at speed 2/√3 m/s, and it hits another ball that is attached to the string. Ball 2 has 3 times the mass of ball 1. After the crash, ball one stucks in ball 2 and the spring gets .02m shorter at its minimum length. There are frictions with n=1/12 and g=10m/s^2. Find the constant k of the spring.

Homework Equations


ΔP=0=>mu=4mu', u'=u/4, you can't use hooke's law as it isn't in the textbook.
Fy=0<=>N=mg
M=3m, M'=4m

The Attempt at a Solution


I used conservation of energy principle to get 1/2Mu'^2=1/2kx^2-nM'g=>Mu'^2+2nM'g=kx^2=>(Mu'^2+2nM'g)/x^2=k and thn just plug in numbers, but the problem is I ended up with a k as a function of m.
 
Physics news on Phys.org
Your equation for the conservation of energy cannot be correct. It has nM'g as an addend, and its dimension is that of force.

Another issue is when one ball gets stuck in another ball in a collision, there is a loss of energy, while you assume it is fully conserved.
 
voko said:
Your equation for the conservation of energy cannot be correct. It has nM'g as an addend, and its dimension is that of force.

Another issue is when one ball gets stuck in another ball in a collision, there is a loss of energy, while you assume it is fully conserved.

What would be the correct equation?

I found that 1/3 of kinetic energy turned into heat in a question I skipped here. How could I use that to find k?
 
The correct equation would have the kinetic energy of the two balls immediately after the collision, and the work of the spring and friction over the distance of maximum compression.
 
voko said:
The correct equation would have the kinetic energy of the two balls immediately after the collision, and the work of the spring and friction over the distance of maximum compression.

1/2M'u'^2=-Tx+?
What is the work of the spring?
 
How is work related with potential energy?
 
voko said:
How is work related with potential energy?

W=-ΔU. But where is the k I search for?
 
In you very first message, you had ##{1 \over 2} kx^2 ##. Where did that come from?
 

Similar threads

Sliding block hits and compresses a spring
  • · Replies 5 ·
Replies
5
Views
1K
Projectile Motion : Work and Energy
  • · Replies 4 ·
Replies
4
Views
2K
Spring Problem Involving Variables and Constants Only
  • · Replies 3 ·
Replies
3
Views
2K
Conservation of Energy: Spring PE: Toy gun on spring
  • · Replies 4 ·
Replies
4
Views
2K
Difficulty in deciding when to apply work energy theorem
  • · Replies 2 ·
Replies
2
Views
2K
Kinetic Energy & Momentum of a Ball released from Spring
  • · Replies 6 ·
Replies
6
Views
3K
Find elastic energy in the compressed spring.
  • · Replies 12 ·
Replies
12
Views
3K
Hooke's Law using Potential Energy
  • · Replies 21 ·
Replies
21
Views
2K
Initial velocity of bird landing on horizontal wire modeled as spring
  • · Replies 7 ·
Replies
7
Views
1K
A rocket on a spring, related to potential/kinetic energy
  • · Replies 3 ·
Replies
3
Views
2K