Conservation of energy and conservation of momentum

In summary, using both conservation of energy and conservation of momentum, the spring constant k can be derived as k=2mg/H[1+mg/(m+M)H]. The question involves a mass spring system oscillating at close to the speed of light and requires definitions for symbols such as initial mass and initial velocity. After some trial and error, the individual was able to solve the problem and arrive at the correct answer.
  • #1
sauri
51
0
Using both cinservation of energy and conservation of momentum, show that the spring constant k is given by k=2mg/H[1+mg/(m+M)H]

I thought that this would go easier if I rewrote the expression for kinetic energy in terms of momentum, but I can't exactly get around figuring the change in momentum to build an equation. would (m1v1/2) be correct?
 
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  • #2
Do you have defintions for your symbols?
 
  • #3
as in initial mass and initial velocity?
 
  • #4
sauri said:
as in initial mass and initial velocity?

"Initial mass?" : Perhaps you'd better tell us what the question is.

-Dan
 
  • #5
topsquark said:
"Initial mass?" : Perhaps you'd better tell us what the question is.

-Dan

Hmm, a mass spring system oscillating at close to the speed of light. I've never done relativistic effects with SHM before...could be interesting...
 
  • #6
It seems I have taken a wrong approach. I need to show that the spring constant k can be given by 2mg/H[1+mg/(m+M)H] using thr conservation of energy and momentum.
 
  • #7
Does the question not give you any definitions for the symbols used?
 
  • #8
I worked it out. No matter
 
  • #9
sauri said:
I worked it out. No matter

:mad: Then at least have the decency to tell us! You've got ME curious, anyway.

-Dan
 

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

2. How is energy conserved in a closed system?

In a closed system, energy can be transferred from one form to another, but the overall amount of energy remains constant. For example, when a ball is dropped from a certain height, its potential energy is converted into kinetic energy as it falls. When it hits the ground, the kinetic energy is then converted into sound and heat energy.

3. What is the difference between potential and kinetic energy?

Potential energy is the energy that an object possesses due to its position or state, while kinetic energy is the energy an object possesses due to its motion. Both forms of energy are conserved in a closed system.

4. How does conservation of momentum relate to conservation of energy?

The law of conservation of momentum states that the total momentum of an isolated system remains constant. This means that in a closed system, the total amount of momentum before and after a collision or interaction remains the same. This is related to the conservation of energy because momentum is a product of mass and velocity, and changes in energy are often a result of changes in velocity.

5. Can conservation of energy and conservation of momentum be violated?

No, the laws of conservation of energy and conservation of momentum are fundamental principles in physics and have been extensively tested and proven to hold true in all known physical systems. If any violations were to occur, it would require a fundamental change in our understanding of the universe.

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