How Do You Relate Momentum to Kinetic Energy in Physics?

Click For Summary

Homework Help Overview

The discussion revolves around relating momentum and kinetic energy in physics, specifically how to derive the kinetic energy expression from momentum for a particle of mass m. The original poster presents a problem involving two parts: showing the relationship between kinetic energy and momentum, and expressing momentum in terms of kinetic energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between kinetic energy and momentum, questioning the necessary equations and variables involved. There is an attempt to clarify the differences between the kinetic energy expression and the momentum equation, as well as the implications of substituting variables.

Discussion Status

The discussion is active, with participants providing insights and clarifications regarding the equations involved. Some have noted the substitution of variables and how it leads to the derived expressions, while others are confirming understanding and expressing gratitude for assistance.

Contextual Notes

There is an indication that participants are working within the constraints of a homework assignment, which may limit the information they can use or share. The original poster expresses uncertainty about how to begin the problem, highlighting a common challenge in understanding the concepts involved.

Joyci116
Messages
45
Reaction score
0

Homework Statement


(a) A particle of mass m moves with momentum of magnitude p. Show that the kinetic energy of the particle is given by K=p^{2}/2m. (b) Express the magnitude of the particle's momentum in terms of its kinetic energy and mass.


Homework Equations


Would the p=mv be needed?


The Attempt at a Solution


I don't know how to get it started. I think I can get it if I can get it started.

Thank you.
 
Physics news on Phys.org
What is your [starting] expression for kinetic energy?
How is the new expression different from the old one? Any variables missing from one vs the other?
 
The equation for kinetic energy is k=.5mV^2 and the new equation is K=p^2/2m. Momentum is missing from the first equation and velocity is missing from the second equation.
 
If velocity is missing from the final equation, that means it was substituted in the original equation for K.E. From the equation for momentum (which you listed: p = mv), what is velocity equal to?
 
K=p^2/2m
K=.5mV^2
p=mv
V=p/m
K=.5m(p/m)^2
K=p^2/2m
 
Oh, you had it already! Perfect :smile:
 
Thank you for the help. :)
 
No problem
 

Similar threads

Replies
1
Views
2K
Replies
2
Views
1K
  • · Replies 21 ·
Replies
21
Views
5K
  • · Replies 54 ·
2
Replies
54
Views
11K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 8 ·
Replies
8
Views
1K
  • · Replies 22 ·
Replies
22
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
3
Views
1K