# Kinetic energy with momentum equation

1. Nov 26, 2007

### ~christina~

[SOLVED] kinetic energy with momentum equation

1. The problem statement, all variables and given/known data

A particle of mass m moves with momentum of magnitude p. Show that the kinetic E of particle is given by $$K= p^2/2m$$

express magnitude of particle's momentum interms of it's Kinetic Energy and mass.

2. Relevant equations

Kf + Uf= Ki + Ui

1/2mvf + mgy = 1/2mvi + mgy

pf= pi

mvf= mvi

3. The attempt at a solution

not exactly sur how to incorperate the momentum into the kinetic E equation.

my attempt looks ridiculous.

not sure if it's Kf= Ki
because they just say the Kinetic E

K= 1/2mv^2

p= mv

$$K= \frac{P*v} {2}$$

What am I doing incorrectly?

b) Express magnitude of the particle's momentum in terms of it's kinetic E and mass

I guess I would just rearrange the equation they gave me

$$K= \frac{p^2} {2m}$$

$$p= \rad{K*2m}$$

2. Nov 26, 2007

### danni7070

This would be correct if K = p/2m

But you have to isolate p^2. Dont you miss the $${\sqrt {equation}}$$ ?

3. Nov 26, 2007

### neutrino

Nothing incorrect, just incomplete. Multiply the expression on the right by m/m.

That looks good.

4. Nov 26, 2007

### kalok

becuse:$$P^{2}=m^{2}v^{2}$$
so:$$k=1/2\cdot\frac{P^{2}}{m}$$

You lose one stage:$$v=\frac{p}{m}$$

This equation is important.Because in the Hamitonian equation,all the element must be
expressed by P and q.q is the generalized coordinate .

Last edited: Nov 26, 2007
5. Nov 26, 2007

### ~christina~

Thank you everyone. I get why I have to multiply it by m/m.