How Do You Relate Momentum to Kinetic Energy in Physics?

[Joyci116]

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.

 

[robphy]

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?

 

[Joyci116]

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.

 

[Peter G.]

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?

 

[Joyci116]

K=p^2/2m
K=.5mV^2
p=mv
V=p/m
K=.5m(p/m)^2
K=p^2/2m

 

[Peter G.]

Oh, you had it already! Perfect

 

[Joyci116]

Thank you for the help. :)

 

[Peter G.]

No problem