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Momentum and Kinetic Energy

  • Thread starter Joyci116
  • Start date
  • #1
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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[itex]^{2}[/itex]/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.
 

Answers and Replies

  • #2
robphy
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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?
 
  • #3
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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.
 
  • #4
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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?
 
  • #5
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K=p^2/2m
K=.5mV^2
p=mv
V=p/m
K=.5m(p/m)^2
K=p^2/2m
 
  • #6
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Oh, you had it already! Perfect :smile:
 
  • #7
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Thank you for the help. :)
 
  • #8
442
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No problem
 

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