Kinetic energy and momentum

  • Thread starter Meteo
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  • #1
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Theres some calculations in this problem that I just dont get...

Start with the equations for initial and final momenta and kinetic energies and derive the

theoretical equation for the ratio fo [tex]K_f[/tex] to [tex]K_i[/tex]

[tex]P_i=Mv_i[/tex]
[tex]P_f=(M+m)v_f[/tex]
[tex]K_i=1/2Mv_i^2[/tex]
[tex]K_f=1/2(M+m)V_f^2[/tex]
[tex]K_f/K_i=1/2(M+m)v_f^2/1/2Mv_i^2=M/(M+m)[/tex] this part I dont get. I only get

[tex](M+m)/M[/tex] and im assuming that [tex]v_f[/tex] and [tex]v_i[/tex]

cancel out...

I basically solved for [tex]M=P_i/v_i[/tex] and [tex](M+m)=P_f/v_f
[/tex]
I plug it in to kinetic energy equations and get [tex]K_f/K_i=P_f/P_i[/tex] I guess [tex]

v_f[/tex] and [tex]v_i[/tex] cancel out? Is this answer correct?
 

Answers and Replies

  • #2
2,985
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I dont understand the intial question, are two bodies inelastically colliding? Could you be more specific as to the problem please.
 
  • #3
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Yes, it is an inelastic collision.

Also a seperate question is what would the difference between an elastic and inelastic collision?
 
  • #4
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the intial and final velocities are not going to be the same, in general. A simple example is a fly hitting a winsheild. Its traveling with its initial speed of lets say 2m/s. It hits the truck, and gets stuck on the winsheild, now its moving at the speed of the truck, maybe 30m/s.
 
Last edited:
  • #5
jtbell
Mentor
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Meteo said:
difference between an elastic and inelastic collision?
In an elastic collision, the total kinetic energy is conserved. In an inelastic collision, the total kinetic energy is not conserved.
 
  • #6
2,985
15
I think the most you can do is simplify the ratio as:

[tex] (1 + \frac{m}{M}) (\frac{V_f}{V_i})^2 [/tex]

but if you want it in terms of intial and final momentum it will be:

[tex] ( \frac {M}{M+m})( \frac{ P_f}{P_i})^2 [/tex]
 
Last edited:
  • #7
538
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In an elastic collision , the initial and kinetic energies remain the same But in inelastic collision , some of the initial KE is lost to the surroundings as other forms of energy like heat/sound , but in both the cases , the Total energy is always conserved.

BJ
 

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