How Do You Calculate the Ratio of Final to Initial Kinetic Energy in Collisions?

AI Thread Summary
The discussion focuses on calculating the ratio of final to initial kinetic energy in collisions, specifically inelastic collisions. The equations for initial and final momenta and kinetic energies are established, leading to the theoretical ratio K_f/K_i = M/(M+m). There is confusion regarding the cancellation of velocities in the calculations, with participants clarifying that inelastic collisions do not conserve kinetic energy, unlike elastic collisions. An example illustrates the difference between the two types of collisions, emphasizing that inelastic collisions result in energy loss to other forms. The conversation concludes with a simplified expression for the ratio in terms of momentum.
Meteo
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Theres some calculations in this problem that I just don't get...

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

theoretical equation for the ratio fo K_f to K_i

P_i=Mv_i
P_f=(M+m)v_f
K_i=1/2Mv_i^2
K_f=1/2(M+m)V_f^2
K_f/K_i=1/2(M+m)v_f^2/1/2Mv_i^2=M/(M+m) this part I don't get. I only get

(M+m)/M and I am assuming that v_f and v_i

cancel out...

I basically solved for M=P_i/v_i and (M+m)=P_f/v_f<br />
I plug it into kinetic energy equations and get K_f/K_i=P_f/P_i I guess <br /> <br /> v_f and v_i cancel out? Is this answer correct?
 
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I don't understand the intial question, are two bodies inelastically colliding? Could you be more specific as to the problem please.
 
Yes, it is an inelastic collision.

Also a separate question is what would the difference between an elastic and inelastic collision?
 
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 let's 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.
 
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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.
 
I think the most you can do is simplify the ratio as:

(1 + \frac{m}{M}) (\frac{V_f}{V_i})^2

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

( \frac {M}{M+m})( \frac{ P_f}{P_i})^2
 
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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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