Theoretical Expression for %loss in Kinetic Energy

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Homework Help Overview

The discussion revolves around deriving an expression for the percentage loss in kinetic energy in a collision scenario, involving variables for mass and initial and final velocities. The subject area includes concepts from mechanics and energy conservation.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to derive a specific equation for percentage loss in kinetic energy but expresses uncertainty about the substitution and simplification process. Some participants question the validity of the proposed approach, while others suggest substituting values for initial and final energies to facilitate simplification.

Discussion Status

The discussion is ongoing, with various attempts to manipulate the equations and clarify the relationships between variables. Some participants are exploring different interpretations of the equations, and there is a lack of consensus on the best approach to take.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the extent of guidance provided. There is a focus on deriving the expression without providing complete solutions.

crazuiee
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Homework Statement


I'm trying to derive an equation which should look like this in the end:
%loss in Kinetic energy= M/m+M*100%, I'm just not sure how to substitute everything, and cancel things out to get the expression. Can someone show me the steps?


Homework Equations


mVi=(M+m)Vf
%loss in Kinetic Energy= 1/2mVi^2-1/2(M+m)Vf^2/ 1/2mVi^2 *100%


The Attempt at a Solution


 
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Pi = mVi
Pi^2 = (mVi)^2 = 2m*(1/2*m*Vi^2) = 2mEi.
So Ei = Pi^2/2m
Similarly find Ef
Then percent change = (Ei - Ef)/Ei*100
 
I'm sorry i really don't see how that's going to work out to M/M+m
 
Substitute the values of Ei and Ef. While simplification substitute the value of Vf in terms of Vi using the first equation in relevant equations.
 
yea...that means nothing to me sorry..
 
(Ei - Ef)/Ei = [1/2*m*vi^2 - 1/2*(m+M)*vf^2]/1/2*m*vi^2.
Cancel 1/2m
= vi^2 - [(m+M)/m*vf^2]/vi^2
Put vi^2 = [(m + M)/m*vf]^2 and simplify.
 

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