Percentage of kinetic energy after an elastic collision

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Homework Help Overview

The problem involves an elastic collision between two objects with different masses, where one object is initially stationary. The original poster seeks to determine the percentage of kinetic energy retained by each object after the collision, using the conservation of momentum and kinetic energy principles.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to relate the initial and final kinetic energies using equations for kinetic energy and conservation laws. Some participants suggest deriving the final velocities in terms of mass and initial velocity, while others express uncertainty about how to proceed with the calculations.

Discussion Status

The discussion is ongoing, with participants exploring different equations and relationships. Some have made attempts to express final velocities, but there is no clear consensus on the next steps or how to calculate the percentages of kinetic energy after the collision.

Contextual Notes

Participants are working under the constraints of an elastic collision scenario and are focused on deriving relationships between kinetic energies and velocities. There is an indication of confusion regarding the application of the derived values in the context of the kinetic energy equations.

clope023
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Homework Statement



A stationary object with mass mb is struck head-on by an object with mass ma that is moving initially at speed v0.

If the collision is elastic, what percentage of the original energy does each object have after the collision?

KA2/K1 = ?

KB2/K1 = ?

Homework Equations



K1 = 1/2mav1a^2 + 1/2mbv1b^2

K2 = 1/2mav2a^2 + 1/2mbv2b^2

The Attempt at a Solution



K1/K2A = (1/2mav1a^2 + 1/2mbv1b^2)/(1/2mav2a^2)

= v1a^2/v2a^2 + mbv1b^2/mav2a^2

I'm not sure how to proceed from here and get a percentage.

any help is appreciated.
 
Physics news on Phys.org
mbvo=mbv1+mav2(mv conserved)
mbvo^2= mbv1^2+mav2^2(KE conserved)
making use of these equations, find v1,v2 in terms of mass. and vo...
 
v0 = v1 + mav2/mb

v1 = v0 - mav2/mb

v2 = mbv0/ma - mbv1/ma




found the velocities, but I'm not sure how to proceed.
 
nobody?

I'm not sure what to do with these values?

plug them into the kinetic energy equations and solve perhaps?
 

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