Percentage of kinetic energy after an elastic collision

AI Thread Summary
In an elastic collision involving two objects, one stationary and the other moving, the discussion focuses on determining the percentage of kinetic energy retained by each object post-collision. The initial kinetic energy is expressed as K1, while the final kinetic energy is K2. The user attempts to derive the final velocities of both objects using conservation of momentum and energy equations but is uncertain about how to calculate the percentage of energy retained. The conversation emphasizes the need to substitute the derived velocities into the kinetic energy equations to find the required percentages. Ultimately, the user seeks guidance on how to proceed with these calculations.
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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