Homework Help: Finding kinetic energy retained by an object after an elastic head-on collision

1. Nov 7, 2008

JuniorJumper

Hi, Im new to the forums & I have a question about the following problem:

A 0.10 kg object moving initially with a velocity of 0.20 m/s makes an elastic head-on collision with a 0.15 kg object initially at rest. What percentage of the original kinetic energy is retained by the 0.10 kg object?

m1=0.10 kg
vi1=0.20 m/s
v1f=-0.0025 m/s

m2=0.15 kg
vi2=0.00 m/s
v2f=0.198 m/s

I calculated the final velocities of both objects after the collision, but can not decide how to find the kinetic energy retained by m1. I tried finding the kinetic energy lost by m1 (0.002) but then I didnt know where to go from there. I know this must be a simple problem, but Im just not seeing it? Thanks for any guidance :)

2. Nov 7, 2008

physics_31415

You must use conservation of energy AND conservation of linear momemtum. Once you have calculated the final velocities correctly (your's appear to be incorrect ) then you can calculate their respective kinetic energies (1/2*mv^2). You can then compare each final kinetic energy to the initial system energy (K1/Kinitial and K2/Kinitial) to obtain your percentages (note that they should add to 100%). Also, since energy is conserved the sum of the final kinetic energies will equal the initial kinetic energy (of the incoming object). Hope this helps! Good luck!