# 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!

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook