# Alternate Solution to Conservation of Momentum Problem

1. Sep 30, 2013

### aboakye

I solved the following problem using Energy instead of conservation of momentum. Unfortunately, my answer is different from the expected solution. I'm not sure why my method doesn't work.

Any insights would be appreciated!

Problem:
A 2000 kg truck is traveling east through an intersection at 2 m/s when it is hit simultaneously from the side and the rear. One car is a 1000 kg compact traveling north at 5 m/s. The other car is a 1500 kg midsize traveling east at 10 m/s. The three vehicles become entangled and slide at one body. What are their speeds and direction just after the collision?

My Attempt:
Energy east/x: (1/2)*1500*100 + (1/2)*2000*4 = 79 kJ
Energy north/y: (1/2)*1000*25 = 12.5 kJ

Final speed: $\sqrt{2.2^{2} + 5.92^{2} }$ = 6.32 m/s
@Angle: tan^{-1}(2.2/5.92) = 20.4°

Solution:
mvxfinal = 1500*100 + 2000*4 solve for v in x-dir
mvyfinal = 1000*5 solve for v in y-dir

2. Sep 30, 2013

### Staff: Mentor

The vehicles become entangled. Kinetic energy is not conserved! (But momentum is.)

3. Sep 30, 2013

### tiny-tim

welcome to pf!

hi aboakye! welcome to pf!

energy is never conserved in a collision unless the question says it is!

(but momentum is always conserved in a collision, in any direction in which there is no external impulse)

4. Sep 30, 2013

### aboakye

Thanks Doc Al & tiny-tim!

That clarifies it