# Alternate Solution to Conservation of Momentum Problem

• aboakye
In summary, the problem involved a collision between a 2000 kg truck, a 1000 kg compact car, and a 1500 kg midsize car. The solution was attempted using energy instead of conservation of momentum, but this did not yield the expected results. The vehicles became entangled and kinetic energy was not conserved, highlighting the importance of considering the specific conditions of a problem.

#### 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

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

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)

Thanks Doc Al & tiny-tim!

That clarifies it