Alternate Solution to Conservation of Momentum 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: [itex]\sqrt{2.2^{2} + 5.92^{2} }[/itex] = 6.32 m/s
@Angle: tan^{-1}(2.2/5.92) = 20.4°

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

 

[Doc Al]

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.)

 

[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)

 

[aboakye]

Thanks Doc Al & tiny-tim!

That clarifies it

 

[Nickie]

I appreciate your alternative approach to solving this problem using energy instead of conservation of momentum. However, I believe the discrepancy in your answer may be due to the fact that energy is not always conserved in collisions. In this case, the collision between the three vehicles is inelastic, meaning that some of the initial kinetic energy is converted into other forms of energy, such as heat or sound. This means that the final energy of the system may not be equal to the initial energy, leading to different results.

In order to accurately solve this problem, it is important to use conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. This takes into account the masses and velocities of all three vehicles and can provide a more precise solution.

Furthermore, it may be helpful to review the equations used in your attempt and ensure that all units are consistent. It is also important to consider the direction of the forces and their effects on the final velocities of the vehicles.

I hope this provides some insights into why your method did not work and encourages you to continue exploring alternative approaches in problem-solving. As scientists, it is important to continuously question and improve our methods in order to deepen our understanding and advance our knowledge.