2D inelastic collision and K of CM

[sci-doo]

Homework Statement

Car 1 (1500kg) is heading north 80km/h, Car 2 (3500kg) is heading east 50km/h. They collide inelastically.
a.) Speed and direction of the wreck (car 1 + car 2)?
b.) The kinetic energy lost?
HERE I HAVE A PROBLEM:
c.) What is the kinetic energy of the two-particle systems center of mass before and after the collision?
d.) Where was the lost kinetic energy hidden before the collision?

2. The attempt at a solution
a. is just vector sum p1+p2 where I can get the velocity by dividing it with the masses (about 12m/s), I can get the angle too (34,438... deg)
b. wrecks K minus K of car 1 and car 2 = - 360532,40... J so about 360 kJ lost
c. But this one I don't understand. I'd say it stays the same, because... well, that's what I calculated (CM from the v-vectors = v of CM), yet I don't really believe it...
d. ... after all shouldn't the K be lost to deformation of bodies (+heat etc.)? Does the K of CM stay the same anyways?

 

[sci-doo]

Ok, I found something useful on the net:
http://courses.washington.edu/ph122mo/A08/MT3info.html"
# Inelastic collisions

* momentum is still conserved
* kinetic energy of center of mass motion cannot be lost
* maximum energy loss for items sticking together after collision


And that is really all I needed to know.

 

[nlightner]

I would like to address the following points:

a. Your approach to calculating the speed and direction of the wreck is correct. However, it is important to note that the final velocity of the two cars will be a combination of both the initial velocities, rather than just the vector sum. This is because the collision is inelastic, meaning that some of the kinetic energy will be lost during the collision.

b. Your calculation of the kinetic energy lost is also correct. The lost kinetic energy is due to the deformation and damage to the cars during the collision. This energy is converted into other forms, such as heat and sound.

c. The kinetic energy of the two-particle system's center of mass (CM) before and after the collision will remain the same. This is because the CM is a property of the system as a whole, and it is not affected by internal interactions between the two cars. Therefore, even though some kinetic energy is lost during the collision, the total kinetic energy of the system (including the CM) will remain constant.

d. The lost kinetic energy is hidden in the deformation and damage to the cars, as well as in the form of heat and sound. As mentioned before, this energy is converted into other forms during the collision. The kinetic energy of the CM is not affected by this as it is a property of the system as a whole.

In summary, the conservation of energy is still applicable in an inelastic collision, but some of the kinetic energy is converted into other forms. The kinetic energy of the CM remains constant as it is a property of the system as a whole.