Question

two cars of equal mass with equal speeds traveling perpendicular to one another collide completely in elastically. what percentage of the cars' total energy is lost in the collision?

Answer 1

ritzi as in spikey sea urchins?

If a collision is elastic, no kinetic energy is lost. That is what an elastic collision means.

Answer 2

two cars of equal mass with equal speeds traveling perpendicular to one another collide completely inelastically. what percentage of the cars' total energy is lost in the collision?

Answer 3

If they stick together then momentum is conserved

x momentum before = m v
y momentum before = m v

x momentum after = 2 m U cos theta
y momentum after = 2 m U sin theta
so
2 U cos theta = v
2 U sin theta = v
or
cos theta = sin theta so theta = 45 degrees
cos theta = cos 45 = sqrt2/2 = sin theta

2 U = v/cos theta = 2 v /sqrt 2
so
U = v/sqrt 2

Ke before = 2 (1/2) m v^2 = m v^2
Ke after = (1/2) (2m) U^2 = m v^2/2
so half the Ke would be lost if there were no bounce at all