Question

A 2.4 Kg object moving to the right at 0.8c collides with a 3.2 kg object moving to left at 0.6c. They stick
together. Find the mass and velocity of the resulting combined object by;
a) assuming that you have no knowledge of relativistic physics,
b) using the special theory of relativity.
c) Compute the chance in the kinetic energy, what does it correspond to?

Answer 1

Well, we knoew that M1 = 2.4kg, and m2 = 3.2kg. We can then use the convservation of momentum law to find the resulting velocity and momentum after the collision. Since they stick together, we can add their masses.

m1v1 + m2v2 = (m1+m2)v
so
(2.4)(.8) + (3.2)(.6) = (2.4+3.2)v
1.92 + (-1.92) = 5.6v
0 = 5.6v
v = 0
Therefore, the carts stick together and stop.

CHANGE IN KINETIC ENERGY:
EK2 - EK1
1/2mv^2 - 1/2mv^2
1/2(2.4)(.8)^2 - 1/2(3.2)(.6)^2
.768 - .576
= .192J