ABSTRACT

First solution: We assume this is an elastic collision; that is, we do not worry about the details of the actual collision. Conservation of momentum doesn’t

help here-there is no momentum either before or after the collision. So we

need to use conservation of energy. After the collision, there is no kinetic

energy, so we have

E′ = Mc2. (10.1)

Before the collision, we know that the energy of each lump is

E = mc2 coshα, (10.2)

but how do we find α? We are given that each lump is moving at 35 c, so

this means we know

tanhα = 3

5 . (10.3)

Yes, we could now use the formula coshα = 1/ √ 1− tanh2 α, but it is easier

to use a triangle. Since tanhα = 35 , we can scale things so that the legs

have “lengths” 3 and 5. Using the hyperbolic Pythagorean theorem, the

hypotenuse has length √ 52 − 32 = 4. This is just the triangle in Figure 4.3.

Thus,