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,