Question

A pair of twins are 18.0 years old. When they leave fir Zog, a planet sixty light-years away. Alice travels on a spaceship traveling at 5e/13 while Beth travels at 12c/13. They reunite as soon as the slower arrives. How old are each of the twins when they reunite? A particle has mass 135 MeV/v^2, and the flies at speed 12c/13, Calculate the particles: a. Energy b. Momentum (magnitude) c. Kinetic Energy In the problem before last, how fast is Beth going with respect to Alice?

Answer 1

Problem 5)

The rest mass of the particle is,

$m_0=135MeV/c^2$

Here ,

$\beta=\frac{v}{c}=\frac{12}{13}$

So,

$\gamma=\frac{1}{\sqrt{1-\beta^2}}=\frac{1}{\sqrt{1-12^2/13^2}}=2.6$

a) So the energy of the particle is,

$E=m\gamma c^2=135\times2.6MeV=351MeV$

b) The momentum is p

$E^2=p^2c^2+(m_0c^2)^2$

$p=\sqrt{E^2-(m_0c^2)^2}/c=\sqrt{351^2-135^2}MeV/c=324MeV/c$

c) Kinetic energy is,

$KE=E-m_0c^2$