THE UNIVERSITY OF BRITISH COLUMBIA
 
Science 1 Physics Assignment # 10:
 
Relativistic Kinematics
 
31 March 1999 - finish by 7 April

1.

RELATIVISTIC ELECTRON:

(a)

An electron has a momentum that is 80 % larger than its classical momentum.

i.

Find the speed of the electron.

ii.

How would your result change if the particle were a ten-gram bullet?

(b)

An electron has a kinetic energy five times greater than its rest mass energy. Find

i.

its total energy;

ii.

its speed.

2.

DECAY KINEMATICS: A $K^\circ$ particle, whose mass is $m_{K^\circ} = 497.7$ Mev/c², decays into a $\pi^+$ and a $\pi^-$, each of which has a mass of $m_{\pi^\pm} = 139.6$ Mev/c². What are the kinetic energies and the velocities of the pions ($\pi^+$ and $\pi^-$) if the $K^\circ$ is at rest prior to the decay?

3.

SCATTERING OF A MASSLESS PARTICLE: [OPTIONAL - this one is hard!]
A massless particle with initial momentum p_i scatters elastically off a particle of mass m that is initially at rest. After the collision the massless particle has a momentum p_f and is moving at an angle $\theta$ with respect to its original direction. Show that the above parameters satisfy the following relation:

$${1 \over p_f} - {1 \over p_i} = {1 - \cos \theta \over mc}$$