Download HW 2 due F Feb 20.

HW2
S15
Modern Physics
Problem 1
Relativistic Collision
due at 5pm F 2/20/2015
A particle of rest mass 2 m0 moving with a speed of 0.9c makes a completely inelastic head-on
collision with a particle of rest mass 4m0 that is initially at rest.
a) What is the rest mass of the resulting single body?
b) Re-work the problem from the rest frame of the particle with 2 m0.
Problem 2
Relativistic Velocity Addition
Rocket A travels to the right and rocket B travels to the left, with velocities 0.9c and 0.94c,
respectively, relative to the earth.
a) What is the velocity of rocket A measured from rocket B?
Solve the problem for all associations of velocities possible in the velocity
transformation formula.
Problem 3
Relativistic Velocity Transformation
At t = 0 observer S emits a photon in the direction of 60° with the x-axis.
a) With what speed is the photon travelling?
b) A second observer, S’, travels with a speed of 0.7c along the common x-x’ axis. What
angle does the photon make with the x—axis of S’?
c) A third observer, S’’, travels with a speed of 0.7c along the common y-y’ axis. What
angle does the photon make with the x-axis of S’’?
Problem 4
Relativistic Doppler Shift
A woman in a rocket moving with 0.6c away from a space platform shines a light of wavelength
500 [nm] toward the platform. What is the frequency of the light seen by an observer S on the
platform? What is the frequency of the light seen by an observer in a second rocket, which
follows the woman’s rocket and which leaves the platform with 0.75c?
Problem 5
Relativistic Energy
a) At what fraction of c must a particle move so that its kinetic energy is double its rest
energy?
b) An electron’s velocity is 5*107 [m/s]. How much energy is needed to double the speed?
To raise the speed to 99% of c?
c) How does an observer in frame S’ that moves with 0.5c along the direction of motion of
the electron view the situation?
d) How does an observer in frame S’ that moves with 0.5c perpendicular to the direction of
motion of the electron view the situation?