Homework Statement
A particle of rest mass m0 collides elastically with a stationary particle of equal mass and scatters at angle θ. The incident particle has kinetic energy T0 before the collision and T1 after the collision. (a) Show that T12 (2m0c 2 + T0) 2 = p02 p12 c4 cos2 θ. (b) Using the...
Homework Statement
A rocket, initially at rest, propels itself in a straight line by giving portions of its mass a constant (backward) speed vout relative to its instantaneous rest frame. (a) Is rest mass conserved in this process? (b) Show that m0du′ = −dm0 vout, where m0 is the rocket’s...
Homework Statement
A mirror moves perpendicular to its plane with speed βc. A light ray is incident on the mirror from the “forward” direction (i.e., vm · vl < 0, where vm is the mirror’s 3-velocity and vl is the light ray’s 3-velocity) with incident angle θ (measured with respect to the...
Homework Statement
An inertial observer O bounces a radar signal off an arbitrary event P. If the signal is emitted and received by O at times τ1 and τ2 respectively, as indicated by O’s clock, prove that the squared interval ∆s 2 between O’s origin event (i.e., its spatial origin at time τ =...