Q: (a) Equation 12.40 defines proper velocity in terms
(a) Equation 12.40 defines proper velocity in terms of ordinary velocity. Invert that equation to get the formula for u in terms of η. (b) What is the relation between proper velocity and rapidity (Eq....
See AnswerQ: A car is traveling along the 45◦ line in S (
A car is traveling along the 45◦ line in S (Fig. 12.25), at (ordinary) speed / (a) Find the components ux and uy of the (ordinary) velocity. (b) Find the components η...
See AnswerQ: Find the invariant product of the 4-velocity with itself,
Find the invariant product of the 4-velocity with itself, ημημ. Is ημ timelike, spacelike, or lightlike?
See AnswerQ: A cop pulls you over and asks what speed you were going
A cop pulls you over and asks what speed you were going. “Well, officer, I cannot tell a lie: the speedometer read 4* 108 m/s.” He gives you a ticket, because the speed limit on this highway is 2.5* 1...
See AnswerQ: Consider a particle in hyperbolic motion, / (a
Consider a particle in hyperbolic motion, / (a) Find the proper time τ as a function of t , assuming the clocks are set so that τ = 0 when t = 0. [Hint: Integrate Eq. 12.37.] (b) Find x and v (ordina...
See AnswerQ: (a) Repeat Prob. 12.2(a)
(a) Repeat Prob. 12.2(a) using the (incorrect) definition p=mu, but with the (correct) Einstein velocity addition rule. Notice that if momentum (so defined) is conserved in S, it is not conserved in S¯....
See AnswerQ: (a) What’s the percent error introduced when you use Galileo’s
(a) What’s the percent error introduced when you use Galileo’s rule, instead of Einstein’s, with vAB = 5 mi/h and vBC = 60 mi/h? (b) Suppose you c...
See AnswerQ: If a particle’s kinetic energy is n times its rest energy,
If a particle’s kinetic energy is n times its rest energy, what is its speed?
See AnswerQ: Suppose you have a collection of particles, all moving in the
Suppose you have a collection of particles, all moving in the x direction, with energies E1, E2, E3,……and momenta p1, p2, p3,……Find the velocity of the center of momentum frame, in which the total mom...
See AnswerQ: Check the divergence theorem for the function v = r 2
Check the divergence theorem for the function v = r 2 cos θ rˆ + r 2 cos φ θˆ − r 2 cos θ sin φ φˆ, using as your volume one octant of the sphere of radius R (Fig. 1.48). Make sure you include the ent...
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