Observer A measures the length of two rods, onestationary, the other moving with

Question

Observer A measures the length of two rods, onestationary, the other moving with a speed of 0.915c. She finds that the rods have the samelength, L0. A second observer Btravels along with the moving rod.
(a) What is the length observer Bmeasures for the rod in observer A's frame? (Use L_0 forL0. Express your answer to three decimalplaces.)
1


(b) What is the ratio of the length ofA's rod to the length of B's rod according toobserver B?

(a) What is the length observer Bmeasures for the rod in observer A's frame? (Use L_0 forL0. Express your answer to three decimalplaces.)
1


(b) What is the ratio of the length ofA's rod to the length of B's rod according toobserver B?
(a) What is the length observer Bmeasures for the rod in observer A's frame? (Use L_0 forL0. Express your answer to three decimalplaces.)
1


(b) What is the ratio of the length ofA's rod to the length of B's rod according toobserver B?

Explanation / Answer

(a)
    observer B sees herself at rest, and sees thestationary rod (rod A) as moving past her with a speed of
    v = 0.915 c
    in this case, because rod A (the stationary rod)is at rest in observer A's frame of reference, observer A measuresthe
    proper length
    LpA = L0
    then observer B will measure rod A to have alength of
    LAB = L0 / =L0(1 - 2)
    Inserting = 0.915, we have
    LAB = L0(1- 0.9152)
           = ....... L0
(b)
    observer B measures the proper length for herrod LpB, and this is given by
    then inserting = 0.915, we have
    this is the length that observer B measuresfor the rod B (the moving rod.)
    then the ratio of the lengths of the rodsaccording to observer B is
    LAB / LpB =...........

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