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Chapter 37: 4P (page 1145)

(Come) back to the future. Suppose that a father is 20.00 y older than his daughter. He wants to travel outward from Earth for 2.000 y and then back for another 2.000 y (both intervals as he measures them) such that he is then 20.00 y younger than his daughter. What constant speed parameter β (relative to Earth) is required?

Short Answer

Expert verified

The speed parameter is 0.9949 .

Step by step solution

01

Identification of given data

The duration of travel for father from Earth is t0=2y

The difference in age before and after travel for father is t=20y

The Lorentz factor is used to find the speed parameter which is the ratio of the speed of particle with speed of light.

02

Determination of speed parameter relative to Earth 

The speed parameter for travel is given as:

β=1-2t02t2

Substitute all the values in equation.

β=1-22y220y2β=0.9949

Therefore, the speed parameter is 0.9949.

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Most popular questions from this chapter

A radar transmitterTisfixedto a reference frame S'that is moving to the right with speed v relative to reference frame S(Fig. 37-33). A mechanical timer (essentially a clock) in frame S', having a period τ∘ (measured inS' ), causes transmitter Tto emit timed radar pulses, which travel at the speed of light and are received by R, a receiver fixed in frame S. (a) What is the period τof the timer as detected by observer A, who is fixed in frame S? (b) Show that at receiver R the time interval between pulses arriving fromT is not τor τo, but

τR=τoc+vc-v

(c) Explain why receiver Rand observer A, who are in the same reference frame, measure a different period for the transmitter. (Hint: A clock and a radar pulse are not the same thing.)

A rod lies parallel to the x axis of the reference frame S, moving along this axis at a speed of 0.630c. Its rest length is 1.70 m. What will be its measured length in frame S ?

A pion is created in the higher reaches of Earth’s atmosphere when an incoming high-energy cosmic-ray particle collides with an atomic nucleus. A pion so formed descends toward Earth with a speed of 0.99c. In a reference frame in which they are at rest, pion decay with an average life of 26 ns. As measured in a frame fixed with respect to Earth, how far (on the average) will such a pion move through the atmosphere before it decays?

A relativistic train of proper length 200 m approaches a tunnel of the same proper length, at a relative speed of 0.900c. A paint bomb in the engine room is set to explode (and cover everyone with blue paint) when the front of the train passes the far end of the tunnel (event FF). However, when the rear car passes the near end of the tunnel (event RN), a device in that car is set to send a signal to the engine room to deactivate the bomb. Train view: (a) What is the tunnel length? (b) Which event occurs first, FF or RN? (c) What is the time between those events? (d) Does the paint bomb explode? Tunnel view: (e) What is the train length? (f) Which event occurs first? (g) What is the time between those events? (h) Does the paint bomb explode? If your answers to (d) and (h) differ, you need to explain the paradox, because either the engine room is covered with blue paint or not; you cannot have it both ways. If your answers are the same, you need to explain why?

Question: What must be the momentum of a particle with mass m so that the total energy of the particle is 3.00 times its rest energy?
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