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Chapter 37: Q72P (page 1150)

Find the speed parameter of a particle that takes 2.0 y longer than light to travel a distance of 6.0 ly.

Short Answer

Expert verified

The speed of the particle is 0.75c.

Step by step solution

01

Light Year

A light-year is a unit of distance where 1 ly is the distance that light travels in one year.

So it will take 6 years for the light to cover 6 ly distance. And the particle takes 2 years longer than light for the same distance. Hence the total time taken for the particle is 8 years.

02

The speed of the particle

The speed of the particle is

speed=totaldistancetotaltime=6ly8y=6×9.46×1015m8×3.156×107s=2.25×108m/s=0.75c

The speed of the particle is 0.75c.

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Most popular questions from this chapter

The mass of an electron is 9.10938188×10-31kg. To six significant figures, find (a) data-custom-editor="chemistry" γand (b) data-custom-editor="chemistry" β for an electron with kinetic energy K = 100.000 MeV.

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.)

Figure 37-18 shows two clocks in stationary frame S(they are synchronized in that frame) and one clock in moving frame S'.Clocks C1and C'1read zero when they pass each other. When clocks C1and C2pass each other, (a) which clock has the smaller reading and (b) which clock measures a proper time?

Question: Temporal separation between two events. Events and occur with the following spacetime coordinates in the reference frames of Fig. 37-25: according to the unprimed frame,andaccording to the primed frame, (xA,tA)and(xB,tB). In the unprimed frame ∆t=tB-tA=1.00μsand Δx=xB-xA=240m. (a) Find an expression for Δt'in terms of the speed parameterβand the given data. Graph Δt' versus βfor the following two ranges of β: (b) 0 to 0.01and 0.1 (c) 0.1 to 1. (d) At what value of βis Δt'minimum and (e) what is that minimum? (f) Can one of these events cause the other? Explain.

A spaceship of rest length 130 m races past a timing station at a speed of 0.740c. (a) What is the length of the spaceship as measured by the timing station? (b) What time interval will the station clock record between the passage of the front and back ends of the ship?
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