Considerthe same situation as in the previous question: A train travelling along the x-axis past a platform at a speed V, with a passenger at rest in the train holding a ruler oflength L parallel to the x-axis. If for a stationary observer on the platform the length of the ruler is L/3, the train is travelling at a speed V of:Select one:O a.2√2 cO b.O c. 3€O d. 2c

This question involves the concept of length contraction from the theory of special relativity. The…

Answered: Consider the same situation as in the…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section: Chapter Questions

Problem 2PQ

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A rod of length L0 moving with a speed v along the horizontal direction makes an angle 0 with respect to the x axis. (a) Show that the length of the rod as measured by a stationary observer is L = L0[1 (v2/c2)cos2 0]1/2. (b) Show that the angle that the rod makes with the x axis is given by tan = tan 0. These results show that the rod is both contracted and rotated. (Take the lower end of the rod to be at the origin of the primed coordinate system.)
What is if (b) If
Joe and Moe are twins. In the laboratory frame at location S1 (2.00 km, 0.200 km, 0.150 km). Joe shoots a picture for aduration of t= 12.0 s. For the same duration as measured inthe laboratory frame, at location S2 (1.00 km, 0.200 km,0.300 km), Moe also shoots a picture. Both Joe and Moe begintaking their pictures at t = 0 in the laboratory frame. Determine the duration of each event as measured by an observer ina frame moving at a speed of 2.00 108 m/s along the x axisin the positive x direction. Assume that at t = t = 0, the origins of the two frames coincide.
The truck in Figure P39.1 is moving at a speed of 10.0 m/s relative to the ground. The person on the truck throws a baseball in the backward direction at a speed of 20.0 m/s relative to the truck. What is the velocity of the baseball as measured by the observer on the ground? Figure P39.1
The Sun produces energy at a rate of 4.001026 W by the fusion of hydrogen. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the Sun is 90.0% hydrogen and half of this can undergo fusion before the Sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the Sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?
Unreasonable Results Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth. (a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity? (c) Is there a problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height? (d) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.
A car traveling at 35.0 m/s takes 26.0 minutes to travel a certain distance according to the drivers clock in the car. How long does the trip take according to an observer at rest on Earth? Hint: The following approximation is helpful: [1x]121+12xforx1.
An observer in reference frame S sees two events as simultaneous. Event A occurs at the point (50.0 m, 0, 0) at the instant 9:00:00 Universal time, 15 January 2001. Event B occurs at the point (150 m, 0, 0) at the same moment. A second observer, moving past with a velocity of , also observes the two events. In her reference frame S′, which event occurred first and what time elapsed between the events?
(a) Show that that at large velocities This means that at large velocities(b) Is when as for the astronaut discussed in the twin paradox?
According to special relativity, a particle of rest mass m0 accelerated in one dimension by a force F obeys the equation of motion dp/dt = F. Here p = m0v/(1 –v2/c2)1/2 is the relativistic momentum, which reduces to m0v for v2/c2 << 1. (a) For the case of constant F and initial conditions x(0) = 0 = v(0), find x(t) and v(t). (b) Sketch your result for v(t). (c) Suppose that F/m0 = 10 m/s2 ( ≈ g on Earth). How much time is required for the particle to reach half the speed of light and of 99% the speed of light?
a) Suppose you decide to travel to a star 66 light-years away at a speed that tells you the distance is only 24 light-years. How many years would it take you to make the trip? Express your answer using two significant figures. b)In its own reference frame, a box has the shape of a cube 1.5 mm on a side. This box is loaded onto the flat floor of a spaceship and the spaceship then flies past us with a horizontal speed of 0.90 cc.What is the volume (m3 ) of the box as we observe it?
an airport worker measures the length of a runway to be Lo. a spaceship,s, flies horizontally in a straight line over the runway with a constant speed of .8c with the respect to the runway. according to the pilots wristwatch, the time of flight over the runway was 20 miu/s. the time measured by the airport clock for s to fly over the runway was Tg. the physical dimensions of s can be neglected. does the pilot measure the proper time of flight over the runway? yes/no what is the length of the runway as measured by the pilot? whats the value of Lo? whats the value of tg?

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