Chapter 2: Q20E (page 62)
Through a window in Carl's spaceship, passing al 0.5c, you watch Carl doing an important physics calculation. By your watch it takes him 1 min. How much time did Carl spend on his calculation?
The time spends by Carl in spaceship for calculation is.
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Question: A 1 kg object moves at 0.8c relative to Earth.
(a) Calculate the momentum and the energy of the object.
(b) Determine the Lorentz transformation matrix from the earthโs frame to the objectโs frame.
(c) Find the momentum and total energy of the object in the new frame via matrix multiplication.
In Example 2.5, we noted that Anna could go wherever she wished in as little time as desired by going fast enough to length-contract the distance to an arbitrarily small value. This overlooks a physiological limitation. Accelerations greater than about are fatal, and there are serious concerns about the effects of prolonged accelerations greater than Here we see how far a person could go under a constant acceleration of 1g, producing a comfortable artificial gravity.
(a) Though traveller Anna accelerates, Bob, being on near-inertial Earth, is a reliable observer and will see less time go by on Anna's clock than on his own Thus, , where u is Anna's instantaneous speed relative to Bob. Using the result of Exercise with replacing F/m, substitute for then integrate to show that
(b) How much time goes by for observers on Earth as they โseeโ Anna age 20 years?
(c) Using the result of Exercise 119, show that when Anna has aged a time tโ, she is a distance from Earth (according to Earth observers) of
(d) If Anna accelerates away from Earth while aging 20 years and then slows to a stop while aging another 20. How far away from Earth will she end up and how much time will have passed on Earth?
The boron-nucleus (mass: 14.02266 u) "beta decays," spontaneously becoming an electron (mass: 0.00055 u) and a carbon- nucleus (mass: 13.99995 u). What will be the speeds and kinetic energies of the carbon-nucleus and the electron? (Note: A neutrino is also produced. We consider the case in which its momentum and energy are negligible. Also, because the carbon- nucleus is much more massive than the electron it recoils ''slowly''; .)
Refer to Figure 2.18. (a) How long is a spaceship? (b) At what speed do the ships move relative to one another? (c) Show that Annaโs times are in accord with the Lorentz transformation equations. (d) Sketch a set of diagrams showing Annaโs complementary view of the passing of the ships. Include times in both frames.
What is the momentum of a proton accelerated through gigavolts (GV)?
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