Embed Size px x x x x Inha University Department of PhysicsChapter 1. Problem Solutions1. If the speed of light were smaller than it is, would relativistic phenomena be more or less conspicuous than they are now? An athlete has learned enough physics to know that if he measures from the earth a time interval on a moving spacecraft, what he finds will be greater than what somebody on the spacecraft would measure.

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Chapter 1. Problem Solutions. If the speed of light were smaller than it is, would relativistic phenomena be more or less conspicuous than they are now? If we could attain the absolute speeds obtainable to us in the universe as it is, but with the speed of light being smaller, we would be able to move at speeds that would correspond to larger fractions of the speed of light, and in such instances relativistic effects would be more conspicuous.

An athlete has learned enough physics to know that if he measures from the earth a time interval on a moving spacecraft, what he finds will be greater than what somebody on the spacecraft would measure.

He therefore proposes to set a world record for the m dash by having his time taken by an observer on a moving spacecraft. Is this a good idea? Actually, when the effects of length contraction are included discussed in Section 1. Inha University. Department of Physics.

Two observers, A on earth and B in a spacecraft whose speed is 2. To B , does A 's watch seem to run fast, run slow, or keep the same time as his own watch? In Equation 1. In this problem, the time t is the time that observer A measures as the time that B's clock takes to record a time change of t o.

How fast must a spacecraft travel relative to the earth for each day on the spacecraft to correspond to 2 d on the earth? A certain particle has a lifetime of 1. How far does it go before decaying if its speed is 0. If one of the characteristic wavelengths of the light the galaxy emits is nm, what is the corresponding wavelength measured by astronomers on the earth? For this problem,. A spacecraft receding from the earth emits radio waves at a constant frequency of 10 9 Hz.

If the receiver on earth can measure frequencies to the nearest hertz, at what spacecraft speed can the difference between the relativistic and classical Doppler effects be detected?

For the classical effect, assume the earth is stationary. The classical and relativistic frequencies, v c and v r respectively, are. The last expression for v o , is motivated by the derivation of Equation 1. Use of the above forms for the frequencies allows the calculation of the ratio. Attempts to solve this equation exactly are not likely to be met with success, and even numerical solutions would require a higher precision than is commonly available. However, recognizing that.

The denominator will. If the angle between the direction of motion of a light source of frequency v o and the direction from it to an observer is 0, the frequency v the observer finds is given by.

Show that this formula includes Eqs. An astronaut whose height on the earth is exactly 6 ft is lying parallel to the axis of a spacecraft moving at 0. What is his height as measured by an observer in the same spacecraft? By an observer on the earth? From Equation 1. How much time does a meter stick moving at 0. The meter stick is parallel to its direction of motion. A spacecraft antenna is at an angle of 10 o relative to the axis of the spacecraft.

If the spacecraft moves away from the earth at a speed of 0. To an observer on the earth, the length in the direction of the spacecraft's axis will be contracted as described by Equation 1. The angle as seen from the earth will then be. The generalization of the above is that if the angle is 00 as measured by an observer on the spacecraft, an observer on the earth would measure an angle q given by. A woman leaves the earth in a spacecraft that makes a round trip to the nearest star, 4 light-.

All definitions are arbitrary, but some are more useful than others. Dynamite liberates about 5. What fraction of its total energy content is this? At what speed does the kinetic energy of a particle equal its rest energy? Solving for v ,. An electron has a kinetic energy of 0. Find its speed according to classical and relativistic mechanics. Relativistically, solving Equation 1.

The two speeds are comparable, but not the same; for larger values of the ratio of the kinetic and rest energies, larger discrepancies would be found.

A particle has a kinetic energy 20 times its rest energy. Find the speed of the particle in terms of c. How much work in MeV must be done to increase the speed of an electron from 1. Prove that. Figure 1. A burst of electromagnetic radiation of energy E o is emitted by one end of the box. If the CM of the box is to remain in its original place, the radiation must have transferred mass from one end to the other.

In its own frame of reference, a proton takes 5 min to cross the Milky Way galaxy, which is. Find the momentum of an electron whose kinetic energy equals its rest energy of keV.

The result of Problem does not give an answer accurate to three significant figures. The value of the speed may be substituted into Equation 1.

Expanding the binomial, cancelling the m 2 c 4 term, and solving for m ,. The particle's speed may be found any number of ways; a very convenient result is that of Problem. An observer detects two explosions, one that occurs near her at a certain time and another. Another observer finds that the two explosions occur at the, same place.

What time interval separates the explosions to the second observer? Inserting this into Equation 1. Algebraically and numerically, the different methods give the same result. In the reference frame of the fixed stars, the speed of the spacecraft is v and the signal arrives at an angle q to the axis of the spacecraft. Take the direction of the ship's motion assumed parallel to its axis to be the positive x -direction, so that in the frame of the fixed stars the unprimed frame , the signal arrives at an angle 0 with respect to the positive x -direction.

A man on the moon sees two spacecraft, A and B , coming toward him from opposite directions at the respective speeds of 0. For the speed with which he is approaching B? For the speed with which he is approaching A? The relative velocities will have. The speed with which B is seen to approach A , to an observer in A , is then. Note that Equation 1. Chapter 2. If Planck's constant were smaller than it is, would quantum phenomena be more or less conspicuous than they are now?

That is, quantum phenomena would be less conspicuous than they are now. Is it correct to say that the maximum photoelectron energy KE m a x is proportional to the frequency n of the incident light? If not, what would a correct statement of the relationship between KE m a x and n be? So that while KE m a x is a linear function of the frequency n of the incident light, KE m a x is not proportional to the frequency.

Find the energy of a nm photon. From Equation 2. Or, in terms of joules,. How many photons per. Light from the sun arrives at the earth, an average of 1. Assume that sunlight is monochromatic with a frequency of 5. The total power is then,. Using the result from part a ,.

The maximum wavelength for photoelectric emission in tungsten is nm. What wavelength. What is the maximum wavelength of light that will cause photoelectrons to be emitted from. What will the maximum kinetic energy of the photoelectrons be if nm light falls on a sodium surface?

A metal surface illuminated by 8. Subtracting to eliminate the work function f and dividing by n 1 - n 2 ,. Keeping an extra figure gives. This last calculation, while possibly more cumbersome than direct substitution, reflects the result of solving the system of equations using a symbolic-manipulation program; using such a program for this problem is, of course, a case of "swatting a fly with a sledgehammer".

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## Solution Manual of Physics by Arthur Beiser

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