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physics
modern physics

Questions and Answers of Modern Physics

The ocean can be as deep as 10 km. (a) Assuming the density for seawater is constant at the value given in Table 9.2, what is the absolute pressure at such depths? (b) What would be the percentage
In preparation for its tire rotation, a car weighing 2.25 tons is placed on a hydraulic garage lift. The mechanic then raises the car 30.0 cm. (a) Calculate the work done on the car when it is
A spherical object has an outside diameter of 48.0 cm. Its outer shell is composed of aluminum and is 2.00 cm thick. The remainder is uniform plastic with a density of 800 kg/m3. (a) Determine the
As a medical technologist, you are attending to a worker who has been wounded by an accidental industrial explosion. After measuring her arterial blood pressure to be 132/86, you determine her major
A metal wire 1.0 mm in diameter and 2.0 m long hangs vertically with a 6.0-kg object suspended from it. If the wire stretches 1.4 mm under the tension, what is the value of Young’s modulus for the
An engineer is designing a water filter that works by forcing water through a circular plate that has many identical holes in it. The plate is to be welded into a pipe so the water stream and the
When railroad tracks are installed, gaps are left between the rails. (a) Should a greater gap be used if the rails are installed on (1) a cold day or (2) a hot day? Or (3) does the temperature not
A boy wants to store a 5-m-long pole in a shed that is only 4 m long (it does have both front and rear doors). He claims that if he runs through the shed sufficiently fast, according to an observer
You are standing on the Earth and observe a spacecraft speeding by with your professor on board. (a) If both you and your professor are observing your wristwatch, who is measuring the proper time?
If an electron has a kinetic energy of 2 keV, could the classical expression for kinetic energy be used to compute its speed accurately? What if its kinetic energy is 2 MeV? Explain.
If a proton has a kinetic energy of 2 MeV, could the classical expression for kinetic energy be used to compute its speed accurately? What if its kinetic energy is 2000 MeV? Explain.
A puzzle like that in Fig. 26.18 was given to Albert Einstein on his 76th birthday by Eric M. Rogers, a physics professor at Princeton University. The goal is to get the ball into the cup without
It is conjectured that an enormous black hole exists at the center of our galaxy, the Milky Way. Our solar system is located near the outer edge of the galaxy, some 30 000 light- years from the
If you are located at a certain distance above the event horizon of a black hole, you can look straight ahead and see the back of your head. Explain how this is possible.
A car accelerating from rest is a noninertial system. Explain the “forces” (and draw the free-body diagram) that the driver uses to explain why a coffee mug on the slippery dashboard might slide
At an astronomical meeting, it is reported two galaxies had been detected, approaching each other with speeds of 0.700c and 0.600c (relative to the Earth), respectively. As a cub reporter, you are
As a space station commander, you see two rockets traveling to opposite ends of the galaxy. Rocket A is traveling at 0.800c and rocket B is traveling in exactly the opposite direction at 0.700c. Will
Events A and B happen on your x-axis. They are separated by 500 m. You observe that A occurs 1.00 μs before B. Could A have caused B? Explain.
In Question 4, does there exist an inertial reference frame moving along the x-axis whose observer might observe the two events at the same location? If so, what direction would that frame’s
In the gedanken experiment shown in Fig. 26.16, two events in the same inertial reference frame O are related by cause and effect: (1) A gun at the origin fires a bullet along the x-axis with a speed
In a gedanken experiment (Fig. 26.17), two events that cannot be related by cause and effect occur in the same inertial reference frame O: (1) Strobe light A, at the origin of the x- axis, flashes;
Two identical high-speed rockets pass your (inertial) space station. Their pilots each claim that their rocket is 100 m long. You measure the length of rocket A to be 89 m and that of rocket B to be
A person 1.20 km away from you fires a gun. A wind is blowing at 10.0 m/s. How much different from the “no wind” time of travel is there for the sound to reach you compared to the situation when
Your pulse rate is 70 beats/min, and your physics professor in a spacecraft is moving with a speed of 0.85c relative to you. (a) According to your professor, your pulse rate is (1) greater than 70
You fly your 15.0-m-long spaceship at a speed of c/3 relative to your friend. Your velocity is parallel to the ship’s length. (a) How long is your spaceship, as observed by your friend? (b) What
An astronaut in a spacecraft moves past a field 100 m long (according to a person standing on the field) and parallel to the field’s length at a speed of 0.75c. (a) Will the length of the field,
The proper lifetime of a muon is 2.20μs. If the muon has a lifetime of 34.8 μs according to an observer on Earth, what is the muon’s speed, expressed as a fraction of c, relative to the observer?
One of a pair of 25-year-old twins takes a round trip through space while the other twin remains on Earth. The traveling twin moves at a speed of 0.95c for a total of 39 years, according to Earth
Alpha Centauri, a star close to our solar system, is about 4.3 light-years away. Suppose a spaceship traveled this distance at a constant speed of 0.90c relative to Earth. (a) How long did the trip
A cylindrical spaceship of length 35.0 m and diameter 8.35 m is traveling in the direction of its cylindrical axis (length). It passes by the Earth at a relative speed of 2.44 x 108 m/s. (a) What
A pole vaulter at the Relativistic Olympics sprints past you to do a vault at a speed of 0.65c. When he is at rest, his pole is 7.0 m long. (a) What length do you perceive the pole to be as he
The distance to Planet X from Earth is 1.00 light-year. (a) How long does it take a spaceship to reach X, according to the pilot of the spaceship, if the speed of the ship is 0.700c relative to X?
A student notes that the length of a 12-in.-long ruler held by her professor (who is moving relative to her) is the same as that of her meterstick (when oriented parallel to his ruler). (a) What is
A small airplane has an airspeed (speed with respect to air) of 200 km/h. Find the time for the airplane to travel 1000 km if there is (a) No wind, (b) A headwind of 35 km/h, and (c) A tailwind of
Sirius is about 9.0 light-years from Earth. (a) To reach the star by spaceship in 12 years (ship time), how fast must you travel? (b) How long would the trip take according to an Earth-based
(a) To see that length contraction is negligible at everyday speeds, determine the length contraction (∆L) of an automobile 5.00 m long when it is traveling at 100 km/h. The diameter of an atomic
An electron travels at a speed of 0.600c. What is its kinetic and total energy?
An electron is accelerated from rest through a potential difference of 2.50 MV. Find the electron’s (a) Speed, (b) Kinetic energy, and (c) Momentum.
How fast must an object travel for its total energy to be (a) More than its rest energy and (b) More than its rest energy?
An average home uses about 1.5 x 104 kWh of electricity per year. How much matter would have to be converted to energy (assuming 33% efficiency) to supply energy for 1 year to a city with 250 000
The United States uses approximately 3.0 trillion kWh of electricity annually. If 20% of this electrical energy were supplied by nuclear generating plants, how much nuclear mass would have to be
To travel to a nearby star, a spaceship travels at 0.99c to take advantage of time dilation. If the ship has a mass of 3.0 x 106 kg, how much work must be done to get it up to speed from rest?
An electron has a total energy of 5.6 MeV. What is its (a) Kinetic energy and (b) Momentum?
(a) How much work (expressed in keV) is required to accelerate an electron from rest to 0.50c? (b) How much kinetic energy would it have at this speed? (c) What would be its momentum?
A speedboat can travel with a speed of 50 m/s in still water. If the boat is in a river that has a flow speed of 5.0 m/s, (a) Find the maximum and minimum values of the boat’s speed relative to an
A proton is traveling at a speed of 0.55c. What are its (a) Total energy, (b) Kinetic energy, and (c) Momentum?
A proton moving with a constant speed has a total energy 3.5 times its rest energy. What are the proton’s (a) Speed, (b) Kinetic energy, and (c) Momentum?
The Sun’s mass is 1.989 x 1030 kg and it radiates at a rate of 3.827 x 1023 kW. (a) Over time, must the mass of the Sun (1) increase, (2) remain the same, or (3) decrease? (b) Estimate the
Phase changes require energy in the form of latent heat (Chapter 11). (a) If 1 kg of ice at 0oC is converted to water at 0oC, will the water have (1) more, (2) the same, or (3) less mass compared to
A particle of mass m, initially moving with speed v, collides head on elastically with an identical particle initially at rest. (a) Do you expect the total mass of the two particles after the
(a) Using the relativistic expression for total energy E and the magnitude p of the momentum of a particle, show that the two quantities are related by E2 = p2c2 + (mc2)2. (b) Use this expression to
The operator of a linear accelerator tells a tour group that it is used to give protons an energy of 600 MeV. (a) This 600 MeV must refer to the proton’s (1) total energy, (2) kinetic energy, (3)
If the Sun became a black hole, what would be its average density, assuming it to be a sphere with a radius equal to the Sun’s Schwarzschild radius? Compare your answer to the actual average
In Exercise 37, what would be the acceleration due to gravity at a distance of two Schwarzschild radii from the center of the “black hole” Sun? Compare your answer to the actual gravitational
In Exercise 37, what would be the escape speed at a distance of two Schwarzschild radii from the center of the “black hole” Sun? Compare your answer to the actual escape speed at a distance of
A boat can make a round trip between two locations, A and B, on the same side of a river in a time t if there is no current in the river. (a) If there is a constant current in the river, the time
A black hole has an event horizon radius of 5.00 x 103m. (a) What is its mass? (b) Determine the gravitational acceleration it produces at a distance of 5.01 x 103m from its center. (c) Determine
Suppose two black holes meet and “coalesce” into one larger black hole. If they each have the same mass M and Schwarzschild radius R, (a) Express the single black hole’s Schwarzschild radius
Let’s try a generalization of Exercise 41. Experimental evidence strongly indicates the existence of a huge black hole at the center of our galaxy (the Milky Way). This black hole is absorbing
After jettisoning a stage, a rocket has a velocity of + 0.20c relative to the jettisoned stage. An observer on Earth sees the jettisoned stage moving with a velocity of + 7.5 x 107 m/s, relative to
In moving away from Planet Z, a spacecraft fires a probe with a speed of 0.15c, relative to the spacecraft, back toward Z. If the speed of the spacecraft is 0.40c relative to Z, what is the velocity
A rocket launched outward from Earth has a speed of 0.100c relative to Earth. The rocket is directed toward an incoming meteor that may hit the planet. If the meteor moves with a speed of 0.250c
Two spaceships, A and B, each with a speed of 0.60c relative to Earth, approach each other head on. (a) The speed of ship A relative to ship B is (1) greater than c, (2) equal to c, (3) less than c.
In a colliding-beam apparatus, two beams of protons are aimed directly at each other. The first beam contains protons moving at a speed of 0.800c to the right, and the second beam’s protons have a
A spaceship containing an astronaut travels at a speed of 0.60c relative to a second inertial observer. (a) Who measures proper time intervals in the ship and the proper length of the ship: (1) the
An electron is accelerated to a speed of 1.50 x 108 m/.s At that speed, compare the relativistic results o the classical results for (a) The electron’s kinetic energy, (b) Its total energy, and
The apparatus used by the French scientist Armand Fizeau in 1849 for measuring the speed of light is illustrated in Fig. 26.19. Teeth on a rotating wheel periodically interrupt a beam of light. The
A relativistic rocket is measured to be 50 m long, 2.5 m high, and 2.0 m wide by its pilot. It is traveling at 0.65c (in the direction parallel to its length) relative to an inertial observer. (a)
(a) If the mass of 1.0 kg of coal (or any substance) could be completely converted into energy, how many kilo-watt-hours of energy would be produced? (b) Assume that the average U. S. family of four
In proton– antiproton annihilation, a proton and an antiproton (which has the same mass as the proton, but carries a negative charge) interact, and both masses are completely converted to
At a typical nuclear power plant, refueling occurs about every 18 months. Assuming that a plant has operated continuously since the last refueling and produces 1.2 GW of electric power at an
Many radioactive sources emit neutrons. One way of detecting them is by measuring the light (energy) given off when they are captured by protons (for example, when they enter water, which contains
A particle of mass m is initially traveling to the right at 0.900c. It collides and sticks to a particle of mass 2minitially moving to the left at 0.750c. Determine (a) The total mass (in terms of
Roughly speaking, the observable mass in our universe is all attributed to stars and gas clouds in the galaxies. (a) Assuming that each galaxy contains the mass of 200 -billion Suns and there are
Suppose, in Fig. 26.4a, that the observer was 600 m to the left of event B, and A and B were separated by 900 m. She observes that the light flash from event B arrives exactly after that from event
Suppose, in Fig. 26.4a, that the distance between events A and B is 6000 m. The observer is stationed exactly in the middle as shown; however, she does not receive the signals simultaneously. Her
Suppose, in Fig. 26.4a, that the distance between events A and B is 1200 m. The observer is stationed exactly in the middle as shown, but does not receive the signals simultaneously. Her detector
A spacecraft moves past a student with a relative velocity of 0.90c. If the pilot of the spacecraft observes 10 min to elapse on his watch, how much time has elapsed according to the student’s
Some stars appear reddish, and others appear blue. Which of these two types of stars have the higher surface temperature? Explain.
In Compton scattering, if the photon is scattered at a angle, in which direction will the electron recoil? Why?
What physical quantities in a hydrogen atom are deter-mined by the principal quantum number?
In what sense is a laser an “amplifier” of energy? Explain why this concept does not violate conservation of energy.
Explain the difference between spontaneous emission and stimulated emission.
Make a graph showing how the wavelength of the most intense radiation component of blackbody radiation varies with the body’s absolute temperature. By what ratio does λmax change (final/initial)
Is it more dangerous to stand in front of a beam of X-ray radiation with a very low intensity or a beam of red light with a much higher intensity? How does the photon model of light explain this
Light of the same frequency is incident on two materials with different work functions. Discuss how the stopping voltage of the photoelectrons is affected by the work function.
A photon can undergo Compton scattering from either an electron or a neutron. How does the maximum wave-length shift for Compton scattering from a neutron com-pare with that from an electron? Explain.
The Sun’s energy production (near its center) is initially in the form of X-rays and gamma rays. By the time it reaches the surface, it is mostly in the visible range. Use Compton scattering to
The walls of a blackbody cavity are at a temperature of 20oC. What is the wavelength of the radiation of maxi-mum intensity?
The wavelength at which the Sun emits its most intense light is about 550 nm. Assuming the Sun radiates as a perfect blackbody, estimate (a) Its surface temperature and (b) Its total emitted power.
Each photon in a beam of light has an energy of 6.50 x 10-19 J. What is the light’s wavelength? What type of light is this?
(a) Compared with a quantum of red light , a quantum of violet light has (1) more, (2) the same amount of, (3) less energy. Why? (b) Determine the ratio of the photon energy associated with violet
A source of UV light has a wavelength of 150 nm. How much energy does one of its photons have expressed in (a) Joules and (b) Electron-volts?
The work function of a surface is 5.0 x 10-19 J. If light of wavelength of 300 nm is incident on the surface, what is the maximum kinetic energy of the photoelectrons ejected from the surface?
When light of wavelength of 200 nm is incident on a surface, the maximum kinetic energy of the photo-electrons is measured to be 6.0 x 10-19. What is the work function of the surface?
What is the longest wavelength of light that can cause the release of electrons from a metal that has a work function of 3.50 eV?
Assume that a 100-W light bulb gives off of its energy as visible light. How many photons of visible light are given off in 1.00 min? (Use an average visible wavelength of 550 nm.)
A metal with a work function of 2.40 eV is illuminated by a beam of monochromatic light. If the stopping potential is 2.50 V, what is the wavelength of the light?
Find the approximate temperature of a red star that emits light with a wavelength of maximum emission of 700 nm (deep red).
The work function of metal A is less than that of metal B. (a) The threshold wavelength for metal A is (1) shorter than, (2) the same as, (3) longer than that of metal B. Why? (b) If the threshold

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