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physics
modern physics

Questions and Answers of Modern Physics

The resolution of the eye is ultimately limited by the pupil diameter. What is the smallest diameter spot the eye can produce on the retina if the pupil diameter is 3.55 mm? Assume light with a
What is the minimum angle your eye can resolve, according to the Rayleigh criterion and the above assumptions? A. 0.862 × 10-4 rad B. 1.05 × 10-4 rad C. 1.43 × 10-4 rad D. 1.95 × 10-4 rad
What is the linear separation between horizontal lines on the screen? A. 0.0235 mm B. 0.145 mm C. 0.369 mm D. 0.926 mm
What is the angular separation of the horizontal lines as viewed from a distance of 12.0 feet? A. 1.01 × 10-4 rad B. 2.53 × 10-4 rad C. 2.56 × 10-4 rad D. 12.1 × 10-4 rad
According to the Rayleigh criterion, what is the closest you can be to the TV screen before resolving the individual horizontal lines? (In practice you can be considerably closer than this distance
Suppose we change the slit separation to a value other than 8.5 × 10-5 m, with the result that the linear distance to the tenth bright fringe above the central bright fringe increases from 12 cm to
The wavelength of the light is changed to a value other than 440 nm, with the result that the linear distance to the seventh bright fringe above the central bright fringe is 12 cm. The screen is
The light used in this experiment has a wavelength of 511 nm.(a) If the width of the slit is decreased, will the angle to the first dark fringe above the central bright fringe increase or decrease?
The width of the slit in this experiment is 2.20 × 10-6 m.(a) If the frequency of the light is decreased, will the angle to the first dark fringe above the central bright fringe increase or
Describe some of the everyday consequences that would follow if the speed of light were 35 mi/h?
You are in a spaceship, traveling directly away from the Moon with a speed of 0.9c. A light signal is sent in your direction from the surface of the Moon. (a) As the signal passes your ship, do you
Usain Bolt set a world record for the 100-m dash on August 16, 2009. If observers on a spaceship moving with a speed of 0.9250c relative to Earth saw Usain Bolt's run and measured his time to be
(a) Find the average distance (in the Earth's frame of reference) covered by the muons in Example 29-5 if their speed relative to Earth is 0.850c.(b) What is the average lifetime of these muons?
Referring to Example 29-3,(a) How much does Benny age if he travels to Vega with a speed of 0.9995c?(b) How much time is required for the trip according to Jenny?
An elementary particle called a pi meson (or pion for short) has an average lifetime of 2.6 × 10-8 s when at rest. If a pion moves with a speed of 0.89c relative to Earth, find (a) the average
(a) Is it possible for you to travel far enough and fast enough so that when you return from a trip, you are younger than your stay-at-home sister, who was born 5.0 y after you?(b) Suppose you fly on
In order to cross the galaxy quickly, a spaceship leaves Earth traveling at 0.9999995c. After 15 minutes a radio message is sent from Earth to the spacecraft. (a) In the Earth-galaxy frame of
An observer moving toward Earth with a speed of 0.85c notices that it takes 5.0 min for a person on Earth to fill her car with gas. Suppose, instead, that the observer had been moving away from Earth
An astronaut moving with a speed of 0.75c relative to Earth measures her heart rate to be 71 beats per minute. (a) When an Earth-based observer measures the astronaut's heart rate, is the result
Newly sprouted sunflowers can grow at the rate of 0.30 in. per day. One such sunflower is left on Earth, and an identical one is placed on a spacecraft that is traveling away from Earth with a speed
As measured in Earth's frame of reference, the Earth and the Moon are 384,000 km apart. A spaceship flies past the Earth and the Moon with a constant velocity, and the clocks on the ship show that
Albert is piloting his spaceship, heading east with a speed of 0.95c relative to Earth. Albert's ship sends a light beam in the forward (eastward) direction, which travels away from his ship at a
Captain Jean-Luc is piloting the USS Enterprise XXIII at a constant speed v = 0.825c. As the Enterprise passes the planet Vulcan, he notices that his watch and the Vulcan clocks both read 1:00 p.m.
A plane flies with a constant velocity of 222 m/s. The clocks on the plane show that it takes exactly 2.00 h to travel a certain distance. (a) According to ground-based clocks, will the flight take
How fast does a 275-m spaceship move relative to an observer who measures the ship's length to be 155 m?
Suppose the speed of light in a vacuum were only 25.0 mi/h. Find the length of a bicycle being ridden at a speed of 20.0 mi/h as measured by an observer sitting on a park bench, given that its proper
A rectangular painting is W = 117 cm wide and H = 76.2 cm high, as indicated in FIGURE 29-32. At what speed, v, must the painting move parallel to its width if it is to appear to be square?Figure
The particle accelerator at CERN in Geneva, Switzerland, has a circumference of 27 km. Inside it protons are accelerated to a speed of 0.999999972c. What is the circumference of the accelerator in
A cubical box is 0.75 m on a side.(a) What are the dimensions of the box as measured by an observer moving with a speed of 0.82c parallel to one of the edges of the box?(b) What is the volume of the
When parked, your car is 5.8 m long. Unfortunately, your garage is only 3.7 m long.(a) How fast would your car have to be moving for an observer on the ground to find your car shorter than your
An astronaut travels to a distant star with a speed of 0.75c relative to Earth. From the astronaut's point of view, the star is 7.5 ly from Earth. On the return trip, the astronaut travels with a
Laboratory measurements show that an electron traveled 3.50 cm in a time of 0.200 ns.(a) In the rest frame of the electron, did the lab travel a distance greater than or less than 3.50 cm?
A street performer tosses a ball straight up into the air (event 1) and then catches it in his mouth (event 2). For each of the following observers, state whether the time they measure between these
You and a friend travel through space in identical spaceships. Your friend informs you that he has made some length measurements and that his ship is 150 m long but that yours is only 110 m long.
A ladder 5.0 m long leans against a wall inside a spaceship. From the point of view of a person on the ship, the base of the ladder is 3.0 m from the wall, and the top of the ladder is 4.0 m above
When traveling past an observer with a relative speed v, a rocket is measured to be 9.00 m long. When the rocket moves with a relative speed 2v, its length is measured to be 5.00 m. (a) What is the
The starships Picard and La Forge are traveling in the same direction toward the Andromeda galaxy. The Picard moves with a speed of 0.90c relative to the La Forge. A person on the La Forge measures
A spaceship moving toward Earth with a speed of 0.85c launches a probe in the forward direction with a speed of 0.15c relative to the ship. Find the speed of the probe relative to Earth?
Suppose the probe in Problem 34 is launched in the opposite direction to the motion of the spaceship. Find the speed of the probe relative to Earth in this case?Refer to Problem 34A spaceship moving
Suppose the speed of light is 35 mi/h. A paper girl riding a bicycle at 22 mi/h throws a rolled-up newspaper in the forward direction, as shown in FIGURE 29-33. If the paper is thrown with a speed of
Two asteroids head straight for Earth from the same direction. Their speeds relative to Earth are 0.80c for asteroid 1 and 0.60c for asteroid 2. Find the speed of asteroid 1 relative to asteroid 2?
Two rocket ships approach Earth from opposite directions, each with a speed of 0.85c relative to Earth. What is the speed of one ship relative to the other?
A spaceship and an asteroid are moving in the same direction away from Earth with speeds of 0.77c and 0.41c, respectively. What is the relative speed between the spaceship and the asteroid?
A clock in a moving rocket is observed to run slow. (a) If the rocket reverses direction, does the clock run slow, fast, or at its normal rate? (b) Choose the best explanation from among the
An electron moves to the right in a laboratory accelerator with a speed of 0.84c. A second electron in a different accelerator moves to the left with a speed of 0.43c relative to the first electron.
A uranium nucleus is traveling at 0.95c in the positive direction relative to the laboratory when it suddenly splits into two pieces. Piece A is propelled in the forward direction with a speed of
Two rocket ships are racing toward Earth, as shown in FIGURE 29-34. Ship A is in the lead, approaching the Earth at 0.80c and separating from ship B with a relative speed of 0.50c.(a) As seen from
A 2.8 × 106-kg spaceship moves away from Earth with a speed of 0.86c. What is the magnitude of the ship's (a) Classical and (b) Relativistic momentum?
An asteroid with a mass of 8.2 × 1011 kg is observed to have a relativistic momentum of magnitude 7.74 × 1020 kg ( m/s. What is the speed of the asteroid relative to the observer?
An object has a relativistic momentum that is 8.50 times greater than its classical momentum. What is its speed?
A football player with a mass of 88 kg and a speed of 2.0 m/s collides head-on with a player from the opposing team whose mass is 120 kg. The players stick together and are at rest after the
A space probe with a rest mass of 8.2 × 107 kg and a speed of 0.50c smashes into an asteroid at rest and becomes embedded within it. If the speed of the probe-asteroid system is 0.26c after the
At what speed does the classical momentum, p = mv, give an error, when compared with the relativistic momentum, of(a) 1.00% and(b) 5.00%?
A proton has 1836 times the rest mass of an electron. At what speed will an electron have the same momentum as a proton moving at 0.0100c?
Suppose you are a traveling salesman for SSC, the Spacely Sprockets Company. You travel on a spaceship that reaches speeds near the speed of light, and you are paid by the hour. (a) When you return
Star A has a mass of 3.0 × 1028 kg and is traveling in the positive direction at 0.35c relative to the galaxy. Star B has mass 2.0 × 1029 kg and is traveling in the negative direction at 0.15c. The
Particles A through D have the following rest energies and total energies:Rank these particles in order of increasing(a) Rest mass,(b) Kinetic energy, and(c) Speed. Indicate ties where appropriate.
Find the work that must be done on a proton to accelerate it from rest to a speed of 0.95c?
A spring with a force constant of 595 N/m is compressed a distance of 37 cm. Find the resulting increase in the spring's mass?
The 15 gallons of gasoline required to refuel your vehicle has a mass of about 41 kg and releases 1.8 × 109 J when burned in the engine. If its rest energy could be converted entirely to usable
What minimum energy must a gamma ray have to create an electron-anti electron pair?
When a proton encounters an antiproton, the two particles annihilate each other, producing two gamma rays. Assuming the particles were at rest when they annihilated, find the energy of each of the
If a neutron moves with a speed of 0.99c, what are its (a) Total energy, (b) Rest energy, and (c) Kinetic energy?
A rocket with a mass of 2.7 × 106 kg has a relativistic kinetic energy of 2.7 × 1023 J. (a) How fast is the rocket moving? (b) What is the rocket's total energy?
An object has a total energy that is 4.8 times its rest energy.(a) What is the speed of the object?(b) What is the ratio of the object's relativistic kinetic energy to its rest energy?
A neon sign in front of a café flashes on and off once every 3.5 s, as measured by the head cook. How much time elapses between flashes of the sign as measured by an astronaut in a spaceship
At the CERN particle accelerator in Geneva, Switzerland, protonsare accelerated to a speed of 0.999999972c. What is the totalenergy of each proton?
A nuclear power plant converts fuel energy at an average rate of 2.8 × 103 MW during a year of operation. Find the corresponding change in mass of reactor fuel over the entire year?
A helium atom has a rest mass of mHe = 4.002603 u. When disassembled into its constituent particles (2 protons, 2 neutrons, 2 electrons), the well-separated individual particles have the following
What is the percent difference between the classical kinetic energy KcI = ½ m0(2, and the correct relativistic kinetic energy, K = m0c2 / (1 - (2 / c2 - m0c2, at a speed of(a) 0.10c and(b) 0.90c?
Consider a baseball with a rest mass of 0.145 kg.(a) How much work is required to increase the speed of the baseball from 25.0 m/s to 35.0 m/s?(b) Is the work required to increase the speed of the
A lump of putty with a mass of 0.240 kg and a speed of 0.980c collides head-on and sticks to an identical lump of putty moving with the same speed. After the collision the system is at rest. What is
Find the radius to which the Sun must be compressed for it to become a black hole?
Recent measurements show that the black hole at the center of the Milky Way galaxy, which is believed to coincide with the powerful radio source Sagittarius A*, is 2.6 million times more massive than
Two observers are moving relative to one another. Which of the following quantities will they always measure to have the same value: (a) Their relative speed; (b) The time between two events; (c) The
You are standing next to a runway as an airplane lands. (a) If you and the pilot observe a clock in the cockpit, which of you measures the proper time? (b) If you and the pilot observe a large clock
A lighthouse sweeps its beam of light around in a circle once every 8.5 s. To an observer in a spaceship moving away from Earth, the beam of light completes one full circle every 16 s. What is the
An apple drops from the bough of a tree to the ground. Is the mass of the apple near the top of its fall greater than, less than, or the same as its mass after it has landed? Explain.
Consider two apple pies that are identical in every respect, except that pie 1 is piping hot and pie 2 is at room temperature. (a) If identical forces are applied to the two pies, is the acceleration
An uncharged capacitor is charged by moving some electrons from one plate of the capacitor to the other plate. (a) Is the mass of the charged capacitor greater than, less than, or the same as the
Protons in cosmic rays have been observed with kinetic energies as large as 1.0 × 1020 eV. (a) How fast are these protons moving? Give your answer as a fraction of the speed of light. (b) Show that
At the CERN particle accelerator in Geneva, Switzerland, protons are accelerated to a speed of 0.999999972c. In the tunnel next to the beam line a worker drops a wrench from a height of 1.1 m above
A 14C nucleus, initially at rest, emits a beta particle. The beta particle is an electron with 156 keV of kinetic energy.(a) What is the speed of the beta particle?(b) What is the momentum of the
A clock at rest has a rectangular shape, with a width of 24 cm and a height of 12 cm. When this clock moves parallel to its width with a certain speed v its width and height are the same. Relative to
A starship moving toward Earth with a speed of 0.850c launches a shuttle craft in the forward direction. The shuttle, which has a proper length of 12.5 m, is only 6.55 m long as viewed from Earth.
When a particle of charge q and momentum p enters a uniform magnetic field at right angles it follows a circular path of radius R = p/qB, as shown in FIGURE 29-35. What radius does this expression
A 2.5-m titanium rod in a moving spacecraft is at an angle of 45° with respect to the direction of motion. The craft moves directly toward Earth at 0.98c. As viewed from Earth, (a) How long is the
As a spaceship flies past with speed v, you observe that 1.0000 s elapses on the ship's clock in the same time that 1.0000 min elapses on Earth. How fast is the ship traveling, relative to the Earth?
Electrons are accelerated from rest through a potential difference of 276,000 V. What is the final speed predicted(a) Classically and(b) Relativistically?
The rest energy, m0c2, of a particle with a kinetic energy K and a momentum p can be determined as follows:Suppose a pion (a subatomic particle) is observed to have a kinetic energy K = 35.0 MeV and
Consider a "relativistic air track" on which two identical air carts undergo a completely inelastic collision. One cart is initially at rest; the other has an initial speed of 0.650c. (a) In
In Conceptual Example 29-7 we considered an astronaut at rest on an inclined bed inside a moving spaceship. From the point of view of observer 1, on board the ship, the astronaut has a length L0 and
A pulsar is a collapsed, rotating star that sends out a narrow beam of radiation, like the light from a lighthouse. With each revolution, we see a brief, intense pulse of radiation from the pulsar.
Show that an object with momentum p and rest mass m0 has a speed given by
When at rest, the Σ- particle has a lifetime of 0.15 ns before it decays into a neutron and a pion. One particular Σ- particle is observed to travel 3.0 cm in the lab before decaying. What was its
Find the speed of an electron accelerated through a voltage of 25.0 kV-ignoring relativity. Express your answer as a fraction times the speed of light. (Speeds over about 0.1c are generally regarded
When relativistic effects are included, do you expect the speed of the electrons to be greater than, less than, or the same as the result found in the previous problem?Figure 29-36: A cathode-ray
Find the speed of the electrons in Problem 87, this time using a correct relativistic calculation. As before, express your answer as a fraction times the speed of light.a. 0.301cb. 0.312cc. 0.412cd.
How fast should your spacecraft travel so that clocks on board will advance 10.0 times slower than clocks on Earth?
Suppose the accelerating voltage in Problem 87 is increased by a factor of 10. What is the correct relativistic speed of an electron in this case?a. 0.205cb. 0.672cc. 0.740cd. 0.862cFigure 29-36: A

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