- A 2 000-kg car moving at 20.0 m/s collides and locks together with a 1 500-kg car at rest at a stop sign. Show that momentum is conserved in a
- A ball is thrown at 20.0 m/s inside a boxcar moving along the tracks at 40.0 m/s. What is the speed of the ball relative to the ground if the ball is
- In a laboratory frame of reference, an observer notes that Newton’s second law is valid. Show that it is also valid for an observer moving at a
- Show that Newton’s second law is not valid in a reference frame moving past the laboratory frame of Problem 3 with a constant acceleration.
- How fast must a meter stick be moving if its length is measured to shrink to 0.500 m?
- At what speed does a clock move if it is measured to run at a rate that is half the rate of a clock at rest with respect to an observer?
- An astronaut is traveling in a space vehicle that has a speed of 0.500c relative to the Earth. The astronaut measures her pulse rate at 75.0 beats
- An astronomer on Earth observes a meteoroid in the southern sky approaching the Earth at a speed of 0.800c. At the time of its discovery the
- An atomic clock moves at 1 000 km/h for 1.00 h as measured by an identical clock on the Earth. How many nanoseconds slow will the moving clock be
- A muon formed high in the Earth’s atmosphere travels at speed v = 0.990c for a distance of 4.60 km before it decays into an electron, a neutrino,
- A spacecraft with a proper length of 300 m takes 0.750 μs to pass an Earth observer. Determine the speed of the spacecraft as measured by the
- (a) An object of proper length Lp takes a time interval ∆t to pass an Earth observer. Determine the speed of the object as measured by the
- In 1963 Mercury astronaut Gordon Cooper orbited the Earth 22 times. The press stated that for each orbit he aged 2 millionths of a second less than
- A friend passes by you in a spacecraft traveling at a high speed. He tells you that his craft is 20.0 m long and that the identically constructed
- The identical twins Speedo and Goslo join a migration from the Earth to Planet X. It is 20.0 ly away in a reference frame in which both planets are
- An interstellar space probe is launched from the Earth. After a brief period of acceleration it moves with a constant velocity, with a magnitude of
- An alien civilization occupies a brown dwarf, nearly stationary relative to the Sun, several light years away. The extraterrestrials have come to
- Police radar detects the speed of a car (Fig. P39.19) as follows. Microwaves of a precisely known frequency are broadcast toward the car. The moving
- The red shift A light source recedes from an observer with a speed vsource that is small compared with c. (a) Show that the fractional shift in the
- A physicist drives through a stop light. When he is pulled over, he tells the police officer that the Doppler shift made the red light of wavelength
- Suzanne observes two light pulses to be emitted from the same location, but separated in time by 3.00 μs. Mark sees the emission of the same two
- A moving rod is observed to have a length of 2.00 m and to be oriented at an angle of 30.0° with respect to the direction of motion, as shown in
- 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,
- A red light flashes at position xR = 3.00 m and time tR = 1.00 x 10-9 s, and a blue light flashes at xB = 5.00 m and tB = 9.00 x 10-9 s, all measured
- A Klingon spacecraft moves away from the Earth at a speed of 0.800c (Fig. P39.26). The starship Enterprise pursues at a speed of 0.900c relative to
- Two jets of material from the center of a radio galaxy are ejected in opposite directions. Both jets move at 0.750c relative to the galaxy. Determine
- A spacecraft is launched from the surface of the Earth with a velocity of 0.600c at an angle of 50.0° above the horizontal positive x axis. Another
- Calculate the momentum of an electron moving with a speed of (a) 0.010 0c, (b) 0.500c, and (c) 0.900c.
- The non-relativistic expression for the momentum of a particle, p = mu, agrees with experiment if u
- A spacecraft is launched from the surface of the Earth with a velocity of 0.600c at an angle of 50.0° above the horizontal positive x axis. Another
- A golf ball travels with a speed of 90.0 m/s. By what fraction does its relativistic momentum magnitude p differ from its classical value mu? That
- Show that the speed of an object having momentum of magnitude p and mass m is u= c/√1 + (mc/p) 2.
- An unstable particle at rest breaks into two fragments of unequal mass. The mass of the first fragment is 2.50 x 10-28 kg, and that of the other is
- Determine the energy required to accelerate an electron from (a) 0.500c to 0.900c and (b) 0.900c to 0.990c.
- A proton in a high-energy accelerator moves with a speed of c/2. Use the work–kinetic energy theorem to find the work required to increase its
- Show that, for any object moving at less than one-tenth the speed of light, the relativistic kinetic energy agrees with the result of the classical
- Find the momentum of a proton in MeV/c units assuming its total energy is twice its rest energy.
- Find the kinetic energy of a 78.0-kg spacecraft launched out of the solar system with speed 106 km/s by using (a) The classical equation K = ½
- A proton moves at 0.950c. Calculate its (a) Rest energy, (b) Total energy, and (c) Kinetic energy.
- A cube of steel has a volume of 1.00 cm3 and a mass of 8.00 g when at rest on the Earth. If this cube is now given a speed u = 0.900c, what is its
- An unstable particle with a mass of 3.34 x 10-27 kg is initially at rest. The particle decays into two fragments that fly off along the x axis with
- An object having mass 900 kg and traveling at speed 0.850c collides with a stationary object having mass 1 400 kg. The two objects stick together.
- Show that the energy–momentum relationship E2 = p2c2 + (mc2)2 follows from the expressions E = y mc2 and p = y mu.
- In a typical color television picture tube, the electrons are accelerated through a potential difference of 25 000 V. (a) What speed do the
- Consider electrons accelerated to an energy of 20.0 GeV in the 3.00-km-long Stanford Linear Accelerator. (a) What is the y factor for the
- Compact high-power lasers can produce a 2.00-J light pulse of duration 100 fs, focused to a spot 1 +m in diameter. (See Mourou and Umstader,
- A pion at rest (mπ = 273me) decays to a muon (mμ ≈ 207me) and an antineutrino. The reaction is written π− →
- According to observer A, two objects of equal mass and moving along the x axis collide head on and stick to each other. Before the collision, this
- Make an order-of-magnitude estimate of the ratio of mass increase to the original mass of a flag, as you run it up a flagpole. In your solution
- When 1.00 g of hydrogen combines with 8.00 g of oxygen, 9.00 g of water is formed. During this chemical reaction, 2.86 x 105 J of energy is released.
- In a nuclear power plant the fuel rods last 3 yr before they are replaced. If a plant with rated thermal power 1.00 GW operates at 80.0% capacity for
- The total volume of water in the oceans is approximately 1.40 x 109 km3. The density of sea water is 1 030 kg/m3, and the specific heat of the water
- The power output of the Sun is 3.77 x 1026 W. How much mass is converted to energy in the Sun each second?
- An Earth satellite used in the global positioning system moves in a circular orbit with period 11 h 58 min.(a) Determine the radius of its orbit.(b)
- An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 30.0 yr in the spacecraft’s frame of reference. Assume that
- The cosmic rays of highest energy are protons that have kinetic energy on the order of 1013 MeV. (a) How long would it take a proton of this energy
- An electron has a speed of 0.750c. (a) Find the speed of a proton that has the same kinetic energy as the electron. (b) What If? Find the speed
- Ted and Mary are playing a game of catch in frame S", which is moving at 0.600c with respect to frame S, while Jim, at rest in frame S watches the
- A rechargeable AA battery with a mass of 25.0 g can supply a power of 1.20 W for 50.0 min. (a) What is the difference in mass between a charged and
- The net nuclear fusion reactions inside the Sun can b written as 41H → 4He + ∆E. The rest energy of each hydrogen atom is 938.78 MeV and
- An object disintegrates into two fragments. One of the fragments has mass 1.00 MeV/c2 and momentum 1.75 MeV/c in the positive x direction. The other
- An alien spaceship traveling at 0.600c toward the Earth launches a landing craft with an advance guard of purchasing agents and physics teachers. The
- A physics professor on the Earth gives an exam to her students, who are in a spacecraft traveling at speed v relative to the Earth. The moment the
- Spacecraft I, containing students taking a physics exam, approaches the Earth with a speed of 0.600c (relative to the Earth), while spacecraft II,
- Energy reaches the upper atmosphere of the Earth from the Sun at the rate of 1.79 x 1017 W. If all of this energy were absorbed by the Earth and not
- A super train (proper length 100 m) travels at a speed of 0.950c as it passes through a tunnel (proper length 50.0 m). As seen by a trackside
- Imagine that the entire Sun collapses to a sphere of radius Rg such that the work required to remove a small mass m from the surface would be equal
- A particle with electric charge q moves along a straight line in a uniform electric field E with a speed of u. The electric force exerted on the
- An observer in a coasting spacecraft moves toward a mirror at speed v relative to the reference frame labeled by S in Figure P39.70. The mirror is
- The creation and study of new elementary particles is an important part of contemporary physics. Especially interesting is the discovery of a very
- A particle of mass m moving along the x axis with a velocity component +u collides head-on and sticks to a particle of mass m/3 moving along the x
- A rod of length L0 moving with a speed v along the horizontal direction makes an angle 4 0 with respect to the x" axis. (a) Show that the length of
- Suppose our Sun is about to explode. In an effort to escape, we depart in a spacecraft at v = 0.800c and head toward the star Tau Ceti, 12.0 ly away.
- A 57Fe nucleus at rest emits a 14.0-keV photon. Use conservation of energy and momentum to deduce the kinetic energy of the recoiling nucleus in
- Prepare a graph of the relativistic kinetic energy and the classical kinetic energy, both as a function of speed, for an object with a mass of your
- What two speed measurements do two observers in relative motion always agree on?
- A spacecraft with the shape of a sphere moves past an observer on Earth with a speed 0.5c. What shape does the observer measure for the spacecraft as
- The speed of light in water is 230 Mm/s. Suppose an electron is moving through water at 250 Mm/s. Does this violate the principle of relativity?
- Two identical clocks are synchronized. One is then put in orbit directed eastward around the Earth while the other remains on the Earth. Which clock
- Explain why it is necessary, when defining the length of a rod, to specify that the positions of the ends of the rod are to be measured
- A train is approaching you at very high speed as you stand next to the tracks. Just as an observer on the train passes you, you both begin to play
- List some ways our day-to-day lives would change if the speed of light were only 50 m/s.
- Does saying that a moving clock runs slower than a stationary one imply that something is physically unusual about the moving clock?
- How is acceleration indicated on a space–time graph?
- A particle is moving at a speed less than c/2. If the speed of the particle is doubled, what happens to its momentum?
- Give a physical argument that shows that it is impossible to accelerate an object of mass m to the speed of light, even with a continuous force
- The upper limit of the speed of an electron is the speed of light c. Does that mean that the momentum of the electron has an upper limit?
- Because mass is a measure of energy, can we conclude that the mass of a compressed spring is greater than the mass of the same spring when it is not
- It is said that Einstein, in his teenage years, asked the question, “What would I see in a mirror if I carried it in my hands and ran at the speed
- Some distant astronomical objects, called quasars, are receding from us at half the speed of light (or greater). What is the speed of the light we
- Photons of light have zero mass. How is it possible that they have momentum?
- “Newtonian mechanics correctly describes objects moving at ordinary speeds and relativistic mechanics correctly describes objects moving very
- Two cards have straight edges. Suppose that the top edge of one card crosses the bottom edge of another card at a small angle, as in Figure Q39.18a.
- Describe how the results of Example 39.7 would change if, instead of fast space vehicles, two ordinary cars were approaching each other at highway
- Two objects are identical except that one is hotter than the other. Compare how they respond to identical forces.
- With regard to reference frames, how does general relativity differ from special relativity?
- Two identical clocks are in the same house, one upstairs in a bedroom, and the other downstairs in the kitchen. Which clock runs more slowly? Explain.
- A thought experiment Imagine ants living on a merry goround turning at relativistic speed, which is their two-dimensional world. From measurements on
- You are in a windowless car in as exceptionally smooth train moving at constant velocity. It there any physical experiment you can do in the train
- You might have had the experience of being at a red light when, out of the corner od your eye, you see the car beside you creep forward.