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physics
particle physics

Questions and Answers of Particle Physics

The gravitational vector field \(\vec{g}(\vec{r})\) is defined as the gravitational force exerted on a small object located at a particular position \(\vec{r}\) divided by that object's mass. (a)
Some writers of fiction have placed human beings on asteroids or other "planetoids" whose radius, in the illustrations accompanying the stories, seems not too much greater than the height of the
You wish to put a satellite in orbit around Earth. (a) Which takes more energy per kilogram of satellite: launching the satellite from the ground to a height of \(1600 \mathrm{~km}\) above the ground
Unable to sleep, you crawl out of bed one evening and stare out your window at the night sky, finding Jupiter and sitting back to contemplate its grandcur. Remembering your physics, you imagine
After seeing an old movie, you become concerned about a large asteroid that could be gravitationally attracted to Earth from very far away. You realize that long ago such an asteroid's speed relative
You are working on a project to plot the course of a spy satellite. The satellite has a polar orbit (which means it passes over both of Earth's poles during each orbit), and it is outfitted with a
While helping an astronomy professor, you discover a binary star system in which the two stars are in circular orbits about the system's center of mass. From their color and brightness, you determine
Scientists still are not entirely sure whether the universe is open (which means it will keep expanding forever) or closed (which means it will eventually fall back in on itself in a "Big Crunch").
Compare the gravitational force exerted by Earth on you with \((a)\) that exerted by a person standing \(1 \mathrm{~m}\) away from you and (b) that exerted by Earth on Pluto.
Of all the objects in Table 13.1, Pluto has the orbit with the greatest eccentricity. (a) What is the ratio of the orbit's semiminor axis \(b\) to its semimajor axis \(a\) ? (b) What is the ratio of
Cavendish is said to have "weighed Earth" because his determination of \(G\) provided the first value for the planet's mass \(m_{\mathrm{E}}\). Given that the radius of Earth is about \(6400
The distance between Earth's surface and an object of mass \(m\) is changed by an amount \(\Delta x\). Show that when \(x \approx R_{\mathrm{E}}\) and \(\Delta x \ll R_{\mathrm{E}}\), where
A satellite of mass \(m_{\text {sat }}\) is in an elliptical orbit around a star of mass \(m_{\text {star }} \gg m_{\text {sat }}\). If the mechanical energy of the starsatellite system is \(E_{\text
Determine the ratio of Earth's gravitational force exerted on a \(1.0-\mathrm{kg}\) object at the following positions to that at sea level: (i) the top of Mt. Everest, altitude \(8848 \mathrm{~m}\);
The orbital period of Jupiter around the Sun is 11. 86 times that of Earth. What is the ratio of their distances to the Sun?
If the speed of a planet in its orbit around the Sun changes, how can the planet's angular momentum be constant?
A brick of unknown mass is placed on a spring scale. When in equilibrium, the scale reads 13. 2 N. Which of the following statements is/are true? (i) Earth always exerts a gravitational force of
Draw a free-body diagram of an individual experiencing weightlessness in an elevator. What must the elevator's acceleration be for this to occur?
If you were to travel in a vertical circle, at what point in the circle would you be most likely to experience weightlessness?
Which of the following are events?(a) The local television station's newscast runs from 11:00 to 11:30 p.m.(b) The ceremonial first pitch is thrown at a baseball game in Omaha, Nebraska.(c) The
You are in a rocket moving away from Earth at onethird the speed of light relative to Earth. A friend is on Earth, and an astronaut in another rocket is moving toward Earth at one-third the speed of
A set of atomic clocks is placed on a square grid as shown in Figure P14.3. In order to synchronize these clocks, you set the time on each to a certain reading before they are allowed to run. Clock
Events 1 and 2 are exploding firecrackers that each emit light pulses. In the reference frame of the detector, event 1 leaves a char mark at a distance \(3.40 \mathrm{~m}\) from the detector, and
Consider the grid of clocks in Figure 14.6. Do observers stationed at clocks far from the reference clock read earlier, later, or the same time as the time on the reference clock \((a)\) if the
Observers A and B are both at rest in the Earth reference frame, in different parts of a large city, awaiting the start of a fireworks show. They want to synchronize their atomic clocks for some
Observer A is stationary in the Earth reference frame, and pilot \(\mathrm{B}\) is flying toward pilot \(\mathrm{A}\) at relative speed \(v_{\mathrm{AB}}\). What speed does observer \(A\) measure for
Alarm clock 1 is positioned at \(x=-d\) and alarm clock 2 at \(x=+d\) in reference frame \(\mathrm{A}\). According to a clock in reference frame \(\mathrm{A}\), both go off at \(t=0\). An observer in
You are traveling toward a large fixed mirror at a constant relative speed \(0.20 c_{0}\). At \(t=0\), when the mirror is a distance \(d\) from you (measured in your reference frame), you emit a
You are in a jet helicopter traveling horizontally at \(180 \mathrm{~m} / \mathrm{s}\) relative to Earth. At one instant you observe the light pulses from two lightning strikes, one directly ahead of
Consider a lightweight, straight, rigid rod that has a proper length of \(1 \times 10^{6} \mathrm{~m}\). If you rotate the rod at 100 turns/s about a perpendicular axis through its center, at what
Observer A on Earth sees spaceship B moving at speed \(v=0.600 c_{0}\) away from Earth and spaceship C moving at the same speed in the opposite direction. Observer A determines that both ships
An astronaut takes what he measures to be a \(10-\) min nap in a space station orbiting Earth at \(8000 \mathrm{~m} / \mathrm{s}\). A signal is sent from the station to Earth at the instant he falls
Standing somewhere between two vertical mirrors, you hold a lantern and at \(t=0\) emit a light pulse that travels in all directions. You observe the pulse reflected from the mirror on your right at
A spaceship of proper length \(\ell=100 \mathrm{~m}\) travels in the positive \(x\) direction at a speed of \(0.800 c_{0}\) relative to Earth. An identical spaceship travels in the negative \(x\)
A spacecraft traveling away from Earth at relative speed \(0.850 c_{0}\) sends a radio message when it is \(65,000,000 \mathrm{~km}\) away from Earth in the Earth reference frame. When the signal is
Spaceships A, B, and C in Figure P14.18 all have the same proper length and all fly with the same speed according to an observer on Earth. Rank the lengths of the three ships as measured by an
The boundary of a lunar base is a square \(1 \mathrm{~km}\) wide and \(1 \mathrm{~km}\) long in the Moon reference frame. Spaceship A flies at high relative speed close to the Moon parallel to the
What is the kinetic energy of a pin in your reference frame if you measure its inertia to be three times its mass?
A golf ball hit from a tee accelerates from rest to a speed of \(40.0 \mathrm{~m} / \mathrm{s}\) relative to the Earth reference frame. By what percent does the mass of the ball increase as it is hit?
One end of a vertical spring of spring constant \(k=1500 \mathrm{~N} / \mathrm{m}\) is attached to the floor. You compress the spring so that it is \(2.40 \mathrm{~m}\) shorter than its relaxed
You pick up your physics book from the floor and put it on your desk. In the Earth reference frame, which of the following quantities have changed for the system made up of Earth and the book: mass,
Observer A is on Earth looking at the Moon, and observer B is on the Moon looking at Earth. Which of the following quantities do the observers agree on for the Earth-Moon system: inertia, energy,
A bullet is fired from a rifle (event 1 ) and then strikes a soda bottle, shattering it (event 2 ). Is there some inertial reference frame in which event 2 precedes event 1 ? If so, does the
Classify the space-time interval between each pair of events as timelike, spacelike, or lightlike: (a) A sunspot erupts on the surface of the Sun and is seen on Earth \(500 \mathrm{~s}\) later. (b) A
Calculate the Lorentz factor for an object moving relative to Earth at(a) \(60 \mathrm{mi} / \mathrm{h}\),(b) \(0.34 \mathrm{~km} / \mathrm{s}\) (speed of sound in air),(c) \(28 \times 10^{3}
You measure the period of light clock \(A\) to be \(T\) as it moves relative to you with a speed \(0<v_{A}<0.5 c_{0}\). You measure the period of an identical light clock (clock B) to be \(3
A space station sounds an alert signal at time intervals of 1. 00 h. Spaceships A and B pass the station, both moving at \(0.400 c_{0}\) relative to the station but in opposite directions. How long
A certain muon detector counts 600 muons per hour at an altitude of \(1900 \mathrm{~m}\) and 380 muons per hour at sea level. Given that the muon half-life at rest is \(1.5 \times 10^{-6}
Planets \(\mathrm{A}\) and \(\mathrm{B}\) are 10 light years apart in the reference frame of planet A. (One light year is the distance light travels in one year.) A deep-space probe is launched from
Section 14. 3 describes how the number of muons reaching Farth's surface is greater than the number expected based on the muon half-life of \(1.5 \times 10^{-6} \mathrm{~s}\). How fast, relative to
One cosmonaut orbited Earth for 437 days, as measured by Earth clocks. His speed of orbit was \(7700 \mathrm{~m} / \mathrm{s}\) relative to Earth during this time interval. Assume two clocks were
A cosmic ray traveling at \(0.400 c_{0}\) relative to Earth passes observer A (event 1) and then a short time interval later passes observer B (event 2). The observers are at rest, \(8.00
An elementary particle is launched from Earth toward the Regulus system, 77. 5 light years distant. At what speed relative to Earth must this particle travel to make this trip in \(10 \mathrm{y}\) in
Spaceships A and B pass a space station at the same instant, the two ships moving in opposite directions at the same speed of \(0.600 c_{0}\) relative to the station. What is the Lorentz factor
Two elementary particles pass each other moving in opposite directions, each moving at speed \(0.800 c_{0}\) relative to Earth. What is the speed of one particle relative to the other?
The radius of Earth is \(6370 \mathrm{~km}\) in the Farth reference frame. In the reference frame of a cosmic ray moving at \(0.800 c_{0}\) relative to Earth, how wide does Earth seem (a) along the
Show that the Lorentz transformation equations (Eqs. 14. 29-14.32) reduce to the Galilean transformation equations in the limit \(v_{\mathrm{AB}} \ll c_{0}\).Data from Eqs. 14. 29-14.32 VABX tBe Ae
An elementary particle moving away from Earth reaches its destination after two wecks (in the reference frame of the particle) traveling at \(0.9990 c_{0}\) relative to Earth. How far has it traveled
Describe the shape of the Moon as measured by an observer in a reference frame traveling past the Moon at a relative speed of (a) 1000 m / s,(b) 0. 50 c0, and(c) 0.95 c0.
When at rest in the Earth reference frame, the delta-wing spaceship in Figure P14.43 is \(7.00 \mathrm{~m}\) long and has a wingspan of \(8.00 \mathrm{~m}\).(a) What is the opening angle \(\alpha\)
Standing at rest in the Earth reference frame, you observe two events, also at rest in that reference frame, occurring at these coordinates: event 1: \(x_{1}=10 \mathrm{~km}, y_{1}=5.0
Use the Lorentz transformation equations (Eq. 14. 29-14.32) to prove that the space-time interval \(s^{2}\) between two events is Lorentz-invariant, which means it has the same value for all possible
An elementary particle travels at \(0.840 c_{0}\) across a solar system that has a diameter of \(8.14 \times 10^{12} \mathrm{~m}\) (both measurements in the reference frame \(S\) of the solar
A space colony defines the origin of a coordinate system in reference frame \(\mathrm{C}\), and you are at rest in this reference frame at position \(x=+3.000 \times 10^{5} \mathrm{~km}\). A ship
Observer \(\mathrm{O}\) at the origin of a coordinate system is at rest relative to two equidistant space stations located at \(x=+3.00 \times 10^{6} \mathrm{~km}\left(\right.\) station A) and
A spaceship travels at \(0.610 c_{0}\) away from Earth. When the ship is \(3.47 \times 10^{11} \mathrm{~m}\) away in the Earth reference frame, the ship clock is set to \(t=0\) and a message (light
According to an observer at rest in the Earth reference frame, ship A travels in one direction at speed \(0.862 c_{0}\) while ship B moves in the opposite direction at \(0.717 c_{0}\). Ship A sends
Two asteroid clusters at rest with respect to each other are \(3.00 \times 10^{9} \mathrm{~m}\) apart, and both measure \(6.00 \times 10^{8} \mathrm{~m}\) across in the reference frame of the
Determine the magnitude of the momentum of a muon in a reference frame in which the muon moves with speed \(0.500 c_{0}\). The mass of a muon is 207 times the mass of an electron.
An electron accelerates from \(0.700 c_{0}\) to \(0.900 c_{0}\) in the Earth reference frame. In this reference frame, by what factor do \((a)\) its mass and \((b)\) its inertia increase?
(a) What is the magnitude of the momentum of an electron in a reference frame in which it is moving at \(0.500 c_{0}\) ? (b) At what speed must the electron move in a reference frame in which it has
Object A, mass \(4.24 \times 10^{5} \mathrm{~kg}\), is at rest in reference frame \(\mathrm{A}\), and object \(\mathrm{B}\), mass \(7.71 \times 10^{4} \mathrm{~kg}\), moves at \(0.875 c_{0}\) in this
A uniform 200-kg cube that has a volume of \(8.00 \mathrm{~m}^{3}\) (measured when the cube is at rest in the Earth reference frame) travels perpendicular to a pair of its faces at \(0.672 c_{0}\)
Muons are formed \(10.0 \mathrm{~km}\) above Earth's surface. What magnitude of momentum (in the Earth reference frame) must they have immediately after formation in order for only one of every
Two chunks of rock, each having a mass of \(1.00 \mathrm{~kg}\), collide in space. Just before the collision, an observer at rest in the reference frame of a nearby star determines that rock
In the Farth reference frame, a \(150 \mathrm{~kg}\) probe travels at \(0.860 c_{0}\) while a \(250-\mathrm{kg}\) probe travels at \(0.355 c_{0}\) in the opposite direction. What are the velocities
At what speed must a particle move in your reference frame so that its kinetic energy is equal to its internal energy?
Particles A, B, and C each have mass \(m\), and their energies are \(E_{\mathrm{A}}=E, E_{\mathrm{B}}=2 E\), and \(E_{\mathrm{C}}=3 E\). Rank the particles, largest first, in order of \((a)\) Lorentz
What is the internal energy of an electron moving at \(0.750 c_{0}\) in the Farth reference frame?
Uranium-238 decays to thorium and helium according to the reaction \({ }^{238} \mathrm{U} \rightarrow{ }^{234} \mathrm{Th}+{ }^{4} \mathrm{He}\). How much energy is released when \(1.00
Assume that 437 days is a reasonable limit for how long a human can endure constant-velocity space travel. Proxima Centauri, the star closest to our Sun, is 4. 24 light years away from Earth. If you
A particle of mass \(m_{\text {orig }}\), initially at rest in the Earth reference frame, decays into two particles 1 and 2 that have masses \(m_{1}\) and \(m_{2}\), respectively. Use conservation of
Which of the following forms of energy contribute to the mass of a gas molecule: \((a)\) energy due to the molecule rotating about its center of mass, \((b)\) energy due to compression of atoms in
At the Large Hadron Collider in Switzerland, two highenergy protons collide to create new particles. Prior to collision, each proton is accelerated to an energy of \(7000 \mathrm{GeV}\) in the Earth
An electron \(\mathrm{e}^{-}\)and positron \(\mathrm{e}^{+}\)moving at the same speed in the Earth reference frame collide head-on and produce a proton \(\mathrm{p}\) and an antiproton
Antihydrogen is the only antimatter element that has been produced in the laboratory, albeit just a few atoms at a time. Each antihydrogen atom consists of a positron in orbit around an antiproton
Galaxy A moves away from galaxy \(\mathrm{B}\) at \(0.600 c_{0}\) relative to B. A spaceship leaves a planet in galaxy A traveling at \(0.500 c_{0}\) relative to galaxy \(\mathrm{A}\). If the
A tree that is \(32.6 \mathrm{~m}\) tall leans \(26.0^{\circ}\) from the vertical in the Farth reference frame. How tall is the tree, and at what angle does it lean, in the reference frame of a
Consider a searchlight on the ground that casts a spot on a cloud \(1000 \mathrm{~m}\) overhead. If the searchlight is rotated rapidly-say, \(30^{\circ}\) in \(1 \mu \mathrm{s}\)-how fast does the
Two events occur at different locations on Farth and are simultaneous in the reference frame of an observer standing on Earth halfway between the events. Are these events simultaneous in any other
Pilot \(\mathrm{A}\) is seated in the middle of a ship that has a proper length of \(250 \mathrm{~m}\), and pilot B is seated in the middle of an identical ship. Pilot B passes A at a speed that A
Relative to Earth, spaceship A travels at \(0.732 c_{0}\) away from Earth, and spaceship B travels at \(0.914 c_{0}\) toward Earth along the same straight line. (a) How fast does A move according to
A proton \(\mathrm{p}_{1}\) moving in the Earth reference frame collides with a proton \(p_{2}\) that is at rest in that reference frame. The collision creates a particle that has mass \(m\) and an
You are consulting for an episode of Stars Wars, Part XVI. As this episode opens, starship Orion zooms past a space station at \(t=0\) ship's time, traveling at a constant \(0.6000 c_{0}\) relative
Your boss wants you to construct a spring that, when compressed, experiences a mass increase of \(1 / 10,000\) of \(1 \%\). He has no idea whether this is possible, but you decide to write a report
The Iorentz. Cup spaceship race is won by the pilot who can travel \(1.00 \times 10^{9} \mathrm{~m}\) in the shortest time interval. The rules state that the start and finish lines must be \(10^{9}
You are flying in a plane, and a friend is on the ground. Which of you measures the proper time interval between(a) the beginning and end of a brief in-flight video program and \((b)\) two
Suppose you want to synchronize the network of clocks in Figure 14.6 by emitting a single light pulse at the origin. This signal triggers each clock to start running from some initial setting. If it
Consider a spring-loaded device that ejects a ball at some unknown everyday speed \(v_{\mathrm{b}}\). To measure this speed, you measure the time interval it takes the ball to pass through a
You are flying in a plane, and a friend is on the ground. Who measures a shorter duration of \((a)\) a nap you take and(b) a nap your friend takes?

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