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physics
particle physics
Questions and Answers of
Particle Physics
A \(0.25-\mathrm{kg}\) bob is suspended from a string that is \(0.60 \mathrm{~m}\) long. When the pendulum is set into small-amplitude oscillation, the amplitude decays to half of its initial value
A restoring force of unknown magnitude is exerted on a object that oscillates with a period of \(0.50 \mathrm{~s}\). When the object is in an evacuated container, the motion is simple harmonic
A \(0.500-\mathrm{kg}\) block oscillates up and down on a vertical spring for which \(k=12.5 \mathrm{~N} / \mathrm{m}\). The initial amplitude of the motion is \(0.100 \mathrm{~m}\).(a) What is the
A damped oscillator has a quality factor of 20 .(a) By what fraction does the energy decrease during each cycle?(b) By what percentage does the damped angular frequency \(\omega_{\mathrm{d}}\) differ
One reference book states that, after a large earthquake, Earth can be treated as an oscillator that has a period of \(54 \mathrm{~min}\) and a quality factor of 400 .(a) What percentage of the
A gong makes a loud noise when struck. The noise gradually gets less and less loud until it fades below the sensitivity of the human ear. The simplest model of how the gong produces the sound we hear
Critical damping is a term used to describe a situation where the damping coefficient \(b\) is just great enough that no oscillation occurs. (In critical damping, a moving part is displaced but
A small \(3.0-\mathrm{kg}\) object dropped from the roof of a tall building acquires a terminal speed of \(25 \mathrm{~m} / \mathrm{s}\). Assume the drag force exerted on the object has the same form
An object resting on a table oscillates on the end of a horizontal spring. Because the table is covered with a viscous substance, the motion is damped and the amplitude gets smaller with each cycle.
Do the turning points in simple harmonic motion have to be equidistant from the equilibrium position?
If the amplitude of a simple harmonic motion doubles, what happens to \((a)\) the energy of the system, \((b)\) the maximum speed of the moving object, and \((c)\) the period of the motion?
A pendulum is swinging in a stationary elevator. What happens to the period when the elevator \((a)\) accelerates upward, (b) travels downward at constant speed, and (c) travels downward and
You measure the oscillation frequency \(f_{\text {whole }}\) of a vertical block-spring system. You then cut the spring in half, hang the same block from one of the halves, and measure the frequency
The hand in Figure P15.80a holds a vertical blockspring system so that the spring is compressed. When the hand lets go, the block, of mass \(m\), descends a distance \(d\) in a time interval \(\Delta
Two oscillatory motions are given by \(x(t)=A \sin (m \omega t)\) and \(y(t)=A \sin (n \omega t+\phi)\), where \(m\) and \(n\) are positive integers. Consider displaying these motions on a single
You have a teardrop-shaped \(2.00-\mathrm{kg}\) object that has a hook at one end and is \(0.28 \mathrm{~m}\) long along its longest axis (Figure P15.83). When you try to balance the object on your
What would be the period of oscillation of this book if you held it at one corner between index finger and thumb and allowed it to swing slightly? To first order, ignore any effect on the oscillation
A \(2.00-\mathrm{kg}\) object is free to slide on a horizontal surface. The object is attached to a spring of spring constant \(200 \mathrm{~N} / \mathrm{m}\), and the other end of the spring is
A hole is drilled through the narrow end of a \(0.960-\mathrm{kg}\) baseball bat, and the bat is hung on a nail so that it can swing freely (Figure P15.85). The bat is \(0.860 \mathrm{~m}\) long, the
A meter stick is free to pivot around a position located a distance \(x\) below its top end, where \(0(a) What is the frequency \(f\) of its oscillation if it moves as a pendulum?(b) To what position
To determine what effect a spring's mass has on simple harmonic motion, consider a spring of mass \(m\) and relaxed length \(\ell_{\text {spring }}\). The spring is oriented horizontally, and one end
(a) Show that for an object moving in simple harmonic motion, the speed of the object as a function of position is given by \(v(x)=\omega \sqrt{A^{2}-x^{2}}\).(b) Noting that \(v_{x}=d x / d t\),
In physics lab, you are measuring the period of a vertically hung spring-ball system in which the mass of the ball is \(0.50 \mathrm{~kg}\). As the system oscillates up and down, it also swings from
The King's clock fails to keep time, and because you designed it, he's holding you responsible. Examining the spring-ball system you used as the central timekeeping oscillator, you realize that a
You are aboard the International Space Station and are required to keep track of your mass because of your long stay in the free-fall conditions of deep space. To carry out this task, you hook a 215
The position of a particle undergoing simple harmonic motion is given by \(x(t)=20 \cos (8 \pi t)\), where \(x\) is in millimeters and \(t\) is in seconds. For this motion, what are the (a)
If the matter that makes up a planet is distributed uniformly so that the planet has a fixed, uniform density, how does the magnitude of the acceleration due to gravity at the planet surface depend
In Figure P13.2, suppose the mass of object 1 is three times the mass of object 2. (a) At Earth's surface, what ratio \(r_{1} / r_{2}\) is needed to have the rod stay horizontal? (b) What is this
Suppose you're making a scale model of the solar system showing the eight planets (not including the dwarf planet Pluto) and having each planet at its farthest position from the Sun. If you use a
Four identical objects are placed at the four corners of a square, far from any star or planet. (a) Choose one object and draw to scale the vectors that represent the gravitational forces exerted on
Two basketballs, each of mass \(0.60 \mathrm{~kg}\) and radius \(0.12 \mathrm{~m}\), are placed on a floor so that they touch each other. Two golf balls, each of mass \(0.045 \mathrm{~kg}\) and
An astronaut on the International Space Station gently releases a satellite that has a mass much smaller than the mass of the station. Describe the motion of the satellite after release.
An isolated object of mass \(m\) can be split into two parts of masses \(m_{1}\) and \(m_{2}\). Suppose the centers of these parts are then separated by a distance \(r\). What ratio of masses \(m_{1}
Particles of mass \(m, 2 m\), and \(3 m\) are arranged as shown in Figure P13.8, far from any other objects. These three particles interact only gravitationally, so that each particle experiences a
Angular momentum can be represented as a vector product and interpreted in terms of the rate of change of an area with respect to time. Give a similar interpretation of another vector product:
Suppose the spring/balance device in Figure P13.10 is adjusted so that the spring is slightly stretched and the balance arm is level when the device is in an elevator at rest relative to the ground
Suppose that you were to step gently onto a bathroom scale, read the dial, and then jump from a chair onto the same scale. (a) Would the dial show different readings in the two cases? (b) Would the
A balance is purposefully prepared in an unbalanced condition, with too much mass on one side. It is carefully held with two hands, one on the base of the balance and one on the heavier end, so that
(a) For what downward acceleration does the spring scale in Figure P13.13 read zero? (b) What would the answer in part \(a\) be if the experiment were done on the Moon? (c) How would your conclusion
You ride your pogo stick (Figure P13.14) across a diving board and into the local swimming pool. Your pogo stick is a special model equipped with a sensor that records the force measured by the
A commercial airliner hits a pocket of turbulence and experiences a downward acceleration of about \(2 \mathrm{~g}\). A person who is not fastened into a seat by a safety belt "falls" to the ceiling
How should the simulator in Figure P13.16 be tilted to simulate a left turn in a bobsled? Assume that the bobsled run has banked turns and that the sled exerts no tangential force on the ice.Data
A vertical accelerometer for measuring Figure P13.17 accelerations on a roller coaster can be constructed using a piece of clear plastic pipe, a cork, a rubber band, and a metal bob (Figure P13.17).
Consider two satellites simultaneously launched \(180 \mathrm{~km}\) apart at the equator, each placed in a circular orbit that passes above the North Pole and its launch point. (a) Describe their
Let us explore whether there is any way to distinguish acceleration due to rotation from acceleration due to a gravitational force. Imagine a deep bowl with a small volume of milk in it. (a) What
What is the magnitude of the gravitational force exerted (a) by the Sun on Mars and (b) by Mars on the Sun? Approximate Mars's orbit as circular.
What is the magnitude of the gravitational force between two \(1.0 \mathrm{~g}\) marbles placed \(100 \mathrm{~mm}\) apart?
The gravitational force between two spherical celestial bodies, one of mass \(2 \times 10^{12} \mathrm{~kg}\) and the other of mass \(5 \times 10^{20} \mathrm{~kg}\), has a magnitude of \(3 \times
Mars has a mass that is about one-ninth of Earth's and a radius that is about half of Earth's. What is the ratio of the acceleration due to gravity on Mars to that on Earth?
Gravity is the weakest of the fundamental interactions (see Section 7. 6).(a) This being so, what makes it such an important force on Earth?(b) What makes it the dominant force in galaxies?Data from
A neutron star has about two times the mass of our Sun but has collapsed to a radius of \(10 \mathrm{~km}\). What is the acceleration due to gravity on the surface of this star in terms of the
Which pulls harder on the Moon: Earth or the Sun?
How far above the surface of Earth do you have to go before the acceleration due to gravity drops by \(0.10 \%\), \(1.0 \%\) and \(10 \%\) ?
(a) As a spacecraft travels along a straight line from Earth to the Moon, at what distance from Earth does the force of gravity exerted by Earth on the coasting spacecraft cancel the force of gravity
From the picture of Saturn in Figure P13.29 and known values, estimate the orbital period of particles in Saturn's rings.Data from Figure P13.29
The Sun and Moon both exert a gravitational force on Earth. (a) Which force has greater magnitude? (b) What is the ratio of the two force magnitudes?
Given that the acceleration due to gravity is \(0.0500 \mathrm{~m} / \mathrm{s}^{2}\) at the surface of a spherical asteroid that has a radius of \(3.75 \times 10^{4} \mathrm{~m}\), determine the
A test object of mass \(m_{\text {test }}\) is placed at the origin of a two-dimensional coordinate system (Figure P13.33). An object 1 , of the same mass, is at (d, 0), and an object 2 , of mass \(2
Using \(g\) for the acceleration due to gravity is valid as long as the height \(b\) above Earth's surface is small. Derive an expression for a more accurate value of the acceleration due to gravity
Calculate the acceleration due to gravity inside Earth as a function of the radial distance \(r\) from the planet's center. (Imagine that a mine shaft has been drilled from the surface to Earth's
What is the gravitational potential energy of the EarthSun system?
The asteroid known as Toro has a radius of about \(5.0 \mathrm{~km}\) and a mass of \(2.0 \times 10^{15} \mathrm{~kg}\). Could a \(70-\mathrm{kg}\) person standing on its surface jump free of Toro?
(a) How much gravitational potential energy does a system comprising a \(100 \mathrm{~kg}\) object and Earth have if the object is one Earth radius above the ground? (b) How fast would a
An object 1 of mass \(m_{1}\) is separated by some distance \(d\) from an object 2 of mass \(2 m_{1}\). An object 3 of mass \(m_{3}\) is to be placed between them. If the potential energy of the
Two particles, each of mass \(m\), are initially at rest very far apart. Obtain an expression for their relative speed of approach at any instant as a function of their separation distance \(d\) if
Consider an alternate universe in which the magnitude of the attractive force of gravity exerted by Earth on a meteor of mass \(m_{\mathrm{m}}\) approaching Earth is given by \(F=C m_{\mathrm{m}}
Derive expressions for the orbital speed and energy for a satellite of mass \(m_{\mathrm{s}}\) traveling in a circular orbit of radius \(a\) around a planet of mass \(m_{\mathrm{p}} \gg
What maximum height above the surface of Earth does an object attain if it is launched upward at \(4.0 \mathrm{~km} / \mathrm{s}\) from the surface?
(a) Derive an expression for the energy needed to launch an object from the surface of Earth to a height \(h\) above the surface. (b) Ignoring Earth's rotation, how much energy is needed to get the
A spacecraft propelled by a solar sail is pushed directly away from the Sun with a force of magnitude \(C / r^{2}\), where \(\mathrm{C}\) is a constant and \(r\) is the spacecraft-Sun radial
In 1865, Jules Verne wrote a story in which three men went to the Moon by means of a shell shot from a large cannon sunk in the ground. (a) What muzzle speed must the cannon have in order for the
The center-to-center distance between a \(200 \mathrm{~g}\) lead sphere and an \(800 \mathrm{~g}\) lead sphere is \(0.120 \mathrm{~m}\). A \(1.00 \mathrm{~g}\) object is placed \(0.0800 \mathrm{~m}\)
Derive an expression for the gravitational potential energy of a system consisting of Earth and a brick of mass \(m\) placed at Earth's center. Take the potential energy for the system with the brick
Is approximating the gravitational potential energy near the surface of the Sun as \(m g_{s} \Delta x\) accurate over a smaller or larger range of values than approximating the gravitational
A uniform rod of mass \(m_{\text {rod }}\) and length \(\ell_{\text {rod }}\) lies along an \(x\) axis far from any stars or planets, with the center of the rod at the origin (Figure P13.50). A ball
The parabolic orbit of any comet around the Sun might be described as a collision between the two objects. Would it be better described as an elastic collision or an inelastic collision?
Assume a particle is located at the surface of the Sun. (a) If the particle has mass \(m\), how fast must it be moving away from the Sun's center of mass to escape the gravitational influence of the
What is the speed of a space probe when it is very far from Earth if it was launched from the surface of Earth at twice its escape speed?
Which trip takes more rocket fuel: from Earth to the Moon or from the Moon to Earth?
A satellite moves at speed \(v\) in very low orbit about a moon that has no atmosphere. You launch a projectile vertically from the same moon's surface at the same speed \(v\). To what height does it
A satellite in an elliptical orbit around Earth has a speed of \(8032 \mathrm{~m} / \mathrm{s}\) when it is at perigec, the position in the orbit closest to Earth. At this position, the satellite is
A certain comet comes in on a parabolic approach around the Sun. Its perihelion is about the same distance from the Sun as the orbit of Mercury. How much faster than Mercury (expressed as a ratio) is
Show that for circular orbits of two objects about their center of mass, \(E=\frac{1}{2} U=-K\). This is a special case of the more general mathematical statement known as the virial theorem.
An attractive central force exerted on a particle of mass \(m\) causes the particle to travel in a bound orbit. The orbit is clliptical with semimajor axis \(a\), and the force has magnitude
A particle is leaving the Moon in a direction that is radially outward from both the Moon and Earth. What speed must it have to escape the Moon's gravitational influence?
A meteoroid passes through a position in space where its speed is very small relative to Earth's and it is at a perpendicular distance of 19 Earth radii above Earth's surface. The meteoroid is moving
A space probe can be either launched at escape speed from Earth or transported to a "parking orbit" above Earth and then launched. (a) If the parking orbit is \(180 \mathrm{~km}\) above Earth's
Two identical stars, each of mass \(3.0 \times 10^{30} \mathrm{~kg}\), revolve about a common center of mass that is \(1.0 \times 10^{11} \mathrm{~m}\) from the center of either star. (a) What is the
Kepler's third law says that the square of the period of any planet is proportional to the cube of its mean distance from the Sun. Show that this law holds for elliptical orbits if one uses the
Two celestial bodies of masses \(m_{1}\) and \(m_{2}\) are orbiting their center of mass at a center-to-center distance of \(d\). Assume each body travels in a circular orbit about the center of mass
To travel between Earth and any other planet requires consideration of such things as expenditure of fuel energy and travel time. To simplify the calculations, one chooses a path such that the
A small disk of mass \(m\) is at the center of a larger disk that has an off-center hole drilled in it (Figure P13.67). What is the direction of the gravitational force exerted by the larger disk on
Is Eq. 13. 37 for the gravitational force exerted by a solid sphere of mass \(m_{5}\) on some object of mass \(m_{0}\) when the two are a radial distance \(r\) apart, \(F_{\mathrm{so}}^{G}=G m_{o}
A uniform ring of mass \(m_{\text {ring }}\) and radius \(R_{\text {ting }}\) is shown in Figure P13.69. A small object of mass \(m_{\mathrm{obi}}\) sits a separation distance \(s\) from the ring on
Two uniform spherical shells are located such that their centers are along the \(x\) axis in Figure P13.70. The inner shell has mass \(m_{\text {inner }}\) and radius \(R\), and its center is at
A thin disk of radius \(R\) has mass \(m_{\text {disk }}\) uniformly distributed over its area. (a) Derive an expression for the magnitude of the gravitational force this disk exerts on a particle of
In a system of \(N\) particles, how many terms are there in the expression for the gravitational potential energy of the system?
You equip a rocket with enough fuel to reach escape speed from Earth. If you plan to launch the rocket from just above ground level, does it matter whether you launch it vertically, at an angle, or
What is the value of the acceleration \(g_{V_{\text {enus }}}\) due to gravity at the surface of Venus?
Is there any position in the elliptical orbit of a satellite where the tangential component of the acceleration is greater than the component perpendicular to the tangential component? If so, what
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