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physics
particle physics

Principles And Practice Of Physics 2nd Edition Eric Mazur - Solutions

What is a common definition of physics? That is, what is physics about?
I have two coins in my pocket, together worth 30 cents. If one of them is not a nickel, what coins are they?
Calculate:(a) \(f=a /(b c)\), where \(a=2.34\mathrm{~mm}^{2}, b=54.26\mathrm{~m}\), and \(c=0.14\mu \mathrm{m}\);(b) \(g=k t^{3}\), where \(k=1.208\times 10^{-2}\mathrm{~s}^{-3}\) and \(t=2.84\mathrm{~s}\);(c) \(f+g\);(d) the sum of \(b=54.26\mathrm{~m}\) and \(c=1.4\mathrm{~mm} ;(e) h=k(m-n)\),
For a given level of technology, there is a maximum density of "bits" of information that can be stored on a computer's hard-drive disk. The data are stored in a tight spiral, so that "tracks" are essentially circles of increasing radius from inner to outer parts of the disk. As the disk spins at a
What is the ratio of the rotational speed of Earth's daily rotation to that of its annual revolution?
When one race car passes another during a race, the passing car usually tries to pass on the inner lane of a curve in the track. Why?
The toy race track in Figure P11.4 has three lanes, and cars cannot change lanes. The centerlines of any two adjacent lanes are 100 mm apart, and the innermost lane has a radius of 1.00 m.(a) If each car has the same average speed, compare the time intervals needed for the cars to complete 20
Plot, as a function of time, the rotational velocity of your car's wheels as you(a) back out of your driveway,(b) drive down a residential street,(c) turn onto a highway, (d) drive on the highway for a while, (e) exit the highway and stop at a traffic light, (f) drive on a city street, and (g)
Hold a quarter down flat on a table with a finger. Then place a second quarter flat on the table, touching one point on the edge of the first quarter. If you roll the second quarter around the first so that the edges do not slip, describe the revolution and rotation as the second quarter returns to
Suppose the expression for centripetal acceleration is of the form \(a_{c}=v^{p} r^{q}\), where \(p\) and \(q\) are constants. By analyzing the units in this expression, determine the numerical values of \(p\) and \(q\).
Standing in front of a tree, you whirl your sling with a rock in it. If you wish to hit the tree, at what location in the circle in Figure P11.8 (nearest point a, b, c, or d) should you release the rock from the sling?Data from Figure P11.8
The Ferris wheel in Figure P11.9 is turning at constant speed. Draw and label free-body diagrams showing the forces on passengers at the numbered positions. Be careful to show correct relative lengths on your vector arrows.Data from Figure P11.9
To see some of the trouble you can get into with noninertial reference frames, try this experiment. You and a friend stand opposite each other on the edge of a playground merry-go-round and get it rotating. While it is rotating, you attempt to toss a ball to your friend. As seen from above, what
A salad spinner (Figure P11.11) is used to dry lettuce that has been washed. What physics is going on as the spinner does its job?Data from Figure P11.11
In a certain elaborate roller coaster, the cars are not on tracks but inside a U-shaped track much like a bobsled run. The cars are thus free to swing left and right across the U, climbing the walls as they do so. A student on the ride holds a string with a chunk of metal tied to the free end, with
The ball in Figure P11.14 is attached to a vertical rod by two strings of equal strength (able to support much more than one of these balls) and equal length. The strings are light and do not stretch. The rod begins to rotate with its rotational speed increasing slowly, causing the ball to revolve
Suppose that you were to tie a heavy metal washer to one end of a string, hold the string by the other end, and whirl it in a horizontal circle above your head. Pay close attention to where your hand would be and to where the washer would be as you speed up the rotation. Ignore air resistance. (a)
Floor lamps usually have a base with large inertia, while the long body and top have much less inertia. If you want to show off by spinning a floor lamp like a baton, where should you grab the lamp?
A gymnast's backflip is considered more difficult to do in the layout (straight body) position than in the tucked position. Why?
An ice cube and a rubber ball are both placed at one end of a warm cookie sheet, and the sheet is then tipped up. The ice cube slides down with virtually no friction, and the ball rolls down without slipping. If the ball and the ice cube have the same inertia, which one reaches the bottom first?
(a) Is there a choice of rotation axes for a bowling ball and a baseball, each rotating on its own axis, such that the baseball has a greater rotational inertia? If so, describe the axes. If not, explain why not. (b) Repeat for a revolving bowling ball and a revolving baseball.
You stand on the edge of a playground carousel while your friends help you get it going. After they stop pushing, you walk toward the center. (a) What happens to the rotational inertia of the carousel-you system as you move inward from the edge? (b) How does this change in rotational inertia affect
A car's engine is turning the crankshaft at 6000 rev/min. What is the rotational speed \(\omega\) ?
What is the rotational speed of a watch's second hand? Its hour hand?
If your tires are worn, does your odometer (which is keyed to the turns of the axle) underestimate or overestimate the number of miles you drive?
As you drive clockwise around a turn (as viewed from overhead), you see backed-up traffic ahead and so you slow down. Which force diagram in Figure P11.27 best illustrates your acceleration?Data from Figure P11.27 (a) (b) (c)
At the end of a ride, a carnival carousel decelerates smoothly from some initial rotational speed \(\omega\) to a stop.(a) Plot, as a function of time, the speed \(v\) of a carousel horse at radius \(R\) and of another horse at radius \(2 R\).(b) Plot the magnitude of the centripetal acceleration
You attach one end of a string of length \(\ell\) to a small ball of inertia \(m\). You attach the string's other end to a pivot that allows free revolution. You hold the ball out to the side with the string taut along a horizontal line, as in Figure P11.29.(a) If you release the ball from rest,
A pendulum is made of a bob dangling from a lightweight string of length \(\ell\). The bob is pulled sideways so that the string makes an angle \(\theta_{i}\) with respect to the vertical, then released. As it swings down, what is the rotational speed of the bob as a function of the changing angle
Assume that Earth's orbit around the Sun is a perfect circle. Earth's inertia is \(5.97 \times 10^{24} \mathrm{~kg}\), the radius of its orbit is \(1.50 \times 10^{11} \mathrm{~m}\), and its orbital period is 365. 26 days. (a) What is the magnitude of its centripetal acceleration around the Sun?
A ball is suspended by a string from the top of a vertical rod as shown in Figure P11.32. The rod starts at rest and then begins to rotate with a small constant rotational acceleration. Qualitatively plot as a function of time the magnitude of \((a)\) the vertical component and \((b)\) the
You hold a small ice cube near the top edge of a hemispherical bowl of radius \(100 \mathrm{~mm}\). When you release the cube from rest, what is the magnitude of its acceleration at the instant it reaches the bottom of the bowl? Ignore friction.
A \(0.100-\mathrm{kg}\) ball attached to a \(0.20-\mathrm{m}\) rod of very small inertia moves in a vertical circle in such a way that its speed remains constant. Let \(\mathcal{T}_{1}, \mathcal{T}_{2}, \mathcal{T}_{3}\), and \(\mathcal{T}_{4}\) be the tensions in the rod at positions 1, 2, 3, and
An automobile accelerates from rest at \(t=0\) such that its tires undergo a constant rotational acceleration \(\alpha=5.8 \mathrm{~s}^{-2}\). The radius of each tire is \(0.33 \mathrm{~m}\). At \(t=10 \mathrm{~s}\), compute \((a)\) the rotational speed \(\omega\) of the tires, \((b)\) the
For the tread on your car tires, which is greater: the tangential acceleration when going from rest to highway speed as quickly as possible or the centripetal acceleration at highway speed?
A roller-coaster car initially at a position on the track a height \(h\) above the ground begins a downward run on a long, steeply sloping track and then goes into a circular loop-the-loop of radius \(R\) whose bottom is a distance \(d\) above the ground (Figure P11.37). Ignore friction. (a) What
(a) Consider a circular vertical loop-the-loop on a roller coaster. Show that if a car coasts without power around the loop, the difference between the normal force exerted by the car on a passenger at the top of the loop and the normal force exerted by the car on her at the bottom of the loop is
A ball is put into a cone and made to move at a constant specd of \(3.00 \mathrm{~m} / \mathrm{s}\) in a horizontal circle of radius \(0.500 \mathrm{~m}\) (Figure P11.39). (a) What is the centripetal component of the ball's acceleration? (b) What is the tangential component of its acceleration? (c)
A \(0.25-\mathrm{kg}\) ball attached to a string is being spun around on a horizontal surface at a rotational speed of \(2.5 \mathrm{rev} / \mathrm{s}\). What is the ball's kinetic energy if the string is \(1.0 \mathrm{~m}\) long?
Three small, identical \(1.0-\mathrm{kg}\) pucks are attached to identical \(0.50-\mathrm{m}\) strings, tied together at a common center as shown in Figure P11.42. When whirled in circular motion at angular speed \(3.0 \mathrm{~s}^{-1}\), what are \((a)\) the rotational kinetic energy and \((b)\)
As you stand on the sidewalk outside an apartment building, a \(2.0-\mathrm{kg}\) bird flies toward you at \(2.0 \mathrm{~m} / \mathrm{s}\) along a straight line that passes \(3.0 \mathrm{~m}\) above your head and runs parallel to the street. A friend is reclining with his head \(4.0 \mathrm{~m}\)
Puck \(A\), of inertia \(m\), is attached to one end of a string of length \(\ell\), and the other end of the string is attached to a pivot so that the puck is free to revolve on a smooth horizontal surface. Puck B, of inertia \(8 m\), is attached to one end of a string of length \(\ell / 2\), and
You have a pail of water with a rope tied to the handle. If you whirl the pail in a vertical circle fast enough, none of the water spills out, even when the pail is upside down. Explain why.
In Figure P11.47, two identical pucks B and C, each of inertia \(m\), are connected by a rod of length \(\ell\) and negligible inertia that is free to rotate about its center. Then puck A, of initial speed \(v_{\mathrm{i}}\) and inertia \(m / 2\), comes in and hits B. After the collision, in which
A small puck on an air table revolves in a circle with rotational speed \(\omega\), held at radius \(r\) by a weighted string that passes through a hole in the table. You slowly pull down on the weighted end of the string, decreasing the radius \(r\). Assume that the angular momentum of the puck
Two skaters skate toward each other, each moving at \(3.3 \mathrm{~m} / \mathrm{s}\). Their lines of motion are separated by a perpendicular distance of \(2.0 \mathrm{~m}\). Just as they pass each other (still \(2.0 \mathrm{~m}\) apart), they link hands and spin about their common center of mass.
A record player turntable initially rotating at \(33 \frac{1}{3} \mathrm{rev} / \mathrm{min}\) is braked to a stop at a constant rotational acceleration. The turntable has a rotational inertia of \(0.020 \mathrm{~kg} \cdot \mathrm{m}^{2}\). When it is switched off, it slows down to \(75 \%\) of its
A disk of rotational inertia \(I\) about the central axis shown in Figure P11.51 is rotating about this axis with initial rotational velocity \(\omega_{\vartheta, \mathrm{i}}\) on low-friction bearings. A second identical disk is held at rest a few millimeters directly above the first disk and
A popular ride at some playgrounds consists of two circular disks joined by rungs (Figure P11.52). The center of the unit is attached to a horizontal axle around which the unit rotates. The rotational inertia of the unit is \(200 \mathrm{~kg} \cdot \mathrm{m}^{2}\), and its radius is \(1.00
What is the rotational inertia about the \(x\) axis of the rigid object in Figure P11.53? (Treat the balls as particles.)Data from Figure P11.53 Figure P11.53 m 54m
A cubical wire framework in which each edge is \(0.25 \mathrm{~m}\) long has a \(0.20-\mathrm{kg}\) steel ball at each of its eight corners. What is the rotational inertia of this framework around an axis along one edge? Ignore the inertias of the wires.
What is the formula for the rotational inertia of a thin spherical shell of inertia \(m\) and radius \(R\) about an axis tangent to any point on its surface?
A deer's leg is very slender near the hoof, with most of the muscle bunched up near the hip joint. How does this work to the deer's advantage?
A \(20-\mathrm{kg}\) child running at \(1.4 \mathrm{~m} / \mathrm{s}\) jumps onto a playground merry-go-round that has inertia \(180 \mathrm{~kg}\) and radius \(1.6 \mathrm{~m}\). She is moving tangent to the platform when she jumps, and she lands right on the edge. What is the rotational speed of
Earth has an inertia of \(5.97 \times 10^{24} \mathrm{~kg}\) and a radius of \(6.37 \times 10^{6} \mathrm{~m}\). (a) Calculate its rotational inertia about the rotation axis, assuming uniform density. (b) The rotational inertia of Earth about its rotation axis has been measured to be \(8.01 \times
The rotational inertia of any flat object about an axis perpendicular to the object is equal to the sum of the rotational inertias about two mutually perpendicular axes in the plane of the object, if all three axes pass through a common point. Using this "perpendicular-axis theorem," determine
The structure in Figure P11.60 is made of three identical rods of uniform density. Rank the rotational inertias of the structure, from smallest to largest, about the four rotation axes represented by the dashed lines.Data from Figure P11.60 (2) HH (d) HH (a) (b)
Global warming might result in the melting of the polar ice caps. What effect would this melting have on the length of the day?
A hollow cylinder, a solid cylinder, and a billiard ball are all released at the top of a ramp and roll to the bottom without slipping. (a) Rank them, from least to greatest, according to the fraction of the kinetic energy that is rotational as they roll. (b) What are the ratios of their speeds
Estimate the rotational inertia of a \(70-\mathrm{kg}\) athlete about a horizontal axis passing through her waist from left to right.
A \(0.20-\mathrm{kg}\) block and a \(0.25-\mathrm{kg}\) block are connected to each other by a string draped over a pulley that is a solid disk of inertia \(0.50 \mathrm{~kg}\) and radius \(0.10 \mathrm{~m}\). When released, the \(0.25-\mathrm{kg}\) block is \(0.30 \mathrm{~m}\) off the ground.
You accidentally knock a full bucket of water off the side of the well shown in Figure P11.65. The bucket plunges \(15 \mathrm{~m}\) to the bottom of the well. Attached to the bucket is a light rope that is wrapped around the crank cylinder. How fast is the handle turning when the bucket hits
A block of inertia \(m\) is attached to a block of inertia \(2 m\) by a light string draped over a uniform disk of inertia \(3 m\) and radius \(R\) that can rotate on a horizontal axle (Figure P11.66). Initially, the block of inertia \(m\) is held in place so that the string is taut. When this
A thick-walled cylinder of inertia \(m\) has an outer radius \(R_{\text {outer }}\), an inner radius \(R_{\text {innet }}=R_{\text {outer }} / 2\), and a length \(\ell\) (Figure P11.67). It rotates around an axis attached to its outside along its length. What is its rotational inertia about this
A thin \(0.15-\mathrm{kg}\) rectangular sheet has \(40-\mathrm{mm}\) short sides and \(80-\mathrm{mm}\) long sides. Determine the rotational inertia of the sheet about an axis perpendicular to it and located \((a)\) at the center of a long side, \((b)\) at the center of a short side, and \((c)\) at
One type of wagon wheel consists of a \(2.0-\mathrm{kg}\) hoop fitted with four \(0.80-\mathrm{kg}\) thin rods placed along diameters of the hoop so as to make eight evenly spaced spokes. For a hoop of radius \(0.30 \mathrm{~m}\), what is the rotational inertia of the wheel about an axis
A thin rod, \(0.83 \mathrm{~m}\) long, is pivoted such that it hangs vertically from one end. You want to hit the free end of the rod just hard enough to get the rod to swing all the way up and over the pivot. How fast do you have to make the end go?
Big Ben in London is the most accurate mechanical clock of its size. The \(300-\mathrm{kg}\) hour hand is \(2.7 \mathrm{~m}\) long, and the \(100-\mathrm{kg}\) minute hand is \(4.2 \mathrm{~m}\) long. Calculate the rotational kinetic energy of the two-hand system, treating each hand as if it were a
Consider an object that has rotational inertia \(I\) about some arbitrary axis of rotation. The radius of gyration of the object is the distance from this axis where all the object's inertia could be concentrated and still produce. the same rotational inertia \(I\) about the axis. What is the
A thin piece of metal in the shape of a right triangle has inertia \(m\). Its perpendicular sides are of lengths \(\ell\) and \(2 \ell\). Determine the rotational inertia about an axis that runs (a) along side \(\ell\) and \((b)\) along side \(2 \ell\).
A block of inertia \(m\) is attached to a light string wound around a uniform disk also of inertia \(m\) (Figure P11.74). The disk has radius \(R\) and rotates on a fixed horizontal axle through its center. The opposite side of the block is attached to a spring of force constant \(k\) and relaxed
A certain baseball bat is a tapered cylinder that increases in diameter from \(0.040 \mathrm{~m}\) at one end to \(0.070 \mathrm{~m}\) at the other end and is \(0.84 \mathrm{~m}\) long. The bat has uniform density and inertia \(0.85 \mathrm{~kg}\). What is the rotational inertia of this bat around
In the laboratory, you are trying to put pennies on a rotating platform so that they don't slide off. Your partner tells you, "Pennies on the outside stay on better because \(a_{\mathrm{c}}=v^{2} / r\). For larger \(r\), the centripetal acceleration is less, and so the frictional force has an
Solar and lunar eclipses are caused by a fortuitous relationship between the sizes of the Moon and Sun and their distances from Earth. Look up data for the EarthMoon and Earth-Sun distances and the diameters of the Moon and the Sun. (a) Calculate the angular size of the Sun's disk as seen by an
Show that the centripetal acceleration of an object undergoing circular motion at constant speed can be expressed as where \(r\) is the circle radius and \(T\) is the period of the motion. 4m T
If you spin a raw egg, stop it momentarily, and then let go, it begins to spin again. You can't do this with a hardboiled egg. Why?
If you stretch your arm out full length and block the Sun with your thumb, how fast must your thumb move, in millimeters per minute, to track the Sun's motion?
Out looking for Tarzan, Jane swings on a vine to speed her search. (a) During her are downward, how much work is done on her by the tensile force in the vine? (b) At which position along the arc is the force exerted by the vine on Jane greatest?
The Moon orbits Earth while Earth orbits the Sun, and thus the Moon's motion around the Sun is the combination of those two motions. Is the Moon's motion ever retrograde if observed from the Sun, where retrograde means that the Moon appears to move in the direction opposite the direction of Earth's
Suppose several particles are in concentric circular orbits under the influence of some centripetal component of force, the magnitude of which depends on distance from the center of the motion. Each particle has a different orbital radius \(r\) and a corresponding period \(T\). How does the force
Approximate the Sun as a uniform sphere of radius \(6.96 \times 10^{8} \mathrm{~m}\), rotating about its central axis with a period of 25. 4 days. If, at the end of its life, the Sun collapses inward to form a uniform dwarf star that is approximately the same size as Earth, what will the period of
An open door of inertia \(m_{\mathrm{d}}\) and width \(\ell_{\mathrm{d}}\) is at rest when it is struck by a thrown ball of clay of inertia \(m_{\mathrm{b}}\) that is moving at speed \(v_{\mathrm{b}}\) at the instant it strikes the door (Figure P11.85). The impact location is a distance
Your aunt owns an amusement park, and she wants you to add a circular loop to an existing roller-coaster ride. The first hill for the existing roller coaster is \(55 \mathrm{~m}\) tall, and your aunt wants you to build, right after this hill, the tallest loop possible without having the cars fall
The spacecraft in the movie 2001: A Space Odyssey has a rotating cylinder to create the illusion of gravity, inside of which the crew walks and exercises. While watching this old movie, you realize that the radius of the cylinder is roughly three times a crew member's height. You imagine this
A turntable of radius \(0.320 \mathrm{~m}\) is fitted with an electromagnet that causes steel objects to stay in place on the table. A triangular mark on the rim shows the rotational position of the table relative to the surroundings (Figure P11.88). The turntable completes one rotation in \(0.360
You have a toy top that plays music if the rotational speed is at least \(1800 \mathrm{rev} / \mathrm{min}\). The way to get this top spinning is to pull on a string wrapped around a spindle of diameter of \(6.0 \mathrm{~mm}\). The top has a rotational inertia of about \(5.0 \times 10^{-3}
A dart of inertia \(m_{\mathrm{d}}\) is fired such that it strikes with speed \(v_{\mathrm{d}}\), embedding its tip in the rim of a target that is a uniform disk of inertia \(m_{\mathrm{t}}\) and radius \(R_{\mathrm{t}}\). The target is initially rotating clockwise in the view shown in Figure
A smooth-faced cube of inertia \(m\) and side length \(d\) sliding along a highly polished floor at speed \(v\) strikes a door threshold, and the collision makes the cube tilt as shown in Figure P11.91. As the cube tips over, its center of mass is located at a variable horizontal distance \(x ;
For which of the following forces is the force displacement nonzero: \((a)\) the force exerted by a hand compressing a spring,(b) the force exerted by Earth on a ball thrown upward,(c) the force exerted by the ground on you at the instant you jump upward, \((d)\) the force exerted by the floor of
Is the work done by the following forces considered in Exercise 9.1 positive, negative, or zero? In each case the system is the object on which the force is exerted.(a) The force exerted by a hand compressing a spring, \((b)\) the force exerted by Earth on a ball thrown upward,(c) the force
A cart is at rest on a low-friction track. A person gives the cart a shove and, after moving down the track, the cart hits a spring, which slows down the cart as the spring compresses. Draw an energy diagram for the system that comprises the person and the cart over the time interval from the
A block initially at rest is released on an inclined surface. The block slides down, compressing a spring at the bottom of the incline; there is friction between the surface and the block. Consider the time interval from a little after the release, when the block is moving at some initial speed
A puck sliding on a horizontal surface hits the free end of a spring that is held fixed at the other end. There is friction between puck and surface. Consider the interval from the instant before the puck comes in contact with the spring until the instant the puck has zero velocity and the spring
A stunt performer falls from the roof of a two-story building onto a mattress on the ground. The mattress compresses, bringing the performer to rest without his getting hurt. Is the work done by the mattress on the performer positive, negative, or zero? Is the work done by the performer on the
Consider a weightlifter holding a barbell motionless above his head.(a) Is the sum of the forces exerted on the barbell zero? \((b)\) Is the weightlifter exerting a force on the barbell?(c) If the weightlifter exerts a force, does this force do any work on the barbell?(d) Does the energy of the
Do any of the systems in Figure 9. 14 undergo a change in potential energy? If yes, is the change positive or negative? Ignore any friction.Data from Figure 9. 14 (a) (b) 15 Earth Earth Earth Earth Earth Earth Earth Earth
A person pushes a cart up a small hill, gaining speed along the way. Friction in the cart's wheels is negligible. Name the components of the system depicted in each energy diagram shown Figure 9. 15.Data from Figure 9. 15 (a) AK AU AE, AE W AK AU , W AK AU AE, AE W
Suppose a missile that was launched vertically moves along a trajectory and has a constant vertical speed and a constant horizontal acceleration. What is the shape of this trajectory as seen by a stationary observer?
Riding in a train on horizontal tracks, you notice a boy drop a baseball from the roof of his house nearby. (a) What is the shape of the trajectory you see for the ball if the train is moving at constant speed? (b) Would you see the trajectory as a straight line if the train were accelerating?
You are performing an experiment similar to the one shown in Figure 10. 1. The ball is dropped from a height of \(y_{i}=0.200 \mathrm{~m}\) on the pole above the cart just as the pole and cart pass your origin of coordinates. The ball lands inside the cart at the instant the cart passes the

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