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physics
particle physics

Principles And Practice Of Physics 1st Edition Eric Mazur - Solutions

A \(1.0-\mathrm{kg}\) ring with an inner radius of \(0.060 \mathrm{~m}\) and an outer radius of \(0.080 \mathrm{~m}\) is sent rolling without slipping up a ramp that makes an angle of \(30^{\circ}\) with the horizontal. If the initial speed of the ring is \(2.8 \mathrm{~m} / \mathrm{s}\), how far
A certain car engine delivers enough force to create \(380 \mathrm{~N} \cdot \mathrm{m}\) of torque when the engine is operating at 3200 revolutions per minute. Calculate the average power delivered by the engine at this rotation rate.
A \(680-\mathrm{kg}\) disk of radius \(1.2 \mathrm{~m}\) is mounted on a fixed axle. A force exerted on the disk causes a constant torque that gives the disk a rotational acceleration magnitude of \(0.30 \mathrm{~s}^{-2}\) for \(5.0 \mathrm{~s}\). If the disk had an initial rotational speed of
A large steel bar of length \(\ell\) is hinged at one end to a wall. A mechanic holds the other end so that the bar is parallel to the ground and places a penny on the bar right at the end he is holding. (a) What is the rotational acceleration of the bar when he lets go? (b) Does the penny remain
A light, unstretchable string is wound around the perimeter of a \(4.0-\mathrm{kg}\) disk that has a radius of \(0.50 \mathrm{~m}\) and is free to rotate about an axle that runs perpendicular to the disk face and through the disk center. A \(2.0-\mathrm{kg}\) block is connected to the free end of
A \(5,0-\mathrm{kg}\) hollow cylinder of radius \(0.25 \mathrm{~m}\) rotates freely about an axle that runs through its center and along its long axis. A cord is wrapped around the cylinder and is pulled straight from the cylinder with a steady tensile force of \(50 \mathrm{~N}\). As the cord
A marble of inertia \(m\) is held against the side of a hemispherical bowl as shown in Figure P12.69 and then released. It rolls without slipping. The initial position of the marble is such that an imaginary line drawn from it to the center of curvature of the bowl makes an angle of \(30^{\circ}\)
A \(3.0-\mathrm{kg}\) disk of radius \(50 \mathrm{~mm}\) rolls down a ramp inclined at an angle of \(28^{\circ}\) with the vertical. If the disk starts out at rest and the coefficients of static and kinetic friction between the ramp and the disk are both 0.50 , what is the rotational speed of the
An almost-conical toy top (Figure P12.71) that has radius \(R=20 \mathrm{~mm}\) and inertia \(0.125 \mathrm{~kg}\) is spun up using a force of \(5.0 \mathrm{~N}\) and a string that is \(1.0 \mathrm{~m}\) long. What are (a) the work done on the top, (b) its kinetic energy, and (c) its final
Archimedes' screw, one of the first mechanical devices invented for lifting water, is a very large screw fitted tightly inside a shaft (Figure P12.72). The bottom of the device is placed in a pool of water. As someone turns the handle to make the screw turn, water is carried up along the ridges of
You attach a \(0.50-\mathrm{m}\) length of string to a \(50 \mathrm{~g}\) puck and pass the other end of the string through a hole in the center of a table. Grasping the string under the table, you pull just enough string through the hole so that, when your friend gives the puck a sideways push, it
A \(30-\mathrm{kg}\) solid sphere of radius \(0.12 \mathrm{~m}\) is rolling without slipping on a horizontal surface at \(2.0 \mathrm{~m} / \mathrm{s}\). (a) What average torque is required to stop the sphere in \(5.0 \mathrm{rev}\) without inducing skidding? (b) If this torque is caused by a soft
A marble that has a radius of \(10 \mathrm{~mm}\) is placed at the top of a globe of radius \(0.80 \mathrm{~m}\). When released, the marble rolls without slipping down the globe. Determine the angle from the top of the globe to the location where the marble flies off the globe.
A \(4.0-\mathrm{kg}\) bowling ball is thrown down the alley with a speed of \(10.0 \mathrm{~m} / \mathrm{s}\). At first the ball slides with no rotation. The coefficient of friction between ball and alley surface is 0.20 .(a) How long a time interval does it take for the ball to achieve pure
You shove a cube of inertia \(m\) and side length \(d\) so that it slides along a smooth table with speed \(v_{1}\) (Figure P12.77a). The cube then hits a raised lip at the end of the table. After it hits the lip, the cube begins to rotate about it (Figure 12.77b). (a) Show that the magnitude of
When you want to turn a bicycle left, the first thing you do is lean left. Why is it important to do this?
If the magnitude of the vector product of two vectors is the same as the magnitude of the scalar product of the same two vectors, what is the angle between them?
A cyclist exerts a vertical force on a bike pedal. This pedal is at the end of a crank that is \(0.20 \mathrm{~m}\) long and pivoted to rotate about the axle of the chain wheel. If the cyclist pushes downward with a force of \(150 \mathrm{~N}\), determine the magnitude of the torque caused by this
The two arms of the L-shaped handle on the spigot of Figure P12.82 have a length ratio of \(1: \sqrt{3}\). At what angle \(\theta\) do you want to pull down on the end of the handle to maximize the torque your force causes?Data from Figure P12.82 Figure P12.82 THE
A \(3.0-\mathrm{kg}\) rod that is \(1.5 \mathrm{~m}\) long is free to rotate in a vertical plane about an axle that runs through the rod's center, is perpendicular to the rod's length, and runs parallel to the floor. A 1.0-kg block is attached to one end of the rod, and a \(2.0-\mathrm{kg}\) block
A motor drives a disk initially at rest through 23.9 rotations in \(5.0 \mathrm{~s}\). Assume the vector sum of the torques caused by the force exerted by the motor and the force of friction is constant. The rotational inertia of the disk is \(4.0 \mathrm{~kg} \cdot \mathrm{m}^{2}\). When the motor
The angular momentum of the propellers of a small airplane points directly forward from the plane. (a) In what direction do the propellers rotate as seen from the rear of the plane? (b) If the plane is flying horizontally and suddenly pulls upward, in which direction does the nose of the plane tend
A \(40-\mathrm{kg}\) sharpening wheel of radius \(0.10 \mathrm{~m}\) is rotating at 3.3 revolutions per second. A \(6.0-\mathrm{kg}\) axe is pressed against the rim with a force of \(40 \mathrm{~N}\) directed as shown in Figure P12.87. Treat the wheel as a disk, and assume a coefficient of kinetic
A heavy-rimmed bicycle wheel is set Figure P12.88 spinning in the direction shown in Figure P12.88. A string is tied to one end of the axle, and someone is holding up the string. (a) Use torque arguments to explain why the wheel slowly revolves horizontally around the string end of the axle when
A gyroscope consists of a spinning wheel mounted inside a support structure (Figure P12.89). Because of conservation of angular momentum, the gyroscope keeps its orientation in space unless some outside force causes a torque on it. Suppose the \(1.0-\mathrm{kg}\) spinning wheel of a certain
Two identical boxes are placed on opposite ends of the board of a playground seesaw as in Figure P12.90a, so that the system is in mechanical equilibrium. (a) What happens to that equilibrium if you exert a small, brief force, either upward or downward, on either end of the board? (b) With the
For the \(x\) and \(y\) axes of a right-handed Cartesian coordinate system, what is the direction of \(\hat{i} \times[\hat{i} \times[\hat{i} \times(\hat{i} \times \hat{j})] ?\)
Standing on a round raft floating on a pond, how do you turn the raft around \(180^{\circ}\) ?
Dragster drivers have to avoid supplying too much power to the vehicle because too much power causes the front end to rise in a "wheelie," compromising steering control. (a) Why does this happen? (b) What advantage comes from having front-wheel drive in a dragster?
If everyone on Earth simultancously walked from west to east, by what fraction would the length of the day change? Would it lengthen or shorten?
A \(51-\mathrm{kg}\) box is suspended from the right end of a horizontal rod that has very small inertia. The left end of the rod is affixed to a wall by a pin. A wire connects the right end of the rod to the wall directly above the pin, making an angle of \(40^{\circ}\) with the rod. (a) Calculate
A \(35-\mathrm{kg}\) child stands on the edge of a playground merrygo-round that has a radius of \(2.0 \mathrm{~m}\) and a rotational inertia of \(500 \mathrm{~kg} \cdot \mathrm{m}^{2}\). The merry-go-round has a rotational speed of \(0.20 \mathrm{~s}^{-1}\) when the child is standing still. If the
A neutron star is the compact remnant of a very large star that has exploded. Suppose that right after one such explosion, when much of the star's inertia has been blasted away, the star's remaining core has an inertia of \(4 \times 10^{30} \mathrm{~kg}\), a radius of \(13 \times 10^{8}
A horizontal \(2.0-\mathrm{kg}\) rod is \(2.0 \mathrm{~m}\) long. An \(8.0-\mathrm{kg}\) block is suspended from its left end, and a \(4.0-\mathrm{kg}\) block is suspended from its right end. (a) Determine the magnitude and direction of the single extra force necessary to keep the rod in mechanical
What maximum torque can a bicyclist deliver to the pedals?
A solid ball of inertia \(m\) rolls without slipping down a ramp that makes an angle \(\theta\) with the horizontal. (a) What frictional force is exerted on the ball? (b) As a function of \(\theta\), what coefficient of friction is required to prevent slipping?
You make a lawn roller out of a \(125-\mathrm{kg}\) solid cylinder, set to rotate about a central axle. You rig up handles on either side of the axle so that you and a friend can pull on the handles horizontally to pull the roller in a direction perpendicular to its rotation axis (Figure P12.101).
A marble is shot across a smooth wooden floor so that the marble both rotates about a horizontal axis and slides. If at a certain instant the marble's rotational kinetic energy equals the translational kinetic energy of its center of mass, what is the ratio of its center-of-mass speed to the speed
A 12-kg cylinder of radius \(0.10 \mathrm{~m}\) starts at rest and rolls without slipping down a ramp that is \(6.0 \mathrm{~m}\) long and inclined at \(30^{\circ}\) to the horizontal. When the cylinder leaves the end of the ramp, it drops \(5.0 \mathrm{~m}\) to the ground. At what horizontal
A child runs in a straight line tangent to a playground carousel, jumps on, and holds tight as the carousel begins to rotate. Which of the following statements is correct for this collision? (a) The coefficient of restitution is greater than 1 because there is now rotational energy where there was
In a judo hip throw, you pull your \(60-\mathrm{kg}\) opponent onto your back to bring her center of mass just above your hip and then rotate her about your hip. Assume that the lever arm distance of your grip on her is \(0.30 \mathrm{~m}\) from your hip and that her rotational inertia about your
You've been asked to design a flywheel and the associated emergency friction braking system for an electric vehicle. In order to fit the available space, the flywheel must be cast in the form of a solid steel disk with a thickness of \(50 \mathrm{~mm}\) and a radius that cannot exceed \(0.20
A \(3.0-\mathrm{kg}\) block is attached to one end of a light, unstretchable string that is wrapped securely around a cylinder that has a \(0.30-\mathrm{m}\) radius and a rotational inertia of \(0.80 \mathrm{~kg} \cdot \mathrm{m}^{2}\). The cylinder is free to rotate about an axle aligned along its
You are building a pool table and want the design to be such that any ball that rolls into one of the side rails without slipping bounces off the rail and rolls away in another direction, again without slipping. After some experimenting, you decide that you must build the rails to a specific height
A yo-yo is composed of two disks of radius \(a\), with many layers of string wrapped around the axle. The radial distance from the center of the axle to the top layer of string at any instant is \(b\). With the end of the string wrapped around your finger and \(b / a \approx 1\), you let the yo-yo
Consider again the rod in Figure 12.4. Calculate the sum of the torques about the left end of the rod.Data from Figure 12.4 (a) (b) 1 pivot 2 In F forces exerted on rod by weights
You hold a ball in the palm of your hand, as shown in Figure 12.10. The bones in your forearm act like a horizontal lever pivoted at the elbow. The bones are held up by the biceps muscle, which makes an angle of about \(15^{\circ}\) with the vertical. Draw an extended free-body diagram for your
You are moving a large crate mounted on swivel wheels, exerting an off-center force \(\vec{F}_{\mathrm{pc}}^{c}\) as shown in Figure 12.12. Draw an extended free-body diagram for the crate. You can ignore any friction in the wheels.Data from Figure 12.12 F
Three forces are exerted on the lever of Figure 12.7. Forces \(\vec{F}_{1}\) and \(\vec{F}_{3}\) are equal in magnitude, and the magnitude of \(\vec{F}_{2}\) is half as great. Force \(\vec{F}_{1}\) is horizontal, \(\vec{F}_{2}\) and \(\vec{F}_{3}\) are vertical, and the lever makes an angle of
A motor exerts a constant force of \(120 \mathrm{~N}\) tangential to the rim of a \(20-\mathrm{kg}\) cylindrical flywheel of radius \(0.50 \mathrm{~m}\). The flywheel is free to rotate about an axis through its center and runs perpendicular to its face. If the flywheel is initially at rest and the
Consider the spinning disc shown in Figure 12.34, in which, a spinning conical shaft rises up into the opening in the center of the disc, and the disc begins to spin. Suppose the disc's rotational inertia is \(I_{\mathrm{d}}\), that of the shaft is \(I_{\mathrm{s}}\), and the shaft's initial
As you accelerate from rest on a bicycle, how does the magnitude of the force of friction exerted by the road surface on the rear wheel compare with the magnitude of the force of friction exerted by the road surface on the front wheel? Ignore air resistance, assume both wheels have the same inertia
A solid cylindrical object of inertia \(m\), rotational inertia \(I\), and radius \(R\) rolls down a ramp that makes an angle \(\theta\) with the horizontal. By how much does the cylinder's energy increase if it is released from rest and its center of mass drops a vertical distance \(h\) ?
A cannon launches two shells at the same speed, one at \(55^{\circ}\) above horizontal and one at \(35^{\circ}\) above horizontal. Which shell, if either, has the longer range? Which shell, if either, is in the air longer? Assume level ground and ignore air resistance.
Plot the range of a projectile as a function of the launch angle above horizontal.
A ball is thrown at an angle of \(30^{\circ}\) above the horizontal at a speed of \(30 \mathrm{~m} / \mathrm{s}\). Write the ball's velocity in terms of rectangular unit vectors.
What is the difference between leading zeros and trailing zeros? Which ones are considered significant digits?
Explain the difference between number of digits, number of decimal places, and number of significant digits in a numerical value. Illustrate your explanation using the number 0.03720 .
What is the simplest way to convert a quantity given in one unit to the same quantity given in a different unit?
What concept does density represent?
What are the seven SI base units and the physical quantities they represent?
Make an order-of-magnitude estimate of the mass of earth in kilograms.
What two pieces of information are necessary to express any physical quantity?
(a) Using what you know about the diameters of atoms from Section 1.3, estimate the length of one side of a cube made up of \(1 \mathrm{~mol}\) of closely packed carbon atoms. (b) The mass density of graphite (a form of carbon) is \(2.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\). By how much
What principle that relates events depends on the arrow of time? State this principle, and briefly explain what it means.
Why is the ratio on the left in Eq. 1.5 not suitable for converting inches to millimeters? 1 in. 25.4 mm 25.4 mm 1 or 1 (1.5) 1 in.
What does the phrase arrow of time mean?
Use prefixes from Table 1.3 to remove either all or almost all of the zeros in each expression. (a) \(\ell=150,000,000 \mathrm{~m},(b) t=0.000000000012 \mathrm{~s},(c) 1200 \mathrm{~km} / \mathrm{s}\), (d) \(2300 \mathrm{~kg}\). Table 1.3 SI prefixes 10" 10 Prefix Abbreviation 10" Prefix
Physicists study phenomena that extend over what range of sizes? Over what range of time intervals?
A single chemical reaction takes about \(10^{-13} \mathrm{~s}\). What order of magnitude is the number of sequential chemical reactions that could take place during a physics class?
In physics, what is the definition of universe?
(a) State a possible cause for the following events: (i) The light goes out in your room; (ii) you hear a loud, rumbling noise; (iii) a check you wrote at the bookstore bounces. (b) Could any of the causes you named have occurred after their associated event? (c) Describe how you feel when you
A planar shape is formed from four straight-line segments of length \(\ell\) that do not cross. One end of segment 1 is connected to one end of segment 2 such that they make a \(30^{\circ}\) angle. The other end of segment 2 is connected to one end of segment 3 such that they also make a
Assume the radiation from the cesium atom mentioned in Problem 26 moves at the speed of light. How many meters does the radiation travel in the length of time corresponding to the period calculated in Problem 26?Data From Problem 26:A second is defined as the duration of \(9.19 \times 10^{9}\)
What are the benefits of making order-of-magnitude estimates?
When checking calculations, what do the letters in the acronym VENUS stand for?
Summarize the four-stage problem-solving procedure used in this book.
How many significant digits are appropriate in expressing the result of a multiplication or division?
The Sun is approximately 93 million miles from Earth. (a) What is this distance in millimeters? (b) How many Earths could fit side by side in this distance?
To work an order-of-magnitude problem, you need the value of the mass density of water, but you don't know what that value is. Design either a translation strategy or a division strategy for making an order-of-magnitude estimate of this mass density.
What is the purpose of the Concepts part of each chapter in the Principles volume of this book? What is the purpose of the Quantitative Tools part of each Principles chapter?
(a) Express the circumference of a circle of radius \(R=27.3 \mathrm{~mm}\) with the correct number of significant digits. (b) Let \(a=12.3, b=3.241\), and \(c=55.74\). Compute \(a+b+c\). (c) Let \(m=4.00, n=3.00\), and \(k=7\) (exact). Compute \(f=m^{2} / k\), \(g=n^{2} / k\), and \(f+g\).
When solving physics problems, what are the advantages of making simplified visual representations of the situations?
Which types of geometrical symmetry mentioned in the Principles volume does a sphere have?
Picture a long, straight corridor running east-west, with a water fountain located somewhere along it. Starting from the west end of the corridor, a woman walks a short distance east along the corridor and stops before reaching the water fountain. The distance from her to the fountain is twice the
To what order of magnitude should you round the numbers 2900 and 3100? Explain why your answers are different for the two numbers.
You and your spouse are working out a seating arrangement around a circular table for dinner with John and Mary Jones, Mike and Sylvia Masters, and Bob and Cyndi Ahlers. Mike is not fond of the Ahlers, and Sylvia asked that she not be seated next to John. You would like to alternate men and women
What does expressing a value to an order of magnitude mean? Why would we express values in this way?
At room temperature and atmospheric pressure, 1 mol of helium gas has a volume of 24 .5 x 10-3 m3 . The same amount of liquid helium has a volume of 32 .0 x10-6 m3. What are the number and mass densities of(a) the gaseous helium and(b) the liquid helium? The mass of one helium atom is 6. 647 x
What are two types of symmetry that are demonstrated in the reproducibility of experimental results?
Imagine magnifying each atom in an apple to the size of the apple. What would the diameter of the apple then be?
What does symmetry mean in physics?
Based on the early definition of the meter, one ten-millionth of the distance from the equator to the North Pole, what is Earth's radius?
Describe the difference between the two types of reasoning involved in doing science.
You always store your pencils in a cylindrical case. One day while traveling in the tropics, you discover that the cap, which you have placed back on the case day in, day out for years, doesn't fit over the case. What do you conclude?
Name some skills that are useful in doing science.
After reading this section, reflect on your goals for this course. Write down what you would like to accomplish and why you would like to accomplish this. Once you have done that, turn to the final section of the Principles volume, "Solutions to checkpoints," and compare what you have written with
A battery-operated portable music player fails to play when it is turned on. Develop a hypothesis explaining why it fails to play, and then make a prediction that permits you to test your hypothesis. Describe two possible outcomes of the test and what you conclude from the outcomes.
In Exercise 1.2, each of the conclusions drawn from the two possible outcomes contains a hidden assumption. What are the hidden assumptions?Data From Exercise 1.2:A battery-operated portable music player fails to play when it is turned on. Develop a hypothesis explaining why it fails to play, and
Briefly describe the scientific method and what it involves.

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