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university physics

University Physics with Modern Physics 13th edition Hugh D. Young, Roger A. Freedman, A. Lewis Ford - Solutions

What is the difference between tangential and radial acceleration for a point on a rotating body?
In Fig. Q9.4, all points on the chain have the same linear speed. Is the magnitude of the linear acceleration also the same for all points on the chain? How are the angular accelerations of the two sprockets related? Explain.Figure Q9.4 Wrear rear front Rear sprocket Wfront Front sprocket
A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s. How much time elapses until the bowling pin returns to the juggler’s hand?
You throw a glob of putty straight up toward the ceiling, which is 3.60 m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.50 m/s.(a) What is the speed of the putty just before it strikes the ceiling?(b) How much time from when it leaves
A tennis ball on Mars, where the acceleration due to gravity is 0.379g and air resistance is negligible, is hit directly upward and returns to the same level 8.5 s later.(a) How high above its original point did the ball go?(b) How fast was it moving just after it was hit?(c) Sketch graphs of the
You throw a small rock straight up from the edge of a highway bridge that crosses a river. The rock passes you on its way down, 6.00 s after it was thrown. What is the speed of the rock just before it reaches the water 28.0 m below the point where the rock left your hand? Ignore air resistance.
A small object moves along the x-axis with acceleration ax(t) = -(0.0320 m/s3)(15.0 s - t). At t = 0 the object is at x = -14.0 m and has velocity v0x = 8.00 m/s. What is the x-coordinate of the object when t = 10.0 s?
A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = (2.80 m/s3)t, where the +y-direction is upward.(a) What is the height of the rocket above the surface of the earth at t = 10.0
A brick is dropped from the roof of a tall building. After it has been falling for a few seconds, it falls 40.0 m in a 1.00-s time interval. What distance will it fall during the next 1.00 s? Ignore air resistance.
You are standing at rest at a bus stop. A bus moving at a constant speed of 5.00 m/s passes you. When the rear of the bus is 12.0 m past you, you realize that it is your bus, so you start to run toward it with a constant acceleration of 0.960 m/s2. How far would you have to run before you catch up
During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth’s surface and is to reach a maximum height of 960 m above the earth’s surface. The rocket’s engines give the rocket an upward
An object is moving along the x-axis. At t = 0 it has velocity v0x = 20.0 m/s. Starting at time t = 0 it has acceleration ax = -Ct, where C has units of m/s3.(a) What is the value of C if the object stops in 8.00 s after t = 0?(b) For the value of C calculated in part (a), how far does the object
In your physics lab you release a small glider from rest at various points on a long, frictionless air track that is inclined at an angle Î¸ above the horizontal. With an electronic photocell, you measure the time t it takes the glider to slide a distance x from the release point to the
In a physics lab experiment, you release a small steel ball at various heights above the ground and measure the ball’s speed just before it strikes the ground. You plot your data on a graph that has the release height (in meters) on the vertical axis and the square of the final speed (in m2/s2)
A model car starts from rest and travels in a straight line. A smartphone mounted on the car has an app that transmits the magnitude of the car’s acceleration (measured by an accelerometer) every second. The results are given in the table:Time (s) ............................... Acceleration
Redraw Fig. 3.11a if aÌ…(vector) is antiparallel to vÌ…1(vector). Does the particle move in a straight line? What happens to its speed?figure 3.11a Δύ b- + Δύ
A book slides off a horizontal tabletop. As it leaves the table’s edge, the book has a horizontal velocity of magnitude v0. The book strikes the floor in time t. If the initial velocity of the book is doubled to 2v0, what happens to(a) The time the book is in the air,(b) The horizontal distance
At the instant that you fire a bullet horizontally from a rifle, you drop a bullet from the height of the gun barrel. If there is no air resistance, which bullet hits the level ground first? Explain.
A package falls out of an airplane that is flying in a straight line at a constant altitude and speed. If you ignore air resistance, what would be the path of the package as observed by the pilot? As observed by a person on the ground?
Sketch the six graphs of the x- and y-components of position, velocity, and acceleration versus time for projectile motion with x0 = y0 = 0 and 0 < α0 < 90°.
You are a mechanical engineer working for a manufacturing company. Two forces, F̅1(vector) and F̅2(vector), act on a component part of a piece of equipment. Your boss asked you to find the magnitude of the larger of these two forces. You can vary the angle between F̅1 and F̅2(vector) from
You are a team leader at a pharmaceutical company. Several technicians are preparing samples, and you want to compare the densities of the samples (density = mass>volume) by using the mass and volume values they have reported. Unfortunately, you did not specify what units to use. The technicians
You are lost at night in a large, open field. Your GPS tells you that you are 122.0 m from your truck, in a direction 58.0o east of south. You walk 72.0 m due west along a ditch. How much farther, and in what direction, must you walk to reach your truck?
As a test of orienteering skills, your physics class holds a contest in a large, open field. Each contestant is told to travel 20.8 m due north from the starting point, then 38.0 m due east, and finally 18.0 m in the direction 33.0o west of south. After the specified displacements, a contestant
You leave the airport in College Station and fly 23.0 km in a direction 34.0o south of east. You then fly 46.0 km due north. How far and in what direction must you then fly to reach a private landing strip that is 32.0 km due west of the College Station airport?
You are given two vectors Let counterclockwiseangles be positive.(a) What angle does A(Vector) make with the + x-axis? (b) What angle does B(Vector) make with the + x-axis? (c) Vector C(Vector) is the sum of A(Vector) and B(Vector), so C(Vector) A(Vector) B(Vector). What angle does
If A̅(Vector) = 0 for a vector in the xy-plane, does it follow that Ax = -Ay? What can you say about Ax and Ay?
(a) If A̅(Vector) ∙ B̅(Vector) = 0 does it necessarily follow that A = 0 or B = 0? Explain.(b) If A̅(Vector) × B̅(Vector) = 0, does it necessarily follow that A = 0 or B = 0? Explain.
Show that, no matter what A̅(Vector) and B̅(Vector )are, A̅(Vector) ∙ { A̅(Vector) × B̅(Vector)}= 0.
Consider the vector productsandGive an example that illustrates the general rule that these two vector products do not have the same magnitude or direction. Can you choose vectors AÌ…(Vector) BÌ…(Vector) and CÌ…(Vector)such that these two vector products are
Which of the following are legitimate mathematical operations:(a)(b)(c)(d)(e) A· (B – Ċ) (A - В) х С;
Let A̅(Vector) represent any nonzero vector. Why is A̅(Vector)/A a unit vector, and what is its direction? If θ is the angle that A̅(Vector) makes with the +x-axis, explain why (A̅(Vector) /A) ∙ î is called the direction cosine for that axis.
What does A̅(Vector) ∙ A̅(Vector), the scalar product of a vector with itself, give? What about A̅(Vector) × A̅(Vector), the vector product of a vector with itself?
If A̅(Vector) and B̅(Vector) are nonzero vectors, is it possible for both A̅(Vector) ∙ B̅(Vector) and A̅(Vector) × B̅(Vector) to be zero? Explain.
Express each approximation of p to six significant figures:(a) 22/7 and(b) 355/113.(c) Are these approximations accurate to that precision?
(a) Does it make sense to say that a vector is negative? Why?(b) Does it make sense to say that one vector is the negative of another? Why? Does your answer here contradict what you said in part (a)?
Can you find a vector quantity that has a magnitude of zero but components that are not zero? Explain. Can the magnitude of a vector be less than the magnitude of any of its components? Explain.
Air traffic controllers give instructions called “vectors” to tell airline pilots in which direction they are to fly. If these are the only instructions given, is the name “vector” used correctly? Why or why not?
The “direction of time” is said to proceed from past to future. Does this mean that time is a vector quantity? Explain.
Can you find two vectors with different lengths that have a vector sum of zero? What length restrictions are required for three vectors to have a vector sum of zero? Explain.
A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side? When she makes one complete circle around the track? Explain.
Is the vector (î + ĵ + k̂) a unit vector? Is the vector (3.0î - 2.0ĵ) a unit vector? Justify your answers.
Three archers each fire four arrows at a target. Joe’s four arrows hit at points 10 cm above, 10 cm below, 10 cm to the left, and 10 cm to the right of the center of the target. All four of Moe’s arrows hit within 1 cm of a point 20 cm from the center, and Flo’s four arrows hit within 1 cm of
What are the units of volume? Suppose another student tells you that a cylinder of radius r and height h has volume given by πr3h. Explain why this cannot be right.
The quantity π = 3.14159.... is a number with no dimensions, since it is a ratio of two lengths. Describe two or three other geometrical or physical quantities that are dimensionless.
Describe how you could measure the thickness of a sheet of paper with an ordinary ruler.
What physical phenomena (other than a pendulum or cesium clock) could you use to define a time standard?
The U.S. National Institute of Standards and Technology (NIST) maintains several accurate copies of the international standard kilogram. Even after careful cleaning, these national standard kilograms are gaining mass at an average rate of about 1 µg/y (y = year) when compared every 10 years or so
What is your height in centimeters? What is your weight in newtons?
Suppose you are asked to compute the tangent of 5.00 meters. Is this possible? Why or why not?
How many correct experiments do we need to disprove a theory? How many do we need to prove a theory? Explain.
On October 15, 2001, a planet was discovered orbiting around the star HD 68988. Its orbital distance was measured to be 10.5 million kilometers from the center of the star, and its orbital period was estimated at 6.3 days. What is the mass of HD 68988? Express your answer in kilograms and in terms
A parallel-plate capacitor is made from two plates 12.0 cm on each side and 4.50 mm apart. Half of the space between these plates contains only air, but the other half is filled with Plexiglas®of dielectric constant 3.40 (Fig. P24.72).An 18.0-V battery is connected across the plates. (a)
You are working on an electronics project requiring a variety of capacitors, but you have only a large supply of 100-nF capacitors available. Show how you can connect these capacitors to produce each of the following equivalent capacitances: (a) 50 nF;(b) 450 nF;(c) 25 nF;(d) 75 nF.
Electric eels and electric fish generate large potential differences that are used to stun enemies and prey. These potentials are produced by cells that each can generate 0.10 V. We can plausibly model such cells as charged capacitors.(a) How should these cells be connected (in series or in
A parallel-plate air capacitor is to store charge of magnitude 240.0 pC on each plate when the potential difference between the plates is 42.0 V.(a) If the area of each plate is 6.80 cm2, what is the separation between the plates? (b) If the separation between the two plates is double the
In a certain region of space, the magnetic field is not uniform. The magnetic field BÌ… has both a z-component and a component that points radially away from or toward the z-axis. The z-component is given by Bz(Z) = Î²z, where Î² is a positive constant. The radial
The largest cyclotron in the United States is the Tevatronat Fermilab, near Chicago, Illinois. It is called a Tevatron because it can accelerate particles to energies in the TeV range: 1 tera-eV = 1012 eV. Its circumference is 6.4 km, and it currently can produce a maximum energy of 2.0 TeV. In a
The 20.0 cm x 35.0 cm rectangular circuit shown in Fig. E27.45 is hinged along side ab. It carries a clockwise 5.00-A current and is located in a uni-form 1.20-T magnetic field oriented perpendicular to two of its sides, as shown. (a) Draw a clear diagram showing the direction of the force
A straight, 2.5-m wire carries a typical household current of 1.5 A (in one direction) at a location where the earth’s magnetic field is 0.55 gauss from south to north. Find the magnitude and direction of the force that our planet’s magnetic field exerts on this wire if is oriented so that the
A 10.0-cm-long solenoid of diameter 0.400 cm is wound uniformly with 800 turns. A second coil with 50 turns is wound around the solenoid at its center. What is the mutual inductance of the combination of the two coils?
A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop oat the instant
One practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. The coil is initially held with its plane perpendicular to a magnetic field. The coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field.(a)
A single loop of wire with an area of 0.0900 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. (a) What emf is induced in this loop? (b) If the loop has a resistance of
A flat, round iron ring 5.00 cm in diameter has a cur-rent running through it that produces a magnetic field of 75.4 μT at its center. This ring is placed in a uniform external magnetic field of 0.375 T. What is the maximum torque the external field can exert on the ring? Show how the ring should
Two insulated wires perpendicular to each other in the same plane carry currents as shown in Fig. E28.29. Find the magnitude of the net magnetic field these wires produce at points P and Q if the 10.0 A-current is (a) To the right(b) To the left. Figure E28.29 12 A 15 cm 10 A 8.0 (a) > (b) cm
Currents in dc transmission lines can be 100 A or more. Some people have expressed concern that the electromagnetic fields (EMFs) from such lines near their homes could cause health dangers. For a line with current 150 A and at a height of 8.0 m above the ground, what magnetic field does the line
Certain bacteria (such as Aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. If a transmission line carrying 100 A is laid underwater, at what range of distances
The body contains many small currents caused by the motion of ions in the organs and cells. Measurements of the magnetic field around the chest due to currents in the heart give values of about 10 μG.Although the actual currents are rather complicated, we can gain a rough understanding of their
A short current element dt = (0.500 mm) ĵ carries a current of 8.20 A in the same direction as dI. Point P is located at r̅ = |(–0.730 m) î + (0.390 m) k̂. Use unit vectors to express the magnetic field at P produced by this current element.
An inductor with L = 9.50 mH is connected across an ac source that has voltage amplitude 45.0 V.(a) What is the phase angle ϕ for the source voltage relative to the current? Does the source voltage lag or lead the current?(b) What value for the frequency of the source results in a current
A capacitor is connected across an ac source that has volt-age amplitude 60.0 V and frequency 80.0 Hz. (a) What is the phase angle ϕ for the source voltage relative to the current? Does the source voltage lag or lead the current?(b) What is the capacitance C of the capacitor if the current
You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?
A 84.0-nF capacitor is charged to 12.0 V, then disconnected from the power supply and connected in series with a coil that has L = 0.0420 H and negligible resistance. At an instant when the charge on the capacitor is 0.650 μC, what is the magnitude of the current in the inductor and what is the
(a) Take first and second derivatives with respect to time of q given in Eq. (30.28), and show that it is a solution of Eq (30.27).(b) At t = 0 the switch shown in Fig. 30.17 is thrown so that it connects points d and a; at this time, q = Q and i = dq/dt = 0. Show that the constants Ï•
In a proton accelerator used in elementary particle physics experiments, the trajectories of protons are controlled by bending magnets that produce a magnetic field of 4.80 T. What is the magnetic-field energy in a 10.0-cm2 volume of space where B = 4.80 T?
A long, straight solenoid has 800 turns. When the current in the solenoid is 2.90 A, the average flux through each turn of the solenoid is 3.25 × 10-3 Wb. What must be the magnitude of the rate of change of the current in order for the self-induced emf to equal 7.50 mV?
A 2.50-mH toroidal solenoid has an average radius of 6.00 cm and a cross-sectional area of 2.00 cm2.(a) How many coils does it have?(b) At what rate must the current through it change so that a potential difference of 2.00 V is developed across its ends?
Many biologically important molecules are optically active. When linearly polarized light traverses a solution of compounds containing these molecules, its plane of polarization is rotated. Some compounds rotate the polarization clockwise; others rotate the polarization counterclockwise. The amount
A ray of light traveling in a block of glass (n = 1.52) is incident on the top surface at an angle of 57.2° with respect to the normal in the glass. If a layer of oil is placed on the top surface of the glass, the ray is totally reflected. What is the maximum possible index of refraction of the
Light of original intensity l0passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.32. You want to adjust the angle Ï• so that the intensity at point P is equal to l0/10.(a) If the original light is unpolarized, what should Ï•
(a) At what angle above the horizontal is the sun if sun-light reflected from the surface of a calm lake is completely polarized?(b) What is the plane of the electric-field vector in the reflected light?
Unpolarized light with intensity l0 is incident on two polarizing filters. The axis of the first filter makes an angle of 60.0° with the vertical, and the axis of the second filter is horizontal. What is the intensity of the light after it has passed through the second filter?
A narrow beam of white light strikes one face of a slab of silicate flint glass. The light is traveling parallel to the two adjoining faces, as shown in Fig. E33.25. For the transmitted light inside the glass, through what angle ˆ†Î¸ is the portion of the visible spectrum
A piece of glass with a flat surface is at the bottom of a tank of water. If a ray of light traveling in the glass is incident on the interface with the water at an angle with respect to the normal that is greater than 62.0°, no light is refracted into the water. For smaller angles of incidence,
Light enters a solid pipe made of plastic having an index of refraction of 1.60. The light travels parallel to the upper part of the pipe (Fig. E33.17). You want to cut the face AB so that all the light will reflect back into the pipe after it first strikes that face.(a) What is the largest that
A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of θa = 36.2°, the ray refracted into the water makes an angle of 49.8° with the normal to the
As shown in Fig. E33.11, a layer of water covers a slab of material Xin a beaker. A ray of light traveling upward follows the path indicated. Using the information on the figure, find (a) The index of refraction of material X.(b) The angle the light makes with the normal in the air.
A laser beam shines along the surface of a block of transparent material (see Fig. E33.8.). Half of the beam goes straight to a detector, while the other half travels through the block and then hits the detector. The time delay between the arrival of the two light beams at the detector is 6.25 ns.
The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 380 nm (violet) to 750 nm (red), as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the
The electron in a hydrogen atom can be considered to be in a circular orbit with a radius of 0.0529 nm and a kinetic energy of 13.6 eV. If the electron behaved classically, how much energy would it radiate per second (see Challenge Problem 32.57)? What does this tell you about the use of classical
You want to support a sheet of fireproof paper horizontally, using only a vertical upward beam of light spread uniformly over the sheet. There is no other light on this paper. The sheet measures 22.0 cm by 28.0 cm and has a mass of 1.50 g. (a) If the paper is black and hence absorbs all the
Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina weld the detached portions back into place. In one such procedure, a laser beam has a wavelength of 810 nm and delivers 250 mW of power
He–Ne lasers are often used in physics demonstrations. They produce light of wavelength 633 nm and a power of 0.500 mW spread over a cylindrical beam 1.00 mm in diameter (although these quantities can vary).(a) What is the intensity of this laser beam?(b) What are the maximum values of the
If the eye receives an average intensity greater than 1.0 x 102 W/m2, damage to the retina can occur. This quantity is called the damage thresholdof the retina.(a) What is the largest average power (in mW) that a laser beam 1.5 mm in diameter can have and still be considered safe to view
Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 1012 W) pulses of light that last for an extremely short time (a few nanoseconds). These short pulses scramble the interior of a cell without causing it to explode, as long pulses
If the entire apparatus of Exercise 35.11 (slits, screen, and space in between) is immersed in water, what then is the distance between the second and third dark lines?Exercise 35.11Two slits spaced 0.450 mm apart are placed 75.0 cm from a screen. What is the distance between the second and third
Two identical audio speakers connected to the same amplifier produce in-phase sound waves with a single frequency that can be varied between 300 and 600 Hz. The speed of sound is 340 m/s. You find that where you are standing, you hear minimum-intensity sound.(a) Explain why you hear
Two speakers that are 15.0 m apart produce in-phase sound waves of frequency 250.0 Hz in a room where the speed of sound is 340.0 m/s. A woman starts out at the midpoint between the two speakers. The room’s walls and ceiling are covered with absorbers to eliminate reflections, and she listens
Two small stereo speakers A and B that are 1.40 m a part are sending out sound of wavelength 34 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks so that he is always 1.50 m from speaker B(Fig. E35.1). For what values of xwill the sound

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