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physics
college physics 2nd

College Physics 2nd Edition OpenStax - Solutions

Determine the amount of time it takes for X-rays of frequency 3 x 1018 Hz to travel (a) 1 mm and (b) 1 cm.
Some radar systems detect the size and shape of objects such as aircraft and geological terrain. Approximately what is the smallest observable detail utilizing 500-MHz radar?
A radar used to detect the presence of aircraft receives a pulse that has reflected off an object 6 x 10-5 s after it was transmitted. What is the distance from the radar station to the reflecting object?
Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency 1.20 x 1015 Hz?
Electromagnetic radiation having a 15.0- μm wavelength is classified as infrared radiation. What is its frequency?
Combing your hair leads to excess electrons on the comb. How fast would you have to move the comb up and down to produce red light?
Find the frequency range of visible light, given that it encompasses wavelengths from 380 to 760 nm.
(a) Calculate the range of wavelengths for AM radio given its frequency range is 540 to 1600 kHz. (b) Do the same for the FM frequency range of 88.0 to 108 MHz.
(a) Two microwave frequencies are authorized for use in microwave ovens: 900 and 2560 MHz. Calculate the wavelength of each.(b) Which frequency would produce smaller hot spots in foods due to interference effects?
Verify the units obtained for magnetic field strength B in Example 24.1 (using the equation B = E/c) are in fact teslas (T).Data given in Example 24.1What is the maximum strength of the B-field in an electromagnetic wave that has a maximum E-field strength of 1000 V/m?StrategyTo find the -field
The maximum magnetic field strength of an electromagnetic field is 5 x 10-6 T. Calculate the maximum electric field strength if the wave is traveling in a medium in which the speed of the wave is 0.75c.
Figure 22.59 shows a long straight wire just touching a loop carrying a current I1. Both lie in the same plane.(a) What direction must the current I2 in the straight wire have to create a field at the center of the loop in the direction opposite to that created by the loop?(b) What is the ratio of
Measurements affect the system being measured, such as the current loop in Figure 22.53. (a) Estimate the field the loop creates by calculating the field at the center of a circular loop 20.0 cm in diameter carrying 5.00 A.(b) What is the smallest field strength this loop can be used to measure,
How far from the starter cable of a car, carrying 150 A, must you be to experience a field less than the Earth's (5.00 x 10-5 T)? Assume a long straight wire carries the current. (In practice, the body of your car shields the dashboard compass.)
What current is needed in the solenoid described in Exercise 22.58 to produce a magnetic field 104 times the Earth's magnetic field of 5.00 x 10-5 T?Data from Example 22.58 Indicate whether the magnetic field created in each of the three situations shown in Figure 22.56 is into or out of the page
How strong is the magnetic field inside a solenoid with 10,000 turns per meter that carries 20.0 A?
Nonnuclear submarines use batteries for power when submerged. (a) Find the magnetic field 50.0 cm from a straight wire carrying 1200 A from the batteries to the drive mechanism of a submarine.(b) What is the field if the wires to and from the drive mechanism are side by side? (c) Discuss the
Inside a motor, 30.0 A passes through a 250-turn circular loop that is 10.0 cm in radius. What is the magnetic field strength created at its center?
Solve Example 21.5, but use loop abcdefgha instead of loop akledcba. Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.Data given in Example 21.5Find the currents flowing in the circuit in Figure 21.25.StrategyThis circuit is sufficiently
The hot resistance of a flashlight bulb is 2.30Ω, and it is run by a 1.58-V alkaline cell having a 0.100-Ω internal resistance.(a) What current flows?(b) Calculate the power supplied to the bulb using I2 Rbulb.(c) Is this power the same as calculated using V2 Rbulb
What are the largest and smallest resistances you can obtain by connecting a 36.0-Ω, a 50.0-Ω, and a 700-Ω resistor together?
What is the approximate sound intensity level in decibels of a 600-Hz tone if it has a loudness of 20 phons? If it has a loudness of 70 phons?
Apply the loop rule to loop aedcba in Figure 21.25. R₂ 2.5 Ω· a 12 12 13 E₁ = 18 V C F b h 1₁ 13 R₁ ww 6.0 92 E2 = 45 V 0.5 Ω + 12 0.5 Ω d 13 f 1₂ e R3 1.592
Apply the loop rule to loop abcdefghija in Figure 21.50. R₁ 5.0 Ω a R₂ 78 Ω b 14 Ta Έ, = 24.0 V im 0.10 Ω Έγ = 48.00 k 12 0.50 Ω Ω Έg = 60 V M 10.05 Ω h | R₂ Μ 40 Ω Ω R₂ - 20 Ω Θ TA 70.20 Ω g 2. = 36.0 V
Suppose the voltage output of the battery in Figure 21.3 is 12.0 V, and the resistances are R1 = 1.00 Ω, R2 = 6.00 Ω, and R3 = 13.0 Ω.(a) What is the total resistance?(b) Find the current.(c) Calculate the voltage drop in each resistor, and show these add to equal the voltage output of the
In this problem, you will verify statements made at the end of the power losses for Example 20.10. (a) What current is needed to transmit 100 MW of power at a voltage of 25.0 kV? (b) Find the power loss in a 1.00 - Ω transmission line. (c) What percent loss does this represent?Data given in
Find the total capacitance of the combination of capacitors shown in Figure 19.21. Assume the capacitances in Figure 19.21 are known to three decimal places (C1 = 1.000 μF, C2 = 5.000 μF, and C3 = 8.000 μF), and round your answer to three decimal places.StrategyTo find the total capacitance, we
Critical Thinking A frictionless circular track with a diameter of 4.00 m has two spheres of 10.0 kg each anchored very near it. The track is oriented with a diameter along the x-axis. The anchored spheres are just outside the track. One of the anchored spheres is just left of the origin at a
(a) Using the symmetry of the arrangement, determine the direction of the force on q in the figure below, given that qa = qb=+7.50 μC and qc = qd = -7.50 μC. (b) Calculate the magnitude of the force on the charge q, given that the square is 10.0 cm on a side and q = 2.00 μC. qa O qc Oq ab O qd
Figure 18.43 shows the electric field lines near two charges q1 and q2. (a) What is the ratio of their magnitudes?(b) Sketch the electric field lines a long distance from the charges shown in the figure.
A dolphin is able to tell in the dark that the ultrasound echoes received from two sharks come from two different objects only if the sharks are separated by 3.50 m, one being that much farther away than the other. (a) If the ultrasound has a frequency of 100 kHz, show this ability is not limited
If two identical waves are spatially separated, each having an intensity of 1.00 W/m2, interfere perfectly constructively in a particular location, what is the intensity of the wave at this particular location?StrategyWe know from Superposition and Interference that when two identical waves, which
The average intensity of sunlight on Earth's surface is about 700 W/m2. (a) Calculate the amount of energy that falls on a solar collector having an area of 0.500 m2 in 4.00 h.(b) What intensity would such sunlight have if concentrated by a magnifying glass onto an area 200 times smaller than its
Suppose you pour 0.250 kg of 20.0°C water (about a cup) into a 0.500-kg aluminum pan off the stove with a temperature of 150°C. Assume that the pan is placed on an insulated pad and that a negligible amount of water boils off. What is the temperature when the water and pan reach thermal
A 0.500 kg aluminum pan on a stove is used to heat 0.250 liters of water from 20.0°C to 80.0°C. (a) How much heat is required? What percentage of the heat is used to raise the temperature of (b) The pan and (c) The water?StrategyThe pan and the water are always at the same temperature. When
Table 13.5 gives the vapor pressure of water at 20.0°C as 2.33 x 103 Pa. Use the ideal gas law to calculate the density of water vapor in g/m3 that would create a partial pressure equal to this vapor pressure. Compare the result with the saturation vapor density given in the table.StrategyTo solve
Using the law of reflection, explain how powder takes the shine off of a person’s nose. What is the name of the optical effect?
Diffusion by reflection from a rough surface is described in this chapter. Light can also be diffused by refraction. Describe how this occurs in a specific situation, such as light interacting with crushed ice.
Why is the index of refraction always greater than or equal to 1?
Does the fact that the light flash from lightning reaches you before its sound prove that the speed of light is extremely large or simply that it is greater than the speed of sound? Discuss how you could use this effect to get an estimate of the speed of light.
Will light change direction toward or away from the perpendicular when it goes from air to water? Water to glass? Glass to air?
Explain why an object in water always appears to be at a depth shallower than it actually is? Why do people sometimes sustain neck and spinal injuries when diving into unfamiliar ponds or waters?
Why is the front surface of a thermometer curved as shown? 99.0 98.6 ]]]]]]]] 98.0
Explain why a person’s legs appear very short when wading in a pool. Justify your explanation with a ray diagram showing the path of rays from the feet to the eye of an observer who is out of the water.
Suppose light were incident from air onto a material that had a negative index of refraction, say –1.3; where does the refracted light ray go?
A ring with a colorless gemstone is dropped into water. The gemstone becomes invisible when submerged. Can it be a diamond? Explain.
A high-quality diamond may be quite clear and colorless, transmitting all visible wavelengths with little absorption. Explain how it can sparkle with flashes of brilliant color when illuminated by white light.
Is it possible that total internal reflection plays a role in rainbows? Explain in terms of indices of refraction and angles, perhaps referring to Figure 25.46. Some of us have seen the formation of a double rainbow. Is it physically possible to observe a triple rainbow?
The most common type of mirage is an illusion that light from faraway objects is reflected by a pool of water that is not really there. Mirages are generally observed in deserts, when there is a hot layer of air near the ground. Given that the refractive index of air is lower for air at higher
It can be argued that a flat piece of glass, such as in a window, is like a lens with an infinite focal length. If so, where does it form an image? That is, how are di; and d0 related?
You can often see a reflection when looking at a sheet of glass, particularly if it is darker on the other side. Explain why you can often see a double image in such circumstances.
When you focus a camera, you adjust the distance of the lens from the film. If the camera lens acts like a thin lens, why can it not be a fixed distance from the film for both near and distant objects?
A thin lens has two focal points, one on either side, at equal distances from its center, and should behave the same for light entering from either side. Look through your eyeglasses (or those of a friend) backward and forward and comment on whether they are thin lenses.
What are the differences between real and virtual images? How can you tell (by looking) whether an image formed by a single lens or mirror is real or virtual?
Will the focal length of a lens change when it is submerged in water? Explain.
Can you see a virtual image? Can you photograph one? Can one be projected onto a screen with additional lenses or mirrors? Explain your responses.
Is it necessary to project a real image onto a screen for it to exist?
At what distance is an image always located-at d0, di, or f?
Under what circumstances will an image be located at the focal point of a lens or mirror?
What is meant by a negative magnification? What is meant by a magnification that is less than 1 in magnitude?
Can a case 1 image be larger than the object even though its magnification is always negative? Explain.Data from case 1 image
Figure 25.47 shows a light bulb between two mirrors. One mirror produces a beam of light with parallel rays; the other keeps light from escaping without being put into the beam. Where is the filament of the light in relation to the focal point or radius of curvature of each mirror?
Devise an arrangement of mirrors allowing you to see the back of your head. What is the minimum number of mirrors needed for this task?
If you wish to see your entire body in a flat mirror (from head to toe), how tall should the mirror be? Does its size depend upon your distance away from the mirror? Provide a sketch.
It can be argued that a flat mirror has an infinite focal length. If so, where does it form an image? That is, how are di; and d0 related?
Why are diverging mirrors often used for rear-view mirrors in vehicles? What is the main disadvantage of using such a mirror compared with a flat one?
Three ice cubes are used to chill a soda at 20°C with mass msoda = 0.25 kg. The ice is at 0°C and each ice cube has a mass of 6.0 g. Assume that the soda is kept in a foam container so that heat loss can be ignored. Assume the soda has the same heat capacity as water. Find the final temperature
Water is boiling in an aluminum pan placed on an electrical element on a stovetop. The sauce pan has a bottom that is 0.800 cm thick and 14.0 cm in diameter. The boiling water is evaporating at the rate of 1.00 g/s. What is the temperature difference across (through) the bottom of the
A Styrofoam ice box has a total area of 0.950 m2 and walls with an average thickness of 2.50 cm. The box contains ice, water, and canned beverages at 0°C. The inside of the box is kept cold by melting ice. How much ice melts in one day if the ice box is kept in the trunk of a car at
Most houses are not airtight: air goes in and out around doors and windows, through cracks and crevices, following wiring to switches and outlets, and so on. The air in a typical house is completely replaced in less than an hour. Suppose that a moderately-sized house has inside dimensions 12.0m x
The average person produces heat at the rate of about 120 W when at rest. At what rate must water evaporate from the body to get rid of all this energy? (This evaporation might occur when a person is sitting in the shade and surrounding temperatures are the same as skin temperature, eliminating
(a) Suppose there is heat transfer of 40.00 J to a system, while the system does 10.00 J of work. Later, there is heat transfer of 25.00 J out of the system while 4.00 J of work is done on the system. What is the net change in internal energy of the system?(b) What is the change in internal energy
A nuclear power reactor has pressurized water at 300°C. (Higher temperatures are theoretically possible but practically not, due to limitations with materials used in the reactor.) Heat transfer from this water is a complex process (see Figure 15.22). Steam, produced in the steam generator, is
Calculate the total work done in the cyclical process ABCDA shown in Figure 15.12(b) by the following two methods to verify that work equals the area inside the closed loop on the PV diagram. (Take the data in the figure to be precise to three significant figures.)(a) Calculate the work done along
A heat pump used to warm a home must employ a cycle that produces a working fluid at temperatures greater than typical indoor temperature so that heat transfer to the inside can take place. Similarly, it must produce a working fluid at temperatures that are colder than the outdoor temperature so
Spontaneous heat transfer from hot to cold is an irreversible process. Calculate the total change in entropy if 4000 J of heat transfer occurs from a hot reservoir at Th = 600 K(327°C) to a cold reservoir at Tc = 250 K(-23°C), assuming there is no temperature change in either reservoir. (See
(a) Calculate the work output of a Carnot engine operating between temperatures of 600 K and 100 K for 4000 J of heat transfer to the engine.(b) Now suppose that the 4000 J of heat transfer occurs first from the 600 K reservoir to a 250 K reservoir (without doing any work, and this produces the
Find the increase in entropy of 1.00 kg of ice originally at 0°C that is melted to form water at 0°C.StrategyAs before, the change in entropy can be calculated from the definition of ΔS once we find the energy Q needed to melt the ice.
Suppose you toss 100 coins starting with 60 heads and 40 tails, and you get the most likely result, 50 heads and 50 tails. What is the change in entropy?StrategyNoting that the number of microstates is labeled W in Table 15.4 for the 100-coin toss, we can use ΔS = Sf - Si = klnWf - klnWi to
What is the force constant for the suspension system of a car that settles 1.20 cm when an 80.0-kg person gets in?StrategyConsider the car to be in its equilibrium position x = 0 before the person gets in. The car then settles down 1.20 cm, which means it is displaced to a position x = -1.20 x 10-2
One type of BB gun uses a spring-driven plunger to blow the BB from its barrel.(a) Calculate the force constant of its plunger’s spring if you must compress it 0.150 m to drive the 0.0500-kg plunger to a top speed of 20.0 m/s. (b) What force must be exerted to compress the spring?
If the shock absorbers in a car go bad, then the car will oscillate at the least provocation, such as when going over bumps in the road and after stopping (See Figure 16.10). Calculate the frequency and period of these oscillations for such a car if the car’s mass (including its load) is 900 kg
Suppose that a car is 900 kg and has a suspension system that has a force constant k = 6.53 x 104 N/m. The car hits a bump and bounces with an amplitude of 0.100 m. What is its maximum vertical velocity if you assume no damping occurs?StrategyWe can use the expression for vmax given in to
Damping oscillatory motion is important in many systems, and the ability to control the damping is even more so. This is generally attained using non-conservative forces such as the friction between surfaces, and viscosity for objects moving through fluids. The following example considers friction.
Calculate the wave velocity of the ocean wave in Figure 16.28 if the distance between wave crests is 10.0 m and the time for a sea gull to bob up and down is 5.00 s.StrategyWe are asked to find vw. The given information tells us that λ= 10.0 m and T = 5.00 s. Therefore, we can use vw =λ/T to
Scouts at a camp shake the rope bridge they have just crossed and observe the wave crests to be 8.00 m apart. If they shake the bridge twice per second, what is the propagation speed of the waves?
What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at 0.800 m/s?
Radio waves transmitted through space at 3.00 x 108 m/s by the Voyager spacecraft have a of 0.120 m. What is their frequency? wavelength
Energy from the Sun arrives at the top of the Earth's atmosphere with an intensity of 1.30 kW/m2. How long does it take for 1.8 x 109 J to arrive on an area of 1.00 m2?
Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in 30.0°C air. (Assume that the frequency values are accurate to two significant figures.)StrategyTo find wavelength from frequency, we can use Uw = fλ.
Calculate the sound intensity level in decibels for a sound wave traveling in air at 0°C and having a pressure amplitude of 0.656 Pa.StrategyWe are given Δp, so we can calculate I using the equation I = (Δp)2/(2pvw )2 . Using I, we can calculate β straight from its definition in β(dB)= 10
Suppose a train that has a 150-Hz horn is moving at 35.0 m/s in still air on a day when the speed of sound is 340 m/s.(a) What frequencies are observed by a stationary person at the side of the tracks as the train approaches and after it passes?(b) What frequency is observed by the train’s
Show that if one sound is twice as intense as another, it has a sound level about 3 dB higher.StrategyYou are given that the ratio of two intensities is 2 to 1, and are then asked to find the difference in their sound levelsin decibels. You can solve this problem using of the properties of
(a) What length should a tube closed at one end have on a day when the air temperature, is 22.0°C, if its fundamental frequency is to be 128 Hz (C below middle C)?(b) What is the frequency of its fourth overtone?StrategyThe length L can be found from the relationship in but we will first need to
(a) What is the loudness in phons of a 100-Hz sound that has an intensity level of 80 dB?(b) What is the intensity level in decibels of a 4000-Hz sound having a loudness of 70 phons? (c) At what intensity level will an 8000-Hz sound have the same loudness as a 200-Hz sound at 60 dB?Strategy for
(a) Using the values for density and the speed of ultrasound given in Table 17.5, show that the acoustic impedance of fat tissue is indeed 1.34 x 106 kg/(m2.s).(b) Calculate the intensity reflection coefficient of ultrasound when going from fat to muscle tissue.Strategy for (a) The acoustic
Ultrasound that has a frequency of 2.50 MHz is sent toward blood in an artery that is moving toward the source at 20.0 cm/s, as illustrated in Figure 17.46. Use the speed of sound in human tissue as 1540 m/s. (Assume that the frequency of 2.50 MHz is accurate to seven significant figures.)a. What
(a) If a submarine’s sonar can measure echo times with a precision of 0.0100 s, what is the smallest difference in distances it can detect? (Assume that the submarine is in the ocean, not in fresh water.)(b) Discuss the limits this time resolution imposes on the ability of the sonar system to
Suppose a bat uses sound echoes to locate its insect prey, 3.00 m away. (See Figure 17.9.)(a) Calculate the echo times for temperatures of 5.00°C and 35.0°C. (b) What percent uncertainty does this cause for the bat in locating the insect?(c) Discuss the significance of this uncertainty and
(a) What is the fundamental frequency of a 0.672-m-long tube, open at both ends, on a day when the speed of sound is 344 m/s? (b) What is the frequency of its second harmonic?

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