Question: The figure shows some light rays reflected
The figure shows some light rays reflected from a small defect in the glass toward the surface of the glass. (a) If θc = 40.00°, what is the index of refraction of the glass? (b) Is there any point above the glass at which a viewer would not be able to see the defect? Explain. 
> A camera uses a 200.0 mm focal length telephoto lens to take pictures from a distance of infinity to as close as 2.0 m. What are the minimum and maximum distances from the lens to the sensor?
> A police car’s radar gun emits microwaves with a frequency of f1 = 7.50 GHz. The beam reflects from a speeding car, which is moving toward the police car at 48.0 m/s with respect to the police car. The speeder’s radar detector detects the microwave at a
> (a) In the diagram, what are the potentials at points b and c? Let V = 0 at infinity. (b) What is the change in electric potential energy if a third charge q3 = +2.00 nC is moved from point b to point c? (If you have done Problem 15, compare your answer
> A beam of electrons is accelerated across a potential of 15 kV before passing through two slits. The electrons form an interference pattern on a screen 2.5 m in front of the slits. The first-order maximum is 8.3 mm from the central maximum. What is the d
> Show that if two thin lenses are close together (s, the distance between the lenses, is negligibly small), the two lenses can be replaced by a single equivalent lens with focal length feq. Find the value of feq in terms of f1 and f2.
> Women often experience back pain when they are pregnant. Suppose a woman's mass before pregnancy is 68 kg and her center of mass when standing is located directly above the hips. By the thirty- fourth week of pregnancy, she has gained 8.0 kg (the combine
> A 75.0 kg skier starts from rest and slides down a 32.0 m frictionless slope that is inclined at an angle of 15.0° with the horizontal. Ignore air resistance. Calculate the work done by gravity on the skier and the work done by the normal force on the sk
> A sound wave with a frequency of 400.0 Hz is incident upon a set of stairs. The reflected waves from the vertical surfaces of adjacent steps interfere destructively. What is the minimum tread depth of a step for this to occur?
> Jamila has a set of reading glasses with focal length +0.50 m. (a) Are the lenses converging or diverging? (b) An object is placed 40.0 cm in front of one of the lenses. Where is the image formed? (c) What is the size of the image relative to the size
> In order to read his book, Stephen uses a pair of reading glasses. When he holds the book at a distance of 25 cm from his eyes, the glasses form an upright image a distance of 52 cm from his eyes. (a) Is this a converging or diverging lens? (b) What is
> An underground explosion sends out both transverse (S waves) and longitudinal (P waves) mechanical wave pulses (seismic waves) through Earth's crust. Suppose the speed of transverse waves is 8.0 km/s and that of longitudinal waves is 10.0 km/s. On one oc
> A light ray reflects from a plane mirror as shown in the figure. What is the angle of deviation δ?
> A relay race is run along a straight-line track of length 300.0 m running south to north. The first runner starts at the south end of the track and passes the baton to a teammate at the north end of the track. The second runner races back to the start li
> A standard “35 mm” slide measures 24.0 mm by 36.0 mm. Suppose a slide projector produces a 60.0 cm by 90.0 cm image of the slide on a screen. The focal length of the lens is 12.0 cm. (a) What is the distance between the slide and the screen? (b) If the
> (a) In the diagram, what are the potentials at points a and b? Let V = 0 at infinity. (b) What is the change in electric potential energy if a third charge q3 = +2.00 nC is moved from point a to point b? (If you have done Problem 14, compare your answer
> An early cyclotron at Cornell University was used from the 1930s to the 1950s to accelerate protons, which would then bombard various nuclei. The cyclotron used a large electromagnet with an iron yoke to produce a uniform magnetic field of 1.3 T over a r
> A loop of wire is connected to a battery and a variable resistor as shown. Two other loops of wire, B and C, are placed inside the large loop and outside the large loop, respectively. As the resistance in the variable resistor is increased, are there cur
> The projector in a movie theater has a lens with a focal length of 29.5 cm. It projects an image of the 70.0 mm wide film onto a screen that is 38.0 m from the projector. (a) How wide is the image on the screen? (b) What kind of lens is used in the pro
> An object that is 6.00 cm tall is placed 40.0 cm in front of a diverging lens. The magnitude of the focal length of the lens is 20.0 cm. Find the image position and size. Is the image real or virtual? Upright or inverted?
> Sketch a ray diagram to show that if an object is placed less than the focal length from a converging lens, the image is virtual and upright.
> Choose two rays in Fig. 23.7 and use them to prove that the angle of incidence is equal to the angle of reflection. [Hint: Choose a wavefront at two different times, one before reflection and one after. The time for light to travel from one wavefront to
> A stereo system whose amplifier can produce 60 W per channel is replaced by one rated 120 W per channel. Would you expect the new stereo to be able to play twice as loudly as the old one? Explain.
> (a) Find the number of water molecules in 1.00 L of water. (b) What fraction of the liter’s volume is occupied by water nuclei?
> The filament of an incandescent lightbulb is made of tungsten. At room temperature of 20.0°C the filament has a resistance of 10.0 Ω. (a) What is the power dissipated in the lightbulb immediately after it is connected to a 120 V emf (when the filament is
> Verify that the SI unit of impulse is the same as the SI unit of momentum.
> Two plane mirrors form a 70.0° angle as shown. For what angle θ is the final ray horizontal?
> (a) Find the equivalent resistance between terminals A and B to replace all of the resistors in the diagram. (b) What current flows through the emf? (c) What is the current through the 4.00 Ω resistor at the bottom?
> Two metal spheres of the same radius R are given charges of equal magnitude and opposite sign. No other charges are nearby. Sketch the electric field lines when the center-to-center distance between the spheres is approximately 3R.
> In a thunderstorm, charge is separated through a complicated mechanism that is ultimately powered by the Sun. A simplified model of the charge in a thundercloud represents the positive charge accumulated at the top and the negative charge at the bottom a
> A spaceship traveling 12.3 km/s relative to Earth sends out an EM pulse with a wavelength of 850.00 nm (as measured by the source). The pulse is reflected from another spaceship that is moving toward the first spaceship at a speed of 24.6 km/s relative t
> A spherical wave (from a point source) reflects from a planar surface. Draw a ray diagram and sketch some wavefronts for the reflected wave.
> At a marine animal park, Alison is looking through a glass window and watching dolphins swim underwater. If the dolphin is swimming directly toward her at 15 m/s, how fast does the dolphin appear to be moving?
> What is the purpose of the gel that is spread over the skin before an ultrasonic imaging procedure? [Hint: The speed of sound in the gel is similar to the speed in the body, while the speed in air is much slower. What happens to a wave at an abrupt chang
> Light travels in a medium with index n1 toward a boundary with another material of index n2 < n1. (a) Which is larger, the critical angle or Brewster's angle? Does the answer depend on the values of n1 and n2 (other than assuming n2 < n1)? (b) What can
> (a) Sunlight reflected from the still surface of a lake is totally polarized when the incident light is at what angle with respect to the horizontal? (b) In what direction is the reflected light polarized? (c) Is any light incident at this angle transm
> Some glasses used for viewing 3D movies are polarized, one lens having a vertical transmission axis and the other horizontal. While standing in line on a winter afternoon for a 3D movie and looking through his glasses at the road surface, Maurice notices
> A 6.0 kg object is at rest on a frictionless surface when it is struck head-on by a 2.0 kg object moving at 10 m/s. If the collision is elastic, what is the speed of the 6.0 kg object after the collision? [Hint: You will need two equations.]
> In an experiment to measure the index of refraction of human skin, it was found that if a beam of unpolarized light was shone on a skin sample from air at an incident angle of 54.7°, the reflected light was completely polarized. What is the index of refr
> What is the index of refraction of the core of an optical fiber if the cladding has n = 1.20 and the critical angle at the core-cladding boundary is 45.0°?
> (a) Find the potential at points a and b in the following diagram for charges Q1 = +2.50 nC and Q2 = −2.50 nC. (b) How much work must be done by an external agent to bring a point charge q from infinity to point b?
> Sketch the shape of the string at t = 1.6 s.
> Light rays from the Sun, which is at an angle of 35° above the western horizon, strike the still surface of a pond. (a) What is the angle of incidence of the Sun's rays on the pond? (b) What is the angle of reflection of the rays that leave the pond su
> Sketch the shape of the string at t = 2.2 s.
> The intensity of sunlight that reaches Earth's atmosphere is 1400 W/m2. What is the intensity of the sunlight that reaches Jupiter? Jupiter is 5.2 times as far from the Sun as Earth. [Hint: Treat the Sun as an isotropic source of light waves.]
> A motor scooter travels east at a speed of 12 m/s. The driver then reverses direction and heads west at 15 m/s. What is the change in velocity of the scooter? Give magnitude and direction.
> Compare the orbital radii of the He+ and H atoms for levels of equal energy (not the same value of n). Can you draw a general conclusion from your results?
> The radioactive decay of 238U produces alpha particles with a kinetic energy of 4.17 MeV. (a) At what speed do these alpha particles move? (b) Put yourself in the place of Rutherford and Geiger. You know that alpha particles are positively charged (fro
> (a) Using the result of Problem 26, calculate the numerical aperture of a fiber-optic cable whose cladding and core have indices of refraction 1.40 and 1.62, respectively. (b) Light enters the fiber from a balloon of saline solution (n = 1.35), which is
> A useful measure of the quality of a fiber-optic cable such as those used in endoscopes and other medical equipment is the numerical aperture. The larger the numerical aperture, the more light will be carried by the fiber. If light is incident on the fib
> Is there a critical angle for a light ray coming from a medium with an index of refraction 1.2 and incident on a medium that has an index of refraction 1.4? If so, what is the critical angle that allows total internal reflection in the first medium?
> (a) Find the electric potential at points a and b for charges of +4.2 nC and −6.4 nC located as shown in the following figure. (b) What is the potential difference ΔV for a trip from b to a? (c) How much work must be done
> The prism in the figure is made of crown glass. Its index of refraction ranges from 1.517 for the longest visible wavelengths to 1.538 for the shortest. Find the range of refraction angles for the light transmitted into air through the right side of the
> In Figure 23.11, a coin is right up against the far edge of the mug. In picture (a) the coin is just hidden from view and in picture (b) we can almost see the whole coin. If the mug is 6.5 cm in diameter and 8.9 cm tall, what is the diameter of the coi
> Why is it that your own voice sounds strange to you when you hear it played back on a tape recorder, but your friends all agree that it is just what your voice sounds like? [Hint: Consider the medium through which the sound wave travels when you usually
> A glass lens has a scratch-resistant plastic coating on it. The speed of light in the glass is 0.67c, and the speed of light in the coating is 0.80c. A ray of light in the coating is incident on the plastic-glass boundary at an angle of 12.0° with respec
> In a certain region of space, there is a uniform electric field V/m directed due east and a uniform magnetic field / also directed due east. What is the electromagnetic force on an electron moving due south at 5.0 × 106 m/s?
> The Wheatstone bridge is a circuit used to measure unknown resistances. The bridge in the figure is balanced—no current flows through the galvanometer G (a sensitive detector of current whose operation is based on magnetic forces). (a) What is the unkno
> A bicycle travels 3.2 km due east in 0.10 h, then 4.8 km at 15.0° east of north in 0.15 h, and finally another 3.2 km due east in 0.10 h to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip?
> In a synchrotron, charged particles are accelerated as they travel around in circles; in a linear accelerator they move in a straight line. What are some of the advantages and disadvantages of each design?
> In Fig. 20.6, side 3 of the rectangular coil in the electric generator rotates about the axis at constant angular speed m. The figure with this problem shows side 3 by itself. (a) First consider the right half of side 3. Although the speed of the wire d
> A beam of light in air is incident on a stack of four flat transparent materials with indices of refraction 1.20, 1.40, 1.32, and 1.28. If the angle of incidence for the beam on the first of the four materials is 60.0°, what angle does the beam make with
> A 58 kg astronaut is in space, far from any objects that would exert a significant gravitational force on him. He would like to move toward his spaceship, but his jet pack is not functioning. He throws a 720 g socket wrench with a velocity of 5.0 m/s in
> A uniform solid cylinder rolls without slipping down an incline. A hole is drilled through the cylinder along its axis. The radius of the hole is 0.50 times the (outer) radius of the cylinder. (a) Does the cylinder take more or less time to roll down th
> At a point due east of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?
> A sign along the road in Tompkins County reads, “State Law: Noise Limit, 90 decibels.” If you were subjected to such a noise level for an extended period of time, would you need to worry about your hearing being affected?
> The nucleus in a / atom captures one of the atom’s electrons, changing the nucleus to / and emitting a neutrino. What is the total energy of the emitted neutrino? [Hint: You can use the classical expression for the kinetic energy of the / atom
> Rachel is on the roof of a building, h meters above ground. She throws a heavy ball into the air with a speed v, at an angle θ with respect to the horizontal. Ignore air resistance. (a) Find the speed of the ball when it hits the ground in terms of h, v
> At a point due east of the transmitter, what is the direction of the wave’s electric field?
> A point charge q1 = +5.0 µC is fixed in place at x = 0, and a point charge q2 = −3.0 µC is fixed at x = −20.0 cm. Where can we place a point charge q3 = −8.0 µC so that the net electric force on q1 due to q2 and q3 is zero?
> The radio telescope in Arecibo, Puerto Rico, has a diameter of 305 m. It can detect radio waves from space with intensities as small as 10−26 W/m2. (a) What is the average power incident on the telescope due to a wave at normal incidence with intensity
> Fernando detects the electric field from an isotropic source that is 22 km away by tuning in an electric field with an rms amplitude of 55 mV/m. What is the average power of the source?
> A 1.0 m2 solar panel on a satellite that keeps the panel oriented perpendicular to radiation arriving from the Sun absorbs 1.4 kJ of energy every second. The satellite is located at 1.00 AU from the Sun. (The Earth-Sun distance is approximately 1 AU.) Ho
> A car is speeding up and has an instantaneous velocity of 1.0 m/s in the +x-direction when a stopwatch reads 10.0 s. It has a constant acceleration of 2.0 m/s2 in the +x-direction. (a) What is the speed when the stopwatch reads 12.0 s? (b) How far does t
> Julia is delivering newspapers. Suppose she is driving at 15 m/s along a straight road and wants to drop a paper out the window from a height of 1.00 m so it slides along the shoulder and comes to rest in the customer's driveway. At what horizontal dista
> Jennifer lifts a 2.5 kg carton of cat litter from the floor to a height of 0.75 m, starting and ending with the carton held at rest. (a) How much total work is done on the carton during this operation? Jennifer then pours 1.2 kg of the litter into the c
> For low-frequency sounds, the ear uses the phase difference between the sound waves arriving at the two ears to determine direction. Why can't the ear reliably use phase difference for high- frequency sounds? Explain.
> In any hydraulic system, it is important to “bleed” air out of the line. Why?
> It is easier to get a good draft in a chimney on a windy day than when the outside air is still, all other things being equal. Why?
> Your ears “pop” when you change altitude quickly—such as during takeoff or landing in an airplane, or during a drive in the mountains. Curiously, if you are a passenger in a high-speed train, your ears sometimes pop as the speed of the train increases ra
> Before getting an oil change, it is a good idea to drive a few miles to warm up the engine. Why?
> Bernoulli’s equation applies only to steady flow. Yet Bernoulli’s equation allows the fluid velocity at one point to be different than the velocity at another point. For the fluid velocity to change, the fluid must be accelerated as it moves from one poi
> Does a manometer (with one side open) measure absolute pressure or gauge pressure? How about a barometer? A tire pressure gauge? A sphygmomanometer?
> An ideal solenoid has length I. If the windings are compressed so that the length of the solenoid is reduced to 0.50ℓ, what happens to the inductance of the solenoid?
> The bungee jumper of Example 6.4 made a jump into the Gorge du Verdon in southern France from a platform 182 m above the bottom of the gorge. The jumper weighed 780 N and came within 68 m of the bottom of the gorge. The cord’s unstretched length is 30.0
> Animals that can run fast always have thin legs. Their leg muscles are concentrated close to the hip joint; only tendons extend into the lower leg. Using the concept of rotational inertia, explain how this helps them run fast.
> A parallel plate capacitor has a charge of 0.020 µC on each plate with a potential difference of 240 V. The parallel plates are separated by 0.40 mm of air. What energy is stored in this capacitor?
> A cell membrane has a surface area of 1.1×10−7 m2, a dielectric constant of 5.2, and a thickness of 7.2 nm. The potential difference across the membrane is 70 mV. (a) What is the magnitude of the charge on each surface of the membrane? (b) How many ion
> A large barrel lies on its side. In order to roll it across the floor, you apply a horizontal force, as shown in the figure. If the applied force points toward the axis of rotation, which runs down the center of the barrel through the center of mass, it
> Four brass wires are subjected to the same tensile stress. The wires have unstretched lengths and diameters as follows. Rank the four wires in decreasing order of the amount of stretch. (a) length L, diameter d (b) length 2L, diameter d (c) length 4L,
> In the “Pinewood Derby,” Cub Scouts construct cars and then race them down an incline. Some say that, everything else being equal (friction, drag coefficient, same wheels, etc.), a heavier car will win; others maintain that the weight of the car does not
> If a man has an average useful power output of 40.0 W, what minimum time would it take him to lift fifty 10.0 kg boxes to a height of 2.00 m?
> Why do many helicopters have a small propeller attached to the tail that rotates in a vertical plane? Why is this attached at the tail rather than somewhere else? [Hint: Most of the helicopter's mass is forward, in the cab.]
> A pinhole camera doesn't have a lens; a small circular hole lets light into the camera, which then exposes the film. For the sharpest image, light from a distant point source makes as small a spot on the film as possible. What is the optimum size of the
> An object in equilibrium has only two forces acting on it. The forces must be equal in magnitude and opposite in direction in order to give a translational net force of zero. What else must be true of the two forces for the object to be in equilibrium? [
> Paula swims across a river that is 10.2 m wide. She can swim at 0.833 m/s in still water, but the river flows with a speed of 1.43 m/s. If Paula swims in such a way that she crosses the river in as short a time as possible, how far downstream is she when
> A book measures 3 cm by 16 cm by 24 cm. About which of the axes shown in the figure is its rotational inertia smallest?
> Capacitors are used in many applications where you need to supply a short burst of energy. A 100.0 µF capacitor in an electronic flash lamp supplies an average power of 10.0 kW to the lamp for 2.0 ms. (a) To what potential difference must the capacitor i
> Why is it easier to push open a swinging door from near the edge away from the hinges rather than in the middle of the door?
> One of the effects of significant global warming is the melting of part or all of the polar ice caps. This, in turn, would change the length of the day (the period of Earth's rotation). Explain why. Would the day get longer or shorter?
> One way to find the center of gravity of an irregular flat object is to suspend it from various points so that it is free to rotate. When the object hangs in equilibrium, a vertical line is drawn downward from the support point. After drawing lines from
