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Question: The radio telescope in Arecibo, Puerto Rico,


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 1.0 × 10−26 W/m2?
(b) What is the average power incident on Earth’s surface?
(c) What are the rms electric and magnetic fields?


> 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

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> (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.

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> 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 = &acirc;&#136;&#146;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

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> 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

> The figure shows some light rays reflected from a small defect in the glass toward the surface of the glass. (a) If &Icirc;&cedil;c = 40.00&Acirc;&deg;, what is the index of refraction of the glass? (b) Is there any point above the glass at which a vie

> 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 &acirc;&#136;&#146;6.4 nC located as shown in the following figure. (b) What is the potential difference &Icirc;&#148;V 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 &Atilde;&#151; 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

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> 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?

> 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?

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> 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

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> 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.]

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> 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

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> Explain why it is easier to drive a wood screw using a screwdriver with a large-diameter handle rather than one with a thin handle.

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> You are riding your bicycle and approaching a rather steep hill. Which gear should you use to go uphill, a low gear or a high gear? With a low gear the wheel rotates less than with a high gear for one rotation of the pedals.

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> A solenoid is made of 300.0 turns of wire, wrapped around a hollow cylinder of radius 1.2 cm and length 6.0 cm. What is the self- inductance of the solenoid?

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