Question: What is the period of a pendulum

> An AM radio station broadcasts at 570 kHz. (a) What is the wavelength of the radio wave in air? (b) If a radio is tuned to this station and the inductance in the tuning circuit is 0.20 mH, what is the capacitance in the tuning circuit? (c) In the vici

> Small animals eat much more food per kilogram of body mass than do larger animals. The basal metabolic rate (BMR) is the minimal energy intake necessary to sustain life in a state of complete inactivity. The table lists the BMR in kilocalories per day, t

> To make an order-of-magnitude estimate of the energy level spacings in the nucleus, assume that a nucleon is confined to a one- dimensional box of width 10 fm (a typical nuclear diameter). Calculate the energy of the ground state.

> The nucleus of a helium atom contains two protons that are approximately 1 fm apart. How much work must be done by an external agent to bring the two protons from an infinite separation to a separation of 1.0 fm?

> Explain why there is almost no hydrogen (H2) or helium (He) in Earth's atmosphere, yet both are present in Jupiter's atmosphere. [Hint: Escape velocity from Earth is 11.2 km/s and escape velocity from Jupiter is 60 km/s.]

> The potential difference across a cell membrane from outside to inside is initially at −90 mV (when in its resting phase). When a stimulus is applied, Na+ ions are allowed to move into the cell such that the potential changes to +20 mV for a short interv

> Computer speakers that are intended to be placed near a CRT computer monitor are magnetically shielded—either they don't use magnets or they are designed so that their magnets produce only a small magnetic field nearby. Why is the shielding important? Wh

> In an experiment to measure the speed of sound in air, standing waves are set up in a narrow pipe open at both ends using a speaker driven at 702 Hz. The length of the pipe is 2.0 m. What is the air temperature inside the pipe (assumed reasonably near ro

> A circular loop of current carries a steady current. (a) Sketch the magnetic field lines in a plane perpendicular to the plane of the loop. (b) Which side of the loop is the north pole of the magnetic dipole and which is the south pole?

> The magnetic field due to a long straight wire carrying steady current is measured at two points, P and Q. Where is the wire and in what direction does the current flow?

> In 1988 the shroud of Turin, a piece of cloth that some people believe is the burial cloth of Jesus, was dated using 14C. The measured 14C activity of the cloth was about 0.23 Bq/g. According to this activity, when was the cloth in the shroud made?

> A horizontal wire that runs east-west carries a steady current to the east. A C-shaped magnet (see Fig. 19.3a) is placed so that the wire runs between the poles, with the north pole above the wire and the south pole below. What is the direction of the ma

> Abductin, an elastic protein found in the ligaments of scallops, has a Young’s modulus of 4.0 MPa. The inner hinge ligament has a cross-sectional area of 0.78 mm2 and a relaxed length of 1.0 mm. When the muscles in the shell relax, the shell opens. This

> In her bag, a photographer is carrying three camera lenses with focal lengths of 400.0 mm, 50.0 mm, and 28.0 mm. Which lens should she use for (a) wide angle shots (a cathedral, taken from the square in front), (b) everyday use (children at play), and

> A 5.0 kg block of wood is attached to a spring with a spring constant of 150 N/m. The block is free to slide on a horizontal frictionless surface once the spring is stretched and released. A 1.0 kg block of wood rests on top of the first block. The coeff

> A dc motor is connected to a constant emf of 12.0 V. The resistance of its windings is 2.0 ΩAt normal operating speed, the motor takes in 6.0 W of electrical power. (a) What is the initial current drawn by the motor when it is first started up? (b) Wha

> Two magnifying glasses are labeled with their angular magnifications. Glass A has a magnification of “2×” (M = 2) and glass B has a magnification of 4×. Which has the longer focal length? Explain.

> An electron is moved from point A, where the electric potential is VA = −240 V, to point B, where the electric potential is VB = −360 V. What is the change in the electric potential energy?

> Centrifuges are commonly used in biological laboratories for the isolation and maintenance of cell preparations. For cell separation, the centrifugation conditions are typically 1.0 × 103 rev/min using an 8.0 cm radius rotor. (a) What is the radial acce

> The electric field is defined as the electric force per unit charge. Explain why the magnetic field cannot be defined as the magnetic force per unit charge.

> A hollow conducting sphere of radius R carries a negative charge −q. (a) Write expressions for the electric field / inside (r < R) and outside (r > R) the sphere. Also indicate the direction of the field. (b) Sketch a graph of the field strength as a f

> Refer to Problem 110. One capacitor plate has an excess of electrons and the other has a matching deficit of electrons. What is the number of excess electrons?

> Why are electric stoves and clothes dryers supplied with 240 V, but lights, radios, and clocks are supplied with 120 V?

> Suppose a battery is connected to a network of resistors and capacitors. What happens to the energy supplied by the battery?

> Io, one of Jupiter’s satellites, has an orbital period of 1.77 d. Europa, another of Jupiter’s satellites, has an orbital period of about 3.54 d. Both moons have nearly circular orbits. Use Kepler’s third law to find the distance of each satellite from J

> Air at room temperature and atmospheric pressure has a mass density of 1.2 kg/m3. The average molecular mass of air is 29.0 u. How many molecules are in 1.0 cm3 of air?

> Compare the resistance of an ideal ammeter with that of an ideal voltmeter. Which has the larger resistance? Why?

> (a) What fraction of the 238U atoms present at the formation of the Earth still exist? Take the age of the Earth to be 4.5 × 109 yr. (b) Answer the same question for 235U. Could this explain why there are more than 100 times as many 238U atoms as 235U a

> A friend says that electric current “follows the path of least resistance.” Is that true? Explain.

> Current of 83 mA flows through the resistor in the diagram. (a) What is the resistance of the resistor? (b) In what direction does the current flow through the resistor?

> Tim is using a cordless electric weed trimmer with a dc motor to cut the long weeds in his backyard. The trimmer generates a back emf of 18.00 V when it is connected to an emf of 24.0 V dc. The total electrical resistance of the electric motor is 8.00 Ω.

> A pilot is performing vertical loop-the-loops over the ocean at noon. The plane speeds up as it approaches the bottom of the circular loop and slows as it approaches the top of the loop. An observer in a helicopter is watching the shadow of the plane on

> A starship is traveling at a speed of 0.78c toward Earth when it experiences a major malfunction and the crew is forced to evacuate. An escape pod that is 12.0 m long with respect to its passengers is ejected from the starship and sent toward Earth at a

> What are the wavelengths of sound waves at the lower and upper limits of human hearing (10 Hz and 20 kHz, respectively)?

> In many problems in previous chapters, cars and other objects that roll on wheels were considered to act as if they were sliding without friction. (a) Can the same assumption be made for a wheel rolling by itself? Explain your answer. (b) If a moving c

> Jeff needs a 100 Ω resistor for a circuit, but he only has a box of 300 Ω resistors. What can he do?

> What is the minimum speed with which a meteor strikes the top of Earth’s stratosphere (about 40 km above the surface), assuming that the meteor begins as a bit of interplanetary debris far from Earth and stationary relative to Earth? Assume the drag forc

> Aluminum rivets used in airplane construction are made slightly too large for the rivet holes to be sure of a tight fit. The rivets are cooled with dry ice (−78.5°C) before they are driven into the holes. If the holes have a diameter of 0.6350 cm at 20.5

> Why is it warmer in summer than in winter?

> Is it possible for a plane mirror to produce a real image of an object in front of the mirror? Explain. If it is possible, sketch a ray diagram to demonstrate. If it is not possible, sketch a ray diagram to show which way a curved mirror must curve (conc

> Ammeters often contain fuses that protect them from large currents, whereas voltmeters seldom do. Explain.

> A longitudinal wave has a wavelength of 10 cm and an amplitude of 5.0 cm and travels in the y-direction. The wave speed in this medium is 80 cm/s. (a) Describe the motion of a particle in the medium as the wave travels through the medium. (b) How would

> Why is a transverse wave sometimes called a shear wave?

> In each of six situations, a particle (mass m, charge q) moves from a point where the potential is Vi to a point where the potential is Vf. Apart from the electric force, no forces act on the particles. Rank them in order of the particle's change in kine

> A rifle has a mass of 4.5 kg and it fires a bullet of mass 10.0 g at a muzzle speed of 820 m/s. What is the recoil speed of the rifle as the bullet leaves the gun barrel?

> Find the electric field at point A, the upper left corner.

> How many hydrogen atoms are present in 684.6 g of sucrose (C12H22O11)?

> A cell membrane has a surface area of 1.0 × 10−7 m2, a dielectric constant of 5.2, and a thickness of 7.5 nm. The membrane acts like the dielectric in a parallel plate capacitor; a layer of positive ions on the outer surface and a layer of negative ions

> Calculate, according to the Bohr model, the speed of the electron in the ground state of the hydrogen atom.

> Consider the tibia (shinbone) for a person of weight 750 N standing on the ball of one foot as in the following figure. The ankle joint pushes upward on the bottom of the tibia with a force of 2800 N, while the top end of the tibia must feel a net downwa

> A hair dryer has a power rating of 1200 W at 120 V rms. Assume the hair dryer circuit contains only resistance. (a) What is the resistance of the heating element? (b) What is the rms current drawn by the hair dryer? (c) What is the maximum instantaneous

> A cello player can change the frequency of the sound produced by her instrument by (a) increasing the tension in the string, (b) pressing her finger on the string at different places along the fingerboard, or (c) bowing a different string. Explain how

> Akiko rides her bike toward a brick wall with a speed of 7.00 m/s while blowing a whistle that is emitting sound with a frequency of 512.0 Hz. (a) What is the frequency of the sound that is reflected from the wall as heard by Haruki, who is standing sti

> Why is it possible to understand the words spoken by two people at the same time?

> If the length of a guitar string is decreased while the tension remains constant, what happens to each of these quantities? (a) the wavelength of the fundamental, (b) the frequency of the fundamental, (c) the time for a pulse to travel the length of t

> Consider the following equations for traveling waves on two different strings: I. y(x, t) = (1.50 cm) sin [(4.00 cm−1)x + (6.00 s−1)t] II. y(x, t) = (4.50 cm) sin [(3.00 cm−1)x − (3.00 s−1)t] (a) Which wave has the faster wave speed? What is that speed?

> A dc motor has coils with a resistance of 16 Ω and is connected to an emf of 120.0 V. When the motor operates at full speed, the back emf is 72 V. (a) What is the current in the motor when it first starts up? (b) What is the current when the motor is a

> Draw a circuit diagram for automobile headlights, connecting two separate bulbs and a switch to a single battery so that: (1) one switch turns both bulbs on and off and (2) one bulb still lights up even if the other bulb burns out.

> The wavelength of the fundamental standing wave on a cello string depends on which of these quantities: length of the string, mass per unit length of the string, or tension? The wavelength of the sound wave resulting from the string's vibration depends o

> Find the work done by gravity on the hanging crate.

> What are the advantages of using the concepts of stress and strain to describe deformations?

> A wheel of radius 30 cm is rotating at a rate of 2.0 revolutions every 0.080 s. (a) Through what angle, in radians, does the wheel rotate in 1.0 s? (b) What is the linear speed of a point on the wheel’s rim? (c) What is the wheel’s frequency of rotati

> As a Boeing 747 gains altitude, the passenger cabin is pressurized. However, the cabin is not pressurized fully to atmospheric (1.01 × 105 Pa), as it would be at sea level, but rather pressurized to 7.62 × 104 Pa. Suppose a 747 takes off from sea level w

> The lowest frequency string on a guitar is 65.5 cm long and is tuned to 82 Hz. (a) If the string has a mass of 3.31 g, what is the tension in the string? (b) By fingering the guitar at the fifth fret, you shorten the vibrating length of the string, the

> A 2 m long copper pipe is held vertically. When a marble is dropped down the pipe, it falls through in about 0.7 s. A magnet of similar size and shape dropped down the pipe takes much longer. Why?

> Think of a crystalline solid as a set of atoms connected by ideal springs. When a wire is stretched, how is the elongation of the wire related to the elongation of each of the interatomic springs? Use your answer to explain why a given tensile stress pro

> At a baseball game, a radar gun measures the speed of a 144 g baseball to be 137.32 ± 0.10 km/h. (a) What is the minimum uncertainty of the position of the baseball? (b) If the speed of a proton is measured to the same precision, what is the minimum unc

> Think of an example that illustrates why an “anti-Lenz” law would violate the conservation of energy. (The “anti-Lenz” law is: The direction of induced emfs and currents always reinforces the change that produces them.)

> Show that over one complete cycle, the average value of a sin2 ωt is . / Use the trigonometric identity sin2 ωt = (1 − cos 2ωt)/2.

> A car with a mass of 1700 kg is traveling directly northeast (45° between north and east) at a speed of 14 m/s (31 mi/h), and collides with a smaller car with a mass of 1300 kg that is traveling directly south at a speed of 18 m/s (40 mi/h). The two cars

> Vertically polarized light with intensity I0 is normally incident on an ideal polarizer. As the polarizer is rotated about a horizontal axis, the intensity I of light transmitted through the polarizer varies with the orientation of the polarizer (8), whe

> Given two identical, ideal batteries of emf / and two identical incandescent lightbulbs of resistance R (assumed constant), find the total power dissipated in the circuit in terms of / and R.

> The figure shows hysteresis curves for three different materials. A hysteresis curve is a plot of the magnetic field magnitude inside the material (B) as a function of the externally applied field (B0). (a) Which material would make the best permanent m

> A solenoid has 4850 turns per meter and radius 3.3 cm. The magnetic field inside has magnitude 0.24 T. What is the current in the solenoid?

> Two long, straight wires, each with a current of 5.0 A, are placed on two corners of an equilateral triangle with sides of length 3.2 cm as shown. One of the wires has a current into the page and one has a current out of the page. (a) What is the magnet

> You are designing the main solenoid for an MRI machine. The solenoid should be 1.5 m long. When the current is 80 A, the magnetic field inside should be 1.5 T. How many turns should your solenoid have?

> Two metal spheres have charges of equal magnitude, 3.2 × 10−14 C, but opposite sign. If the potential difference between the two spheres is 4.0 mV, what is the capacitance? [Hint: The “plates” are not parallel, but the definition of capacitance holds.]

> The strip in the diagram is used as a Hall probe to measure magnetic fields, (a) What happens if the strip is not perpendicular to the field? Does the Hall probe still read the correct field magnitude? Explain. (b) What happens if the field is in the p

> A 100 W incandescent lightbulb radiates visible light at a rate of about 10 W; the rest of the EM radiation is mostly infrared. Assume that the lightbulb radiates uniformly in all directions. Under ideal conditions, the eye can see the lightbulb if at le

> ɦ Photons of energy E = 4.000 keV undergo Compton scattering. What is the largest possible change in photon energy, measured as a fraction of the incident photon's energy (E − E′)/E?

> Two concentric circular wire loops in the same plane each carry a current. The larger loop has a current of 8.46 A circulating clockwise and has a radius of 6.20 cm. The smaller loop has a radius of 4.42 cm. What is the current in the smaller loop if the

> In naturally occurring potassium, 0.0117% of the nuclei are radioactive 40K. (a) What mass of 40K is found in a broccoli stalk containing 300 mg of potassium? (b) What is the activity of this broccoli stalk due to 40K?

> Two parallel wires in a horizontal plane carry currents I1 and I2 to the right. The wires each have length L and are separated by a distance d. Find the magnitudes and directions of the (a) the magnetic field due to wire 1 at the location of wire 2, (b

> Two long straight parallel wires separated by 8.0 cm carry currents of equal magnitude but heading in opposite directions. The wires are shown perpendicular to the plane of this page. Point P is 2.0 cm from wire 1, and the magnetic field at point P is 1.

> A dolphin wants to swim directly back to its home bay, which is 0.80 km due west. It can swim at a speed of 4.00 m/s relative to the water, but a uniform water current flows with speed 2.83 m/s in the southeast direction. (a) What direction should the d

> Speedometer readings are obtained and graphed as a car skids to a stop along a straight-line path. How far does the car move between t = 0 and t = 16 s? Sketch a motion diagram showing the position of the car at 2 s intervals and sketch a graph of x(t).

> A solenoid of length 0.256 m and radius 2.0 cm has 244 turns of wire. What is the magnitude of the magnetic field well inside the solenoid when there is a current of 4.5 A in the wire?

> Some animals are capable of detecting magnetic fields and use this sense to help them navigate. Suppose a high-voltage direct- current power line carries a current of 5.0 kA. (a) How far from the wire would a homing pigeon have to be so the field due to

> Which decay mode would you expect for radioactive /: α, β−, or β +? Explain. [Hint: Look at the neutron-to-proton ratio.]

> A standing wave has wavenumber 200 rad/m. What is the distance between two adjacent nodes?

> Unpolarized light is incident on a system of three ideal polarizers. The second polarizer is oriented at an angle of 30.0° with respect to the first, and the third is oriented at an angle of 45.0° with respect to the first. If the light that emerges from

> A point charge q = +3.0 nC moves through a potential difference ΔV = Vf − Vi = +25 V. What is the change in the electric potential energy?

> Within cells, small organelles containing newly synthesized proteins are transported along microtubules by tiny molecular motors called kinesins. What force does a kinesin molecule need to deliver in order to accelerate an organelle with mass 0.01 pg (10

> If the molecule is initially at rest at θ = 90.0°, what is its angular speed when it reaches θ = 0, assuming no other forces or torques? [Hint: First find the work done on each point charge.]

> Kieran measures the magnetic field of an electron beam. The beam strength is such that 1.40 × 1011 electrons pass a point every 1.30 μs. What magnetic field does Kieran measure at a distance of 2.00 cm from the beam center?

> Imagine a long straight wire perpendicular to the page and carrying a current I into the page. Sketch some field lines with arrowheads to indicate directions.

> The source and observer of a sound wave are both at rest with respect to the ground. The wind blows in the direction from source to observer. Is the observed frequency Doppler-shifted? Explain.

> Estimate the magnetic field at distances of 1 μm and 1 mm produced by a current of 3 μA along the medial nerve of the human arm. Model the nerve as a straight current-carrying wire. Compare with the magnitude of Earth's magnetic field near the surface, a

> An object of 1.0 kg mass approaches a stationary object of 5.0 kg at 10.0 m/s and, after colliding, rebounds in the reverse direction along the same line with a speed of 5.0 m/s. What is the speed of the 5.0 kg object after the collision?

> Explain how an automobile airbag protects the passenger from injury. Why would the airbag be ineffective if the gas pressure inside is too low when the passenger comes into contact with it? What about if it is too high?