The principal component of natural gas is methane (CH4). How many moles of CH4 are present in 144.36 g of methane?
> /can alpha decay to the ground state of / , or to any of the four excited states of / shown in Fig. 29.7. The maximum kinetic energy of the alpha particles emitted by / is 6.090 MeV. What other alpha particle kinetic energies are possible? [Hint: Estim
> Explain what is meant by a phase difference. Sketch graphs of i(t) and vC(t), given that the current leads the voltage by π/2 radians.
> A solenoid with a radius of 8.0 × 10−3 m and 200 turns/cm is used as an inductor in a circuit. When the solenoid is connected to a source of 15 V rms at 22 kHz, an rms current of 3.5 × 10−2 A is measured. Assume the resistance of the solenoid is negligib
> How long a pipe is needed to make a tuba whose lowest note is low C (frequency 130.8 Hz)? Assume that a tuba is a long straight pipe open at both ends.
> The electric field between plates (A) is zero. As the beam exits the space between plates (B), it has been deflected 2.0 mm downward (Δy = −2.0 mm). In what direction is the beam moving now?
> Two cows, with approximately 1.8 m between their front and hind legs, are standing under a tree during a thunderstorm. See the diagram with Conceptual Question 16. (a) If the equipotential surfaces about the tree just after a lightning strike are as sho
> A spaceship is moving away from Earth with a constant velocity of 0.80c with respect to Earth. The spaceship and an Earth station synchronize their clocks, setting both to zero, at an instant when the ship is near Earth. By prearrangement, when the clock
> A marble column with a cross-sectional area of 25 cm2 supports a load of 7.0 × 104 N. The marble has a Young’s modulus of 60 GPa and a compressive strength of 200 MPa. (a) What is the stress in the column? (b) What is the strain in the column? (c) If
> An elevator starts at rest on the ninth floor. At t = 0, a passenger pushes a button to go to another floor. The graph for this problem shows the acceleration ay of the elevator as a function of time. Let the y-axis point upward. (a) Has the passenger g
> An accelerometer—a device to measure acceleration—can be as simple as a small pendulum hanging in an airplane cockpit. An essentially similar accelerometer is found in the inner ear of vertebrates. Suppose you are flyi
> A tower outside the Houses of Parliament in London has a famous clock commonly referred to as Big Ben, the name of its 13 ton chiming bell. The hour hand of each clock face is 2.7 m long and has a mass of 60.0 kg. Assume the hour hand to be a uniform rod
> The intrinsic magnetic dipole moment of the electron has magnitude 9.3 × 10−24 A·m2. What is the maximum torque on an electron due to its intrinsic dipole moment in a 1.0 T magnetic field?
> A converging lens made of glass (n = 1.5) is placed under water (n = 1.33). Describe how the focal length of the lens under water compares to the focal length in air.
> Why would silver and brass probably not be a good choice of metals for a bimetallic strip (leaving aside the question of the cost of silver)? (See Table 13.2.)
> A locust jumps at an angle of 55.0° and lands 0.800 m from where it jumped. (a) What is the maximum height of the locust during its jump? Ignore air resistance. (b) If it jumps with the same initial speed at an angle of 45.0°, would the maximum height
> A / nucleus (mass 208.0 u) emits a 452 keV photon to jump to a state of lower energy. Assuming the nucleus is initially at rest, calculate the kinetic energy of the nucleus after the photon has been emitted. [Hint: Assume the nucleus can be treated nonr
> A child’s playground swing is supported by chains that are 4.0 m long. If a child in the swing is 0.50 m above the ground and moving at 6.0 m/s when the chains are vertical, what is the maximum height of the swing? Assume the masses of the chains are neg
> Justin moves a desk 5.0 m across a level floor by pushing on it with a constant horizontal force of 340 N. (It slides for a negligibly small distance before coming to a stop when the force is removed.) Then, changing his mind, he moves it back to its sta
> In her job as a dental hygienist, Kathryn uses a concave mirror to see the back of her patient's teeth. When the mirror is 1.20 cm from a tooth, the image is upright and 3.00 times as large as the tooth. What are the focal length and radius of curvature
> How can the lights in a home be dimmed using a coil of wire and a soft-iron core?
> (a) Light of wavelength 300 nm is incident on a metal that has a work function of 1.4 eV. What is the maximum speed of the emitted electrons? (b) Repeat part (a) for light of wavelength 800 nm incident on a metal that has a work function of 1.6 eV. (c)
> For each of the lenses in the figure, state whether the lens is converging or diverging.
> A frog is sitting on a lily pad when it sees a delicious fly. He darts out his tongue at a speed of 3.7 m/s to catch the fly. The tongue has a mass of 0.41 g, and the rest of the frog plus the lily pad have a mass of 12.5 g. What is the recoil speed of t
> Starting from rest, a package slides down a 2.8 m long ramp inclined 53° below the horizontal. If μk = 0.30, find the speed of the package at the bottom of the ramp.
> How much energy is converted by the muscles of an 80.0 kg person in climbing a vertical distance of 15 m? Assume that muscles have an efficiency of 22%; that is, the increase in gravitational potential energy is 22% of the total energy converted.
> Ugonna stands at the top of an incline and pushes a 100 kg crate to get it started sliding down the incline. The crate slows to a halt after traveling 1.50 m along the incline. (a) If the initial speed of the crate was 2.00 m/s and the angle of inclinat
> A wheel of radius r rolls to the right without slipping on a horizontal road. Its axle moves at a constant speed vaxle. (a) Find the velocities of points A, B, and C with respect to the axle. Express your answers in terms of vaxle and r, as needed. [Hin
> What is the potential energy for these two charges?
> A radar pulse has an average wavelength of 1.0 cm and lasts for 0.10 μs. (a) What is the average energy of the photons? (b) Approximately what is the least possible uncertainty in the energy of the photons?
> A scientist working late at night in her low-temperature physics laboratory decides to have a cup of hot tea, but discovers the lab hot plate is broken. Not to be deterred, she puts about 8 oz of water, at 12°C, from the tap into a lab dewar (essentially
> To increase the amount of light collected by the objective lens of a microscope, a technique known as oil immersion microscopy is used. To replace the air between the objective lens and the thin slip of glass (n = 1.51) covering the specimen, a drop of o
> A ball weighing 20.0 N is tied to a string fixed to the ceiling. The string makes a 30.0° angle with the ceiling. Initially, the ball is held in place by a force / that is perpendicular to the string. (a) What is the magnitude of the force
> Refer to Problems 11–14. Find the final speed of the sliding crate if the incline is frictionless.
> A graph is plotted of the vertical velocity component vy of an elevator versus time. The y-axis points up. (a) How high is the elevator above the starting point (t = 0) after 20 s have elapsed? (b) When is the elevator at its highest location above the
> Two blocks are connected by a light string passing over an ideal pulley. The block with mass m1 = 20.0 kg slides on a frictionless horizontal surface, while the block with mass m2 = 1.0 kg hangs vertically. The radius of the pulley is 6.0 cm. (a) Assumi
> A circuit has a resistor and an unknown component in series with a 12 V (rms) sinusoidal ac source. The current in the circuit decreases by 25% when the frequency increases from 150 Hz to 250 Hz. What is the second component in the circuit? Explain your
> Find the orbital radius of a geostationary satellite without using the speed found in Example 5.9. Start by writing an equation that relates the period, radius, and speed of the orbiting satellite. Then apply Newton’s second law to the satellite. You wil
> If the electric force on the drop is found to be 9.6 × 10−16 N and the potential difference between the plates is 480 V, what is the magnitude of the charge on the drop in terms of the elementary charge e? Ignore the small buoyant force on the drop.
> An airplane of mass 2800 kg has just lifted off the runway. It is gaining altitude at a constant 2.3 m/s while the horizontal component of its velocity is increasing at a rate of 0.86 m/s2. Assume g = 9.81 m/s2. (a) Find the direction of the force exert
> The magnetic field between the poles of a magnet has magnitude 0.55 T. A circular loop of wire with radius 3.2 cm is placed between the poles so the field makes an angle of 22° with the plane of the loop. What is the magnetic flux through the loop?
> Two different monochromatic light sources, one yellow (580 nm) and one violet (425 nm), are used in a photoelectric effect experiment. The metal surface has a photoelectric threshold frequency of 6.20 × 1014 Hz. (a) Are both sources able to eject photoe
> (a) What is the reactance of a 10.0 mH inductor at the frequency f = 250.0 Hz? (b) What is the impedance of a series combination of the 10.0 mH inductor and a 10.0 Ω resistor at 250.0 Hz? (c) What is the maximum current through the same circuit when th
> Three capacitors (2.0 µF, 3.0 µF, 6.0 µF) are connected in series to an ac voltage source with amplitude 12.0 V and frequency 6.3 kHz. (a) What are the peak voltages across each capacitor? (b) What is the peak current that flows in the circuit?
> A small object of mass 0.50 kg is attached by a 0.50 m long cord to a pin set into the surface of a frictionless table top. The object moves in a circle on the horizontal surface with a speed of 2.0π m/s. (a) What is the magnitude of the radial accelera
> Earth’s orbit around the Sun is nearly circular. The period is 1 yr = 365.25 d. (a) In an elapsed time of 1 d, what is Earth’s angular displacement in radians? (b) What is the change in Earth’s velocity, /? (c) What is Earth’s average acceleration du
> Consider two protons (charge +e), separated by a distance of 2.0 × 10−15 m (as in a typical atomic nucleus). The electric force between these protons is equal in magnitude to the gravitational force on an object of what mass near Earth’s surface?
> A helicopter is lifting two crates simultaneously. One crate with a mass of 200 kg is attached to the helicopter by a cable. The second crate with a mass of 100 kg is hanging below the first crate and attached to the first crate by a cable. As the helico
> Credit cards have a magnetic strip that encodes information about the credit card account. Why do devices that read the magnetic strip often include the instruction to swipe the card rapidly? Why can’t the magnetic strip be read if the card is swiped too
> In air under ordinary conditions (room temperature and atmospheric pressure), the average intermolecular distance is about 4 nm and the mean free path is about 0.1 µm. The diameter of a nitrogen molecule is about 0.3 nm. Which two distances should we com
> The maximum strain of a steel wire with Young’s modulus 200 GPa, just before breaking, is 0.20%. What is the stress at its breaking point, assuming that strain is proportional to stress up to the breaking point?
> At a baseball game, a spectator is 60.0 m away from the batter. How long does it take the sound of the bat connecting with the ball to travel to the spectator's ears? The air temperature is 27.0°C.
> The circuit is used to study the charging of a capacitor. (a) At t = 0, the switch is closed. What initial charging current is measured by the ammeter? (b) After the current has decayed to zero, what are the voltages at points A, B, and C?
> Derive the rotational form of Newton's second law as follows. Consider a rigid object that consists of a large number N of particles. Let Fn, mn, and rn represent the tangential component of the net force acting on the nth particle, the mass of that part
> A vertical metal rod of length 20 cm moves south at constant speed 2.6 m/s in a 0.60 T magnetic field directed west. (a) Which end of the rod has an accumulation of excess electrons? (b) What is the potential difference between the ends of the rod?
> A laboratory observer measures an electron's kinetic energy to be 1.02 × 10−13 J. What is the electron's speed?
> Compare the amount of energy released when 1.0 kg of the uranium isotope 235U undergoes the fission reaction of Eq. (29-47) with the energy released when 1.0 kg of hydrogen undergoes the fusion reaction of Eq. (29-49).
> A variable inductor with negligible resistance is connected to an ac voltage source. How does the current in the inductor change if the inductance is increased by a factor of 3.0 and the driving frequency is increased by a factor of 2.0?
> Why is the muon sometimes called a “heavy electron”?
> Before a lightning strike can occur, the breakdown limit for damp air must be reached. If this occurs for an electric field of 3.33 × 105 V/m, what is the maximum possible height above Earth for the bottom of a thundercloud, which is at a potential 1.00
> Two atomic clocks are synchronized. One is put aboard a spaceship that leaves Earth at t = 0 at a speed of 0.750c. (a) When the spaceship has been traveling for 48.0 h (according to the atomic clock on board), it sends a radio signal back to Earth. When
> An airplane is traveling from New York to Paris, a distance of 5.80 × 103 km. Ignore the curvature of Earth. (a) If the cruising speed of the airplane is 350.0 km/h, how much time will it take for the airplane to make the round-trip on a calm day? (b)
> A horizontal desk surface measures 1.3 m × 1.0 m. If Earth’s magnetic field has magnitude 0.044 mT and is directed 65° below the horizontal, what is the magnetic flux through the desk surface?
> A block (mass m) hangs from a spring (spring constant k). The block is released from rest a distance d above its equilibrium position. (a) What is the speed of the block as it passes through the equilibrium point? (b) What is the maximum distance below
> (a) Explain why a transformer works for ac but not for dc. (b) Explain why a transformer designed to be connected to an emf of amplitude 170 V would be damaged if connected to a dc emf of 170 V.
> A submarine of mass 2.5 × 106 kg and initially at rest fires a torpedo of mass 250 kg. The torpedo has an initial speed of 100.0 m/s. What is the initial recoil speed of the submarine? Ignore the drag force of the water.
> A man is doing push-ups. He has a mass of 68 kg and his center of gravity is located at a horizontal distance of 0.70 m from his palms and 1.00 m from his feet. Find the forces exerted by the floor on his palms and feet.
> Suppose you are facing due north at sunrise. Sunlight is reflected by a store's display window as shown. Is the reflected light partially polarized? If so, in what direction?
> The Hubble Space Telescope uses a mirror of radius 1.2 m. Is its resolution better when detecting visible light or UV? Explain.
> A drag racer crosses the finish line of a 400.0 m track with a final speed of 104 m/s. (a) Assuming constant acceleration during the race, find the racer's time and the minimum coefficient of static friction between the tires and the road. (b) If, beca
> The charge on a capacitor in an ac circuit is q(t) = Q sin ωt. Using a small-angle approximation (Appendix A.9), we can write q(t) ≈ Qωt for times |t| ≪ 1/ω. What is the slope of the graph of q(t) at t = 0? This is equal to the current at t = 0, which is
> The number density of free electrons in silver is 5.85 × 1028 m−3. A strip of silver of thickness 0.050 mm and width 20.0 mm is placed in a magnetic field of 0.80 T. A current of 10.0 A is sent down the strip. (a) What is t
> If the magnetic fields produced by the x-, y-, and z-coils in an MRI (see Section 19.8) are changed too rapidly, the patient may experience twitching or tingling sensations. What do you think might be the cause of these sensations? Why does the much stro
> The mayor of a city proposes a new law to require that magnetic fields generated by the power lines running through the city be zero outside of the electric company's right of way. What would you say at a public discussion of the proposed law?
> In astronomy it is common to expose a photographic plate to a particular portion of the night sky for quite some time in order to gather plenty of light. Before leaving a plate exposed to the night sky, Matt decides to test his technique by exposing two
> At a point due north of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?
> On a cold, autumn day, Tuan is staring out of the window watching the leaves blow in the wind. One bright yellow leaf is reflecting light that has a predominant wavelength of 580 nm. (a) What is the frequency of this light? (b) If the window glass has
> A helium atom (mass 4.00 u) moving at 618 m/s to the right collides with an oxygen molecule (mass 32.0 u) moving in the same direction at 412 m/s. After the collision, the oxygen molecule moves at 456 m/s to the right. What is the velocity of the helium
> A string 2.0 m long is held fixed at both ends. If a sharp blow is applied to the string at its center, it takes 0.050 s for the pulses to travel to the ends of the string and return to the middle. What are the lowest three standing wave frequencies for
> A patient’s heart pumps 5.0 L of blood per minute into the aorta, which has a diameter of 1.8 cm. The average force exerted by the heart on the blood is 16 N. What is the average mechanical power output of the heart?
> Light travels through tanks filled with various substances. The indices of refraction of the substances n and the lengths of the tanks are given. Rank them in order of the time it takes light to traverse the tank, from greatest to smallest. (a) n = 5/4,
> Suppose you have a filling in one of your teeth, and, while eating some ice cream, you suddenly realize that the filling came out. One of the reasons the filling may have become detached from your tooth is the differential contraction of the filling rela
> A rotating flywheel slows down with constant angular acceleration due to friction in its bearings. At t = 0, its angular velocity is 420 rad/s. At t = 60 s, its angular velocity is 340 rad/s. (a) What is the angular velocity at t = 180 s? (b) Through h
> Two objects with masses m1 and m2 approach each other head-on with equal and opposite momenta so that the total momentum is zero. Show that, if the collision is elastic, the final speed of each object must be the same as its initial speed. (The final vel
> Estimate the magnetic field required at the LHC to make 7.0 TeV protons travel in a circle of circumference 27 km. Start by deriving an expression, using Newton's second law, for the field magnitude B in terms of the particle's momentum p, its charge q,
> The solar energy arriving at the top of Earth's atmosphere from the Sun has intensity 1.4 kW/m2. (a) How much mass does the Sun lose per day? (b) What percent of the Sun's mass is this?
> A flat square of side s0 at temperature T0 expands by Δs in both length and width when the temperature increases by ΔT. The original area is and the final area is (s0 + Δs)2 = A. Show that if Δs â
> Figure 29.7 is an energy level diagram for 208Tl. What are the energies of the photons emitted for the six transitions shown?
> At a point due north of the transmitter, how should a second ipole antenna be oriented to serve as a receiver?
> Find the height h of the pits on a CD (Fig. 25.6a). When the laser beam reflects partly from a pit and partly from land (the flat aluminum surface) on either side of the pit, the two reflected beams interfere destructively; h is chosen to be the smallest
> The inside of a cell membrane is at a potential of 90.0 mV lower than the outside. How much work does the electric field do when a sodium ion (Na+) with a charge of +e moves through the membrane from outside to inside?
> What is the maximum possible value of the angular momentum for an outer electron in the ground state of a bromine atom?
> Telescopes used in astronomy have large lenses (or mirrors). One reason is to let a lot of light in—important for seeing faint astronomical bodies. Can you think of another reason why it is an advantage to make these telescopes so large?
> Atmospheric pressure is about 1.0 × 105 Pa on average. (a) What is the downward force of the air on a desktop with surface area 1.0 m2? (b) Convert this force to pounds to help others understand how large it is. (c) Why does this huge force not cause
> Two gears A and B are turning in mesh. Gear A’s radius to the point of contact between the gears is 8.0 cm and that of gear B is 4.0 cm. (a) What is the linear speed of the contact point when gear A’s angular velocity
> Show, from XC = 1/(ωC), that the units of capacitive reactance are ohms.
> Aliens from the planet Jeenkah have based their temperature scale on the boiling and freezing temperatures of ethyl alcohol. These temperatures are 78°C and −114°C, respectively. The people of Jeenkah have six digits on each hand, so they use a base-12 n
> Imagine a person standing naked in a room at 23.0°C. The walls are well insulated, so they also are at 23.0°C. The person's surface area is 2.20 m2, and his basal metabolic rate is 2167 kcal/day. His emissivity is 0.97. (a) If the person's skin temperat
> A certain amount of energy must be supplied to increase the current through an inductor from 0 mA to 10 mA. Does it take the same amount of energy, more, or less to increase the current from 10 mA to 20 mA?
> A metal plate is attached to the end of a rod and positioned so that it can swing into and out of a perpendicular magnetic field pointing out of the plane of the paper as shown. In position 1, the plate is just swinging into the field; in position 2, the
> Why do eyeglasses, camera lenses, and binoculars with antireflective coatings often look faintly purple?
