(a) Which has the larger buoyant force acting on it when immersed in water, 1.0 kg of lead or 1.0 kg of aluminum? Explain. (b) Which has the larger buoyant force acting on it, 1.0 kg of steel that is sinking to the bottom of a lake or 1.0 kg of wood with a density of 500 kg/m3 that is floating on the lake? Explain. (c) Once you have answered the qualitative questions, find the quantitative answers to parts (a) and (b).
> Explain why the annihilation of an electron and a positron creates a pair of photons rather than a single photon.
> Use the photon model to explain why ultraviolet radiation can be harmful to your skin, but visible light is not.
> The photoresponse of the retina of the human eye at low light levels depends on individual photosensitive molecules in rod cells being excited by the incident light. When excited, these molecules change shape, leading to other changes in the cell that tr
> A solar cell is used to generate electricity when sunlight falls on it. How would you expect the current produced by a solar cell to depend on the intensity of the incident light? How would you expect the current to depend on the wavelength of the incide
> You shoot a 51 g pebble straight up with a catapult whose spring constant is 320 N/m. The catapult is initially stretched by 0.20 m. How high above the starting point does the pebble fly? Ignore air resistance.
> According to Figure 30.3, higher energies correspond with times that are closer to the origin of the universe, so particle accelerators at higher energies probe conditions that existed shortly after the Big Bang. At Fermilab's Tevatron, protons and antip
> Explain the difference between speed and velocity.
> A parallel plate capacitor used in a flash for a camera must be able to store 32 J of energy when connected to 300 V. (Most electronic flashes actually use a 1.5 to 6.0 V battery, but increase the effective voltage using a dc-dc inverter.) (a) What shou
> Explain why every line in the absorption spectrum of hydrogen is present in the emission spectrum, but not every line in the emission spectrum is present in the absorption spectrum. [Hint: The excited states are very short-lived.]
> A fluorescent substance absorbs EM radiation of one wavelength and then emits EM radiation of a different wavelength. Which wavelength is longer? Explain.
> Exposure to ultraviolet light is one method used to sterilize medical equipment, disinfect drinking water, and pasteurize fruit juices. Microorganisms are typically small enough that UV light can penetrate to the cell nucleus and damage their DNA molecul
> An ordinary drinking glass is filled to the brim with water (268.4 mL) at 2.0°C and placed on the sunny pool deck for a swimmer to enjoy. If the temperature of the water rises to 32.0°C before the swimmer reaches for the glass, how much water will have s
> In a photoelectric effect experiment, how is the stopping potential determined? What does the stopping potential tell us about the electrons emitted from the metal surface?
> Explain how Rutherford's experiment, in which alpha particles are incident on a thin gold foil, refutes the plum pudding model of the atom.
> What process becomes especially important for photons with energies in excess of 1.02 MeV?
> Why is the Compton shift more noticeable for an incident x-ray photon than for a photon of visible light?
> In both Compton scattering and the photoelectric effect, an electron gains energy from an incident photon. What is the essential difference between the two processes?
> If green light causes the ejection of electrons from a metal in a photoelectric effect experiment and yellow light does not, what would you expect to happen if red light were used to illuminate the same metal? Do you expect more intense yellow light to e
> Two sine waves are described by y1 = A sin (ωt + kx) and y2 = A sin (ωt + kx + π/3). Plot graphs of y1 versus t and y2 versus t on the same axes for the point x = 0. Plot y versus t for the superposition of the two waves at x = 0 and estimate its amplitu
> Describe the photoelectric effect and four aspects of the experimental results that were puzzling to nineteenth-century physicists. How does the photon model of light explain the experimental results in each case?
> In Section 26.2, suppose that another astronaut, Celia, moves in a spaceship to the left with respect to Abe (see Fig. 26.4). What would Celia conclude about the time order of the two flashes?
> A copper bar of thermal conductivity 401 W/(m·K) has one end at 104°C and the other end at 24°C. The length of the bar is 0.10 m, and the cross-sectional area is 1.0 × 10−6 m2. (a) What is the rate of heat conduction along the bar? (b) What is the te
> In an Earth laboratory, an astronaut measures the length of a rod to be 1.00 m. The astronaut takes the rod aboard a spaceship and flies away from Earth at speed 0.5c. Is the length of the rod measured by an observer on Earth greater than, less than, or
> A particle is confined to & finite box of length L. In the nth state, the wave function has n − 1 nodes. The wave function must make a smooth transition from sinusoidal inside the box to a decaying exponential outsideâ€&#
> A pendulum passes x = 0 with a speed of 0.50 m/s; it swings out to A = 0.20 m. What is the period T of the pendulum? (Assume the amplitude is small.)
> A thin soap film (n = 1.35) is suspended in air. The spectrum of light reflected from the film is missing two visible wavelengths of 500.0 nm and 600.0 nm, with no missing wavelengths between the two. (a) What is the thickness of the soap film? (b) Are
> Harry and Sally are on opposite sides of the room at a wedding reception. They simultaneously (in the frame of the room) take flash pictures of the bride and groom cutting the cake in the center of the room. What would an observer moving at constant velo
> A constant force is applied to a particle initially at rest. Sketch qualitative graphs of the particle's speed, momentum, and acceleration as functions of time. Assume that the force acts long enough so the particle achieves relativistic speeds.
> An astronaut in top physical condition has an average resting pulse on Earth of about 52 beats per minute. Suppose the astronaut is in a spaceship traveling at 0.87c (γ = 2) with respect to Earth when he takes his own resting pulse. Does he measure about
> A proton (mass 1.67 × 10−27 kg, charge +e) is fired directly at a lithium nucleus (mass 1.16 × 10−26 kg, charge +3e). If the proton's velocity is 5.24 × 105 m/s when it is far from the nucleus, how far apart will the two particles be when the proton is a
> A particle with nonzero mass m can never move faster than the speed of light. Is there also a maximum momentum that the particle can have? A maximum kinetic energy? Explain.
> As you talk on a cell phone, does the mass of the phone's battery change at all? If so, does it increase or decrease?
> An electron is moving at nearly light speed. A constant force of magnitude F is acting on the electron in the direction of its motion. Is the acceleration of the electron less than, equal to, or greater in magnitude than F/m? Explain.
> A quasar is a bright center in a far distant galaxy where some energetic action is taking place (probably due to energy being released as matter falls into a black hole at the center of the galaxy). Through her telescope Mavis observes a quasar 12 × 109
> Does a stretched spring have the same mass as when it is relaxed? Explain.
> A cylindrical brass container with a base of 75.0 cm2 and height of 20.0 cm is filled to the brim with water when the system is at 25.0°C. How much water overflows when the temperature of the water and the container is raised to 95.0°C?
> Explain why it is impossible for a particle with mass to move faster than the speed of light.
> When the spring on a toy gun is compressed by a distance x, it will shoot a rubber ball straight up to a height of h. Ignoring air resistance, how high will the gun shoot the same rubber ball if the spring is compressed by an amount 2x? Assume x ≪ h.
> A particle with charge +e has a total energy of 0.638 MeV when it is moving at 0.600c. If this particle then enters a linear accelerator, what is its speed after it has been accelerated through a 2.6 MV potential difference?
> A friend argues with you that relativity is absurd: “It's obvious that moving clocks don't run slow and that moving objects aren't shorter than when they're at rest.” How would you reply?
> The drawing shows a snapshot of a transverse wave traveling along a string at 10.0 m/s. The equation for the wave is y(x, t) = A cos (ωt + kx). (a) Is the wave moving to the right or to the left? (b) What are the numerical values of A, Ï
> In a double-slit experiment, what is the linear distance on the screen between adjacent maxima if the wavelength is 546 nm, the slit separation is 0.100 mm, and the slit-screen separation is 20.0 cm?
> A spherical rain drop of radius 1.0 mm has a charge of +2.0 nC. The electric field in the vicinity is 2.0 kN/C downward. The terminal speed of an identical but uncharged drop is 6.5 m/s. The drag force is related to the drop’s speed by
> In an experiment to measure the Coulomb constant, a tiny sphere with charge +7.0 nC is suspended from a spring. When two other tiny charged spheres, each with a charge of −4.0 µC, are placed in the positions shown in the figure, the spring stretches 0.50
> The graph shows the position x of a switch engine in a rail yard as a function of time t. At which of the labeled times t0 to t7 is (a) ax 0, (d) vx = 0, (e) the speed decreasing?
> Humans cool off by perspiring; the evaporating sweat removes heat from the body. If the skin temperature is 35.0°C and the air temperature is 28.0°C, what is the entropy change of the universe due to the evaporation of 150 mL of sweat? Take the latent he
> In gel electrophoresis, the mobility μ of a molecule in a particular gel matrix is defined as μ = v1/E, where v1 is the terminal speed of the molecule and E is the applied electric field strength. In one case, a molecule has mobility 3.0 × 10−8 C·m/(N·s)
> A student eats 2000 kcal per day. (a) Assuming that all of the food energy is released as heat, what is the rate of heat released (in watts)? (b) What is the rate of change of entropy of the surroundings if all of the heat is released into air at room t
> The Bohr model of the hydrogen atom proposed that the electron orbits around the proton in a circle of radius 5.3 × 10−11 m. The electric force is responsible for the radial acceleration of the electron. What is the speed of the electron in this model?
> Within an insulated system, 418.6 kJ of heat is conducted through a copper rod from a hot reservoir at +200.0°C to a cold reservoir at +100.0°C. (The reservoirs are so big that this heat exchange does not change their temperatures appreciably.) What is t
> A very small charged block with a mass of 2.35 g is placed on an insulated, frictionless plane inclined at an angle of 17.0° with respect to the horizontal. The block does not slide down the plane because of a 465 N/C uniform electric field th
> Rank these in order of increasing entropy: (a) 1 mol of water at 20°C and 1 mol of ethanol at 20°C in separate containers; (b) a mixture of 1 mol of water at 20°C and 1 mol of ethanol at 20°C; (c) 0.5 mol of water at 20°C and 0.5 mol of ethanol at 20°
> The energy-time uncertainty principle allows for the creation of virtual particles that appear from a vacuum for a very brief period of time Δt, then disappear again. This can happen as long as ΔE Δt = ħ/2, where ΔE is the rest energy of the particle. (
> (a) Write an expression for the magnitude of the electric field at a point (x, 0) on a line perpendicular to the dipole axis. State the direction of the field for x > 0 and for x < 0. (b) Show that when x ≫ d, E ≈ kqd/x3. (c) The field is inversely pro
> Rank these in order of increasing entropy: (a) 0.5 kg of ice and 0.5 kg of (liquid) water at 0°C; (b) 1 kg of ice at 0°C; (c) 1 kg of (liquid) water at 0°C; (d) 1 kg of water at 20°C.
> A pilot wants to fly from Dallas to Oklahoma City, a distance of 330 km at an angle of 10.0° west of north. The pilot heads directly toward Oklahoma City with an airspeed of 200 km/h. After flying for 1.0 h, the pilot finds that he is 15 km off course to
> (a) Write an expression for the electric field at a point (0, y) on the dipole axis for y > d/2. What is the direction of the field? (b) Show that when y ≫ d, E ≈ 2kqd/y3. [Hint: Use the binomial approximation from Appendix A.9.] (c) The field is inverse
> Show that the coefficient of performance for a reversible refrigerator is 1/[(TH/TC) − 1].
> A thin wire with positive charge Q evenly spread along its length is shaped into a semicircle of radius R. (a). What is the direction of the electric field at the center of curvature of the semicircle? Explain. (b) Is the magnitude of the field at the
> The gauge pressure of the air in an automobile tire is 32 lb/in2. Convert this to (a) Pa, (b) mmHg, (c) atm.
> Show that the coefficient of performance for a reversible heat pump is 1/(1 − TC/TH).
> In a cathode ray tube, electrons initially at rest are accelerated by a uniform electric field of magnitude 4.0 × 105 N/C during the first 5.0 cm of the tube’s length; then they move at essentially constant velocity another 45 cm before hitting the scree
> An engine operates between temperatures of 650 K and 350 K at 65.0% of its maximum possible efficiency. (a) What is the efficiency of this engine? (b) If 6.3 × 103 J is exhausted to the low temperature reservoir, how much work does the engine do?
> A charge of 63.0 nC is located at a distance of 3.40 cm from a charge of −47.0 nC. What are the x- and y-components of the electric field at a point P that is directly above the 63.0 nC charge at a distance of 1.40 cm? Point P and the t
> (a) For a reversible engine, will you obtain a better efficiency by increasing the high-temperature reservoir by an amount ΔT or decreasing the low-temperature reservoir by the same amount ΔT? Explain. (b) To illustrate your answer to this question, cal
> The main energy expenditure involved in running is the work done by the muscles to accelerate the legs. When a foot strikes the ground, it is momentarily brought to rest while the remainder of the animal’s body continues to move forward
> (a) What is the maximum temperature of the gas? (b) What would be the efficiency of an ideal engine with reservoirs at the maximum and minimum temperatures of this engine? Compare this to the actual efficiency, 0.444.
> A sample in a centrifuge moves in a circle of radius 8.0 cm at a constant speed of 500 m/s. (a) How much time does it take for the velocity’s direction to change by 45° (1/8 of a revolution)? (b) What is the magnitude of the average acceleration during
> A reversible refrigerator has a coefficient of performance of 3.0. How much work must be done to freeze 1.0 kg of liquid water initially at 0°C?
> (a) How much net work does this engine do per cycle? (b) Assuming that the efficiency of the engine is 0.444, what is the heat input into the gas per cycle? (c) How much heat is exhausted per cycle? (d) It takes 3.0 s for the engine to go through each
> A woman’s systolic blood pressure when resting is 160 mmHg. What is this pressure in (a) Pa, (b) lb/in2, and (c) atm?
> A heat engine uses the warm air at the ground as the hot reservoir and the cooler air at an altitude of several thousand meters as the cold reservoir. If the warm air is at 37°C and the cold air is at 25°C, what is the maximum possible efficiency for the
> A power plant burns coal to produce pressurized steam at 535 K. The steam then condenses back into water at a temperature of 323 K. (a) What is the maximum possible efficiency of this plant? (b) If the plant operates at 50.0% of its maximum efficiency
> An inventor proposes a heat engine to propel a ship, using the temperature difference between the water at the surface and the water 10 m below the surface as the two reservoirs. If these temperatures are 15.0°C and 10.0°C, respectively, what is the maxi
> The efficiency of a muscle during weight lifting is equal to the work done in lifting the weight divided by the total energy output of the muscle (work done plus internal energy dissipated in the muscle). Determine the efficiency of a muscle that lifts a
> An oil-burning electric power plant uses steam at 773 K to drive a turbine, after which the steam is expelled at 373 K. The engine has an efficiency of 0.40. What is the theoretical maximum efficiency possible at those temperatures?
> A 0.50 kg block of iron [c = 0.44 kJ/(kg·K)] at 20.0°C is in contact with a 0.50 kg block of aluminum [c = 0.900 kJ/(kg·K)] at a temperature of 20.0°C. The system is completely isolated from the rest of the universe. Suppose heat flows from the iron into
> An electric power station generates steam at 500.0°C and condenses it with river water at 27°C. By how much would its theoretical maximum efficiency decrease if it had to switch to cooling towers that condense the steam at 47°C?
> A magnesium ion Mg2+ is accelerated through a potential difference of 22 kV. What is the de Broglie wavelength of this ion?
> A motorcycle is speeding on a straight, level highway at constant speed. At t = 0, the motorcycle passes a police car that is initially at rest. The officer gives chase, but the motorcyclist doesn’t notice and keeps moving at constant s
> An engine has a 30.0% efficiency. The engine raises a 5.00 kg crate from rest to a vertical height of 10.0 m, at which point the crate has a speed of 4.00 m/s. How much heat input is required for this engine?
> How many grams of carbohydrate does a person of mass 74 kg need to metabolize to climb five flights of stairs (15 m height increase)? Each gram of carbohydrate provides 17.6 kJ of energy. Assume 10.0% efficiency—that is, 10.0% of the available chemical e
> In Problem 6, what is the pile driver’s speed just before it strikes the pile?
> Two engines operate between the same two temperatures of 750 K and 350 K, and have the same rate of heat input. One of the engines is a reversible engine with a power output of 23 kW. The second engine has an efficiency of 42%. What is the power output o
> A certain engine can propel a 1800 kg car from rest to a speed of 27 m/s in 9.5 s with an efficiency of 27%. What are the rate of heat flow into the engine at the high temperature and the rate of heat flow out of the engine at the low temperature?
> The human body could potentially serve as a very good thermal reservoir, as its internal temperature remains quite constant at around 37°C and is stabilized by continual intake of food. Suppose an inventor designed microscopic engines that could be impla
> A model steam engine of 1.00 kg mass pulls eight cars of 1.00 kg mass each. The cars start at rest and reach a velocity of 3.00 m/s in a time of 3.00 s while moving a distance of 4.50 m. During that time, the net heat input is 135 J. What is the change i
> A new organic semiconductor device is able to generate electricity (which can be used to charge a battery or light an LED) using the warmth of human skin. If your skin temperature is maintained by your body at 35°C and the temperature of the surroundings
> (a) Find the heat flow into or out of the gas during each step, (b) Find the entropy change of the gas during the isothermal step. (c) What is the entropy change of the gas for a complete cycle? Is it equal in magnitude to the entropy change of the envir
> The motor that drives a refrigerator produces 148 W of useful power. The hot and cold temperatures of the heat reservoirs are 20.0°C and −5.0°C. What is the maximum possible amount of ice it can produce in 2.0 h from water that is initially at 8.0°C?
> (a) Calculate the work done by the engine during each step and the net work done per cycle. (b) If the heat input per cycle is 58.3 kJ, what is the efficiency?
> The outdoor temperature on a winter's day is −4°C. If you use 1.0 kJ of electric energy to run a heat pump, how much heat does that put into your house at 21°C? Assume that the heat pump is ideal.
> A crate of oranges weighing 180 N rests on a flatbed truck 2.0 m from the back of the truck. The coefficients of friction between the crate and the bed are μs = 0.30 and μk = 0.20. The truck drives on a straight, level highway at a constant 8.0 m/s. (a)
> Estimate the average blood pressure in a person’s foot if the foot is 1.37 m below the aorta, where the average blood pressure is 104 mmHg. For the purposes of this estimate, assume the blood isn’t flowing.
> You need to move a heavy crate by sliding it across a smooth floor. The coefficient of sliding friction is 0.2. You can either push the crate horizontally or pull the crate using an attached rope. When you pull on the rope, it makes a 30° angle with the
> Draw a PV diagram to illustrate the cycle for this engine. Label the axes with numerical values.
> An ideal refrigerator keeps its contents at 0.0°C and exhausts heat into the kitchen at 40.0°C. For every 1.0 kJ of work done, (a) how much heat is exhausted? (b) How much heat is removed from the contents?
> (a) Find the heat flow into or out of the gas during each of the four steps. (b) What is the net heat flow into the gas per cycle? (c) Calculate the change in entropy of the cold reservoir (not of the gas) in steps B and C and the change in entropy of
> At a tea party, a coffeepot and a teapot are placed on the serving table. The coffeepot is a shiny silver-plated pot with emissivity of 0.12; the teapot is ceramic and has an emissivity of 0.65. Both pots hold 1.00 L of liquid at 98°C when the party begi
> Find the change in internal energy of the gas during each of the four steps.
