Two blocks lie side by side on a frictionless table. The block on the left is of mass m; the one on the right is of mass 2m. The block on the right is pushed to the left with a force of magnitude F, pushing the other block in turn. What force does the block on the left exert on the block to its right?
> Show that, for an ideal gas, where P is the pressure, ρ is the mass density, and vrms is the rms speed of the gas molecules.
> (a) Calculate Earth's escape speed—the minimum speed needed for an object near the surface to escape Earth's gravitational pull. [Hint: Use conservation of energy and ignore air resistance.] (b) Calculate the average speed of a hydrogen molecule (H2) at
> What is the kinetic energy per unit volume in an ideal gas at (a) P = 1.00 atm and (b) P = 300.0 atm?
> Michael has set the gauge pressure of the tires on his car to 36.0 lb/in2. He draws chalk lines around the edges of the tires where they touch the driveway surface to measure the area of contact between the tires and the ground. Each front tire has a con
> What is the total translational kinetic energy of the gas molecules of air at atmospheric pressure that occupies a volume of 1.00 L?
> Each of five cylindrical drums with radius R is filled to a height h above the bottom with a liquid of density ρ. Rank the drums in order of the pressure at the bottom of the drum, largest to smallest. (a) R = 40 cm, h = 80 cm, ρ = 1000 kg/m3 (b) R = 40
> John drives 16 km directly west from Orion to Chester at a speed of 90 km/h, then directly south for 8.0 km to Seiling at a speed of 80 km/h, then finally 34 km southeast to Oakwood at a speed of 100 km/h. (a) What was the change in velocity during this
> A bimetallic strip is made from metals with expansion coefficients α1 and α2 (with α2 > α1). The thickness of each layer is s. At some temperature T0, the bimetallic strip is relaxed and straight
> What is the temperature of an ideal gas whose molecules have an average translational kinetic energy of 3.20 × 10−20 J?
> A wine barrel has a diameter at its widest point of 134.460 cm at a temperature of 20.0°C. A circular iron band, of diameter 134.448 cm, is to be placed around the barrel at the widest spot. The iron band is 5.00 cm wide and 0.500 cm thick. (a) To what
> Consider the expansion of an ideal gas at constant pressure. The initial temperature is T0 and the initial volume is V0. (a) Show that ΔV/V0 = β ΔT, where β = 1/T0. (b) Compare the coefficient of volume expansion β for an ideal gas at 20°C to the value
> Rank the time intervals in order of increasing speed.
> Two slits separated by 20.0 µm are illuminated by light of wavelength 0.50 µm. If the screen is 8.0 m from the slits, what is the distance between the m = 0 and m = 1 bright fringes?
> The inner tube of a Pyrex glass mercury thermometer has a diameter of 0.120 mm. The bulb at the bottom of the thermometer contains 0.200 cm3 of mercury. How far will the thread of mercury move for a change of 1.00°C? Remember to take into acco
> A bubble rises from the bottom of a lake of depth 80.0 m, where the temperature is 4°C. The water temperature at the surface is 18°C. If the bubble's initial diameter is 1.00 mm, what is its diameter when it reaches the surface? (Ignore the surface tensi
> A steel ring of inner diameter 7.000 00 cm at 20.0°C is to be heated and placed over a brass shaft of outer diameter 7.002 00 cm at 20.0°C. (a) To what temperature must the ring be heated to fit over the shaft? The shaft remains at 20.0°C. (b) Once the
> In the Netherlands, a dike holds back the sea from a town below sea level. The dike springs a leak 3.0 m below the water surface. If the area of the hole in the dike is 1.0 cm2, what force must the Dutch boy exert to save the town?
> Verify, using the ideal gas law, the assertion in Problem 38 that 1.00 mol of a gas at 0.0°C and 1.00 atm occupies a volume of 0.0224 m3.
> During hibernation, an animal's metabolism slows down, and its body temperature lowers. For example, a California ground squirrel's body temperature lowers from 40.0°C to 10.0°C during hibernation. If we assume that the air in the squirrel's lungs is 75.
> A mass of 0.532 kg of molecular oxygen is contained in a cylinder at a pressure of 1.0 × 105 Pa and a temperature of 0.0°C. What volume does the gas occupy?
> In uniform circular motion, is the velocity constant? Is the acceleration constant? Explain.
> A 10.0 L vessel contains 12 g of N2 gas at 20°C. (a) Estimate the nearest-neighbor distance. (b) Can the gas be considered to be dilute? [Hint: Compare the nearest-neighbor distance to the diameter of an N2 molecule, about 0.3 nm.]
> A tank of compressed air of volume 1.0 m3 is pressurized to 20.0 atm at T = 273 K. A valve is opened, and air is released until the pressure in the tank is 15.0 atm. How many molecules were released?
> The alveoli (see Section 13.8) have an average radius of 0.125 mm and are approximately spherical. If the pressure in the sacs is 1.00 × 105 Pa, and the temperature is 310 K (average body temperature), how many air molecules are in an alveolus?
> Rank the time intervals in order of increasing displacement, from largest negative to largest positive.
> In intergalactic space, there is an average of about one hydrogen atom per cubic centimeter and the temperature is 3 K. What is the absolute pressure?
> Show that, in two gases at the same temperature, the rms speeds are inversely proportional to the square root of the molecular masses:
> The density of platinum is 21 500 kg/m3. Find the ratio of the volume of 1.00 kg of platinum to the volume of 1.00 kg of aluminum.
> An ideal gas that occupies 1.2 m3 at a pressure of 1.0 × 105 Pa and a temperature of 27°C is compressed to a volume of 0.60 m3 and heated to a temperature of 227°C. What is the new pressure?
> Estimate the average distance between molecules in air at 0.0°C and 1.00 atm.
> A hydrogen balloon at Earth's surface has a volume of 5.0 m3 on a day when the temperature is 27°C and the pressure is 1.00 × 105 N/m2. The balloon rises and expands as the pressure drops. What would the volume of the same number of moles of hydrogen be
> A cylinder with an interior cross-sectional area of 70.0 cm2 has a moveable piston of mass 5.40 kg at the top that can move up and down without friction. The cylinder contains 2.25 × 10−3 mol of an ideal gas at 23.0°C. (a) What is the volume of the gas
> A constant volume gas thermometer containing helium is immersed in boiling ammonia (−33°C), and the pressure is read once equilibrium is reached. The thermometer is then moved to a bath of boiling water (100.0°C). After the manometer was adjusted to keep
> From the edge of the rooftop of a building, a boy throws a stone at an angle 25.0° above the horizontal. The stone hits the ground 4.20 s later, 105 m away from the base of the building. (Ignore air resistance.) (a) For the stone's path through the air,
> An ideal gas in a constant-volume gas thermometer (Fig. 13.11) is held at a volume of 0.500 L. As the temperature of the gas is increased by 20.0°C, the mercury level on the right side of the manometer must rise by 8.00 mm in order to keep the gas volume
> What is the mass density of air at P = 1.0 atm and T = (a) −10°C and (b) 30°C? The average molecular mass of air is approximately 29 u.
> The coefficient of static friction between a block and a horizontal floor is 0.35, while the coefficient of kinetic friction is 0.22. The mass of the block is 4.6 kg, and it is initially at rest. (a) What is the minimum horizontal applied force required
> A piano “string” is steel wire with radius 0.50 mm and length 1.2 m. It is under 800 N of tension. (a) What is the speed of transverse waves on the string? (b) What is the fundamental frequency for transverse waves? (c) What is the speed of longitudin
> What is the pressure on a fish 10 m under the ocean surface?
> A ball of mass 0.10 kg moving with speed 2.0 m/s hits a wall and bounces back with speed 1.0 m/s in the opposite direction. What is the change in the ball’s kinetic energy?
> Incandescent lightbulbs are filled with an inert gas to lengthen the filament life. With the current off (at T = 20.0°C), the gas inside a lightbulb has a pressure of 115 kPa. When the bulb is burning, the temperature rises to 70.0°C. What is the pressur
> The A string on a guitar has length 64.0 cm and fundamental frequency 110.0 Hz. The string's tension is 133 N. It is vibrating in its fundamental standing wave mode with a maximum displacement from equilibrium of 2.30 mm. The air temperature is 20.0°C.
> A patient with emphysema is breathing pure O2 through a face mask. The cylinder of O2 contains 0.0170 m3 of O2 gas at a pressure of 15.2 MPa. (a) What volume would the oxygen occupy at atmospheric pressure (and the same temperature)? (b) If the patient
> A 30.0 cm long string has a mass of 0.230 g and is vibrating at its third-lowest natural frequency f3. The tension in the string is 7.00 N. (a) What is f3? (b) What are the frequency and wavelength of the sound in the surrounding air if the speed of soun
> What fraction of the air molecules in a house must be pushed outside while the furnace raises the inside temperature from 16.0°C to 20.0°C? The pressure does not change since the house is not airtight.
> A child swinging on a swing set hears the sound of a whistle that is being blown directly in front of her. At the bottom of her swing when she is moving toward the whistle, she hears a higher pitch, and at the bottom of her swing when she is moving away
> Six cylinders contain ideal gases (not necessarily the same gas) with the properties given (P = pressure, V = volume, N = number of molecules). Rank them in order of temperature, highest to lowest. (a) P = 100 kPa, V = 4 L, N = 6 × 1023 (b) P = 200 kPa,
> Explain why the orbital radius and the speed of a satellite in circular orbit are not independent.
> (a) Show that since the bulk modulus has SI units N/m2 and mass density has SI units kg/m3, Eq. (12-1) gives the speed of sound in m/s. Thus, the equation is dimensionally consistent. (b) Show that no other combination of B and ρ can give dimensions of
> Someone steps on your toe, exerting a force of 500 N on an area of 1.0 cm2. What is the average pressure on that area in atm?
> A tire with an inner volume of 0.0250 m3 is filled with air at a gauge pressure of 36.0 lb/in2. If the tire valve is opened to the atmosphere, what volume outside of the tire does the escaping air occupy? Some air remains within the tire occupying the or
> During a rehearsal, all eight members of the first violin section of an orchestra play a very soft passage. The sound intensity level at a certain point in the concert hall is 38.0 dB. What is the sound intensity level at the same point if only one of th
> A cylinder in a car engine takes Vi = 4.50 × 10−2 m3 of air into the chamber at 30°C and at atmospheric pressure. The piston then compresses the air to one-ninth of the original volume (0.111 Vi) and to 20.0 times the original pressure (20.0 Pi). What is
> When playing fortissimo (very loudly), a trumpet emits sound energy at a rate of 0.800 W out of a bell (opening) of diameter 12.7 cm. (a) What is the sound intensity level right in front of the trumpet? (b) If the trumpet radiates sound waves uniformly
> A flight attendant wants to change the temperature of the air in the cabin from 18.0°C to 21.0°C without changing the pressure. What fractional change in the number of moles of air in the cabin would be required?
> According to a treasure map, a treasure lies at a depth of 40.0 fathoms on the ocean floor due east from the lighthouse. The treasure hunters use sonar to find where the depth is 40.0 fathoms as they head east from the lighthouse. What is the elapsed tim
> Sand is composed of SiO2. Find the order of magnitude of the number of silicon (Si) atoms in a grain of sand. Approximate the sand grain as a sphere of diameter 0.5 mm and an SiO2 molecule as a sphere of diameter 0.5 nm.
> Horseshoe bats use the Doppler effect to determine their location. A Horseshoe bat flies toward a wall at a speed of 15 m/s while emitting a sound of frequency 35 kHz. What is the beat frequency between the emission frequency and the echo?
> At 0.0°C and 1.00 atm, 1.00 mol of a gas occupies a volume of 0.0224 m3. (a) What is the number density? (b) Estimate the average distance between the molecules. (c) If the gas is nitrogen (N2), the principal component of air, what is the total mass a
> The orange jewelweed (Impatiens capensis) has seed pods that explode when lightly touched, launching the seeds as projectiles to disperse them. Suppose a seed is launched at 1.2 m/s from a height of 1.1 m. Assume air resistance is negligible and that the
> A bicycle has wheels of radius 0.32 m. Each wheel has a rotational inertia of 0.080 kg·m2 about its axle. The total mass of the bicycle including the wheels and the rider is 79 kg. When coasting at constant speed, what fraction of the total kinetic energ
> A jetliner flies east for 600.0 km, then turns 30.0° toward the south and flies another 300.0 km. (a) How far is the plane from its starting point? (b) In what direction could the jetliner have flown directly to the same destination (in a straight-line
> Bats of the Vespertilionidae family detect the distance to an object by timing how long it takes for an emitted signal to reflect off the object and return. Typically they emit sound pulses 3 ms long and 70 ms apart while cruising. (a) If an echo is hea
> (a) In Problem 49, find the beat frequency between the outgoing and reflected sound waves. (b) Show that the beat frequency is proportional to the speed of the blood cell if v ≪ u. [Hint: Use the binomial approximation from Appendix A.9.]
> A sound wave arriving at your ear is transferred to the fluid in the cochlea. If the intensity in the fluid is 0.80 times that in air and the frequency is the same as for the wave in air, what will be the ratio of the pressure amplitude of the wave in ai
> Doppler ultrasound is used to measure the speed of blood flow (see Problem 49). The reflected sound interferes with the emitted sound, producing beats. If the speed of red blood cells is 0.10 m/s, the ultrasound frequency used is 5.0 MHz, and the speed o
> Scuba divers are admonished not to rise faster than their air bubbles when rising to the surface. This rule helps them avoid the rapid pressure changes that cause the “bends.” Air bubbles of 1.0 mm radius are rising from a scuba diver to the surface of t
> The bat of Problem 55 emits a chirp that lasts for 2.0 ms and then is silent while it listens for the echo. If the beginning of the echo returns just after the outgoing chirp is finished, how close to the moth is the bat? [Hint: Is the change in distance
> In an aortic aneurysm, a bulge forms where the walls of the aorta are weakened. If blood flowing through the aorta (radius 1.0 cm) enters an aneurysm with a radius of 3.0 cm, how much on average is the blood pressure higher inside the aneurysm than the p
> A bat emits chirping sounds of frequency 82.0 kHz while hunting for moths to eat. If the bat is flying toward the moth at a speed of 4.40 m/s and the moth is flying away from the bat at 1.20 m/s, what is the frequency of the sound wave reflected from the
> If the cardiac output of a small dog is 4.1 × 10−5 m3/s, the radius of its aorta is 0.50 cm, and the aorta length is 40.0 cm, determine the pressure drop across the aorta of the dog. Assume the viscosity of blood is 4.0 × 10−3 Pa·s.
> Find the ratio of the rotational inertia of Earth for rotation about its own axis to its rotational inertia for revolution about the Sun.
> A ship mapping the depth of the ocean emits a sound of 38 kHz. The sound travels to the ocean floor and returns 0.68 s later. (a) How deep is the water at that location? (b) What is the wavelength of the wave in water? (c) What is the wavelength of th
> 100. At 3:00 P.M., a bank robber is spotted driving north on I-15 at milepost 126. His speed is 112.0 mi/h. At 3:37 P.M., he is spotted at milepost 185 doing 105.0 mi/h. During this time interval, what are the bank robber’s displacement, average velocity
> Two children ride on a merry-go-round. One is 2 m from the axis of rotation and the other is 4 m from it. Which child has the larger (a) linear speed, (b) acceleration, (c) angular speed, and (d) angular displacement?
> If you watch water falling from a faucet, you will notice that the flow decreases in radius as the water falls. This can be explained by the equation of continuity, since the cross-sectional area of the water decreases as the speed increases. If the wate
> A ship is lost in a dense fog in a Norwegian fjord that is 1.80 km wide. The air temperature is 5.0°C. The captain fires a pistol and hears the first echo after 4.0 s. (a) How far from one side of the fjord is the ship? (b) How long after the first ech
> Near sea level, how high a hill must you ascend for the reading of a barometer you are carrying to drop by 10 mmHg? Assume the temperature remains at 20°C as you climb. The reading of a barometer on an average day at sea level is 760 mmHg.
> The pitch of the sound from a race car engine drops the musical interval of a fourth when it passes the spectators. This means the frequency of the sound after passing is 0.75 times what it was before. How fast is the race car moving?
> The body of a 90.0 kg person contains 0.020 m3 of body fat. If the density of fat is 890 kg/m3, what percentage of the person’s body weight is composed of fat?
> Blood flow rates can be found by measuring the Doppler shift in frequency of ultrasound reflected by red blood cells (known as angiodynography). If the speed of the red blood cells is v, the speed of sound in blood is u, the ultrasound source emits waves
> The pressure in a water pipe in the basement of an apartment house is 4.10 × 105 Pa, but on the seventh floor it is only 1.85 × 105 Pa. What is the height between the basement and the seventh floor? Assume the water is not flowing; no faucets are opened.
> A 62 kg woman takes 6.0 s to run up a flight of stairs. The landing at the top of the stairs is 5.0 m above her starting place. (a) What is the woman’s average power output while she is running? (b) Would that be equal to her average power input—the ra
> A source and an observer are each traveling at 0.50 times the speed of sound. The source emits sound waves at 1.0 kHz. Find the observed frequency if (a) the source and observer are moving toward each other; (b) the source and observer are moving away
> The deepest place in the ocean is the Marianas Trench in the western Pacific Ocean, which is over 11.0 km deep. On January 23, 1960, the research sub Trieste went to a depth of 10.915 km, nearly to the bottom of the trench. This still is the deepest dive
> Fish don’t move as fast as you might think. A small trout has a top swimming speed of only about 2 m/s, which is about the speed of a brisk walk (for a human, not a fish!). It may seem to move faster because it is capable of large accelerations—it can da
> A speedboat is traveling at 20.1 m/s toward another boat moving in the opposite direction with a speed of 15.6 m/s. The speedboat pilot sounds his horn, which has a frequency of 312 Hz. What is the frequency heard by a passenger in the oncoming boat?
> An 1100 kg airplane starts from rest and accelerates horizontally forward for 8.0 s until it reaches its takeoff speed of 35 m/s. What is the average net force on the airplane during this time?
> An atomizer is a device that delivers a fine mist of some liquid such as perfume by blowing air horizontally over the top of a tube immersed in the liquid. Suppose a perfume with density 800 kg/m3 has a 3.0 cm tube extending vertically from the top of th
> In parts of the midwestern United States, sirens sound when a severe storm that may produce a tornado is approaching. Mandy is walking at a speed of 1.56 m/s directly toward one siren and directly away from another siren when they both begin to sound wit
> A very large vat of water has a hole 1.00 cm in diameter located a distance 1.80 m below the water level. (a) How fast does water exit the hole? (b) How would your answer differ if the vat were filled with gasoline? (c) How would your answer differ if
> At a factory, a noon whistle is sounding with a frequency of 500 Hz. As a car traveling at 85 km/h approaches the factory, the driver hears the whistle at frequency fi. After driving past the factory, the driver hears frequency ff. What is the change in
> Two identical beakers are filled to the brim and placed on balance scales. The base area of the beakers is large enough that any water that spills out of the beakers will fall onto the table the scales are resting on. A block of pine (density = 420 kg/m3
> How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.0 cm and a mass of 15.8 g. The laser scans at a constant tangential velocity of 1.20 m/s. Assume that the music is first detected at a ra
> An ambulance traveling at 44 m/s approaches a car heading in the same direction at a speed of 28 m/s. The ambulance driver has a siren sounding at 550 Hz. At what frequency does the driver of the car hear the siren?
> A 85.0 kg canoe made of thin aluminum has the shape of half of a hollowed-out log with a radius of 0.475 m and a length of 3.23 m. (a) When this is placed in the water, what percentage of the volume of the canoe is below the waterline? (b) How much add
> A cello string has a fundamental frequency of 65.40 Hz. What beat frequency is heard when this cello string is bowed at the same time as a violin string with frequency of 196.0 Hz? [Hint: The beats occur between the third harmonic of the cello string and
> (a) If a freestyle swimmer travels 1.50 km in a time of 14 min 53 s, how fast is his average speed? (b) If the pool is rectangular and 50 m in length, how does the speed you found compare with his sustained swimming speed of 1.54 m/s during one length o
> A block of aluminum that has dimensions 2.00 cm by 3.00 cm by 5.00 cm is suspended by a thread from a spring scale. (a) What is the scale reading in grams? (b) A beaker full of oil (density 850 kg/m3) rests on a second scale, which reads 460.0 g. The b
> A musician plays a string on a guitar that has a fundamental frequency of 330.0 Hz. The string is 65.5 cm long and has a mass of 0.300 g. (a) At what speed do the waves travel on the string? (b) What is the tension in the string? (c) While the guitar
