Prove that the expression for x(t) in Equation 15.55 is a solution to the equation of motion for a damped oscillator, Equation 15.54, if and only if the angular frequency is given by the expression...
Draw the snapshot graph D(x, t = 0 s) at t = 0 s for the wave shown in FIGURE EX16.6. D (cm) t (s) 1 2 3 4 5 6 -1| -2 1 History graph of a wave at x = 2 m Wave moving to the right at 1.0 m/s
What are the amplitude, wavelength, frequency, and phase constant of the traveling wave in FIGURE Q16.7? D (cm) 24 m/s 2- rX (m) 4 8 /12 16\ 20 -2. -4- Snapshot graph at t = 0 s FIGURE Q16.7
FIGURE Q16.9 shows the wave fronts of a circular wave. What is the phase difference between (a) Points A and B (b) Points C and D (c) Points E and F? D E A'
What are the amplitude, frequency, and wavelength of the wave in FIGURE EX16.14? D (cm) 6- 3- t (s) 0.2 /0.4 0.6\ 0.8 /1.0 -3- -6- History graph at x= 0 m Wave traveling left at 2.0 m/s FIGURE EX16.14
A loudspeaker on a tall pole broadcasts sound waves equally in all directions. What is the speakers power output if the sound intensity level is 90 dB at a distance of 20 m?
FIGURE P16.57 shows a snapshot graph of a wave traveling to the right along a string at 45 m/s. At this instant, what is the velocity of points 1, 2, and 3 on the string? D (cm) 45 m/s 2, 3 -2- 30 cm...
The string in FIGURE P16.60 has linear density μ. Find an expression in terms of M, μ, and θ for the speed of waves on the string. -Frictionless
The G string on a guitar is a 0.46-mm-diameter steel string with a linear density of 1.3 g/m. When the string is properly tuned to 196 Hz, the wave speed on the string is 250 m/s. Tuning is done by...
FIGURE P16.46 is a snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left. a. What is the wave speed? b. What is the phase constant of the wave? c. Write the displacement equation for this...
Is the displacement D(x, t) = (0.10 - 0.10x 2 + xt - 2.5t 2 ) m, where x is in m and t is in s, a possible traveling wave? If so, what is the wave speed?
If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat. What has happened to the energy of the wave at those instants?
Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by f n+1 = rf n for...
A gas undergoes the process shown in FIGURE Q18.10. By what factor does the temperature change? FIGURE Q18.10
A student is asked to sketch a pV diagram for a gas that goes through a cycle consisting of (a) An isobaric expansion, (b) A constant-volume reduction in temperature, (c) An isothermal process that...
A demented scientist creates a new temperature scale, the Z scale. He decides to call the boiling point of nitrogen 0Z and the melting point of iron 1000Z. a. What is the boiling point of water on...
A concrete bridge is built of 325-cm-long concrete slabs with an expansion joint between them. The slabs just touch on a 115F day, the hottest day for which the bridge is designed. What is the gap...
A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20C. a. How many moles of oxygen are in the cylinder? b. How many oxygen molecules are in the cylinder? c. What is the...
A gas at temperature T 0 and atmospheric pressure fills a cylinder. The gas is transferred to a new cylinder with three times the volume, after which the pressure is half the original pressure. What...
A gas with initial state variables p 1 , V 1 , and T 1 expands isothermally until V 2 = 2V 1 . What are (a) T 2 (b) p 2 ?
0.0040 mol of gas undergoes the process shown in FIGURE EX18.35. a. What type of process is this? b. What are the initial and final temperatures in °C? p (atm) 3- 2- V (cm) 300 0+ 100 200 FIGURE...
An ideal gas starts with pressure p 1 and volume V 1 . Draw a pV diagram showing the process in which the gas undergoes an isochoric process that doubles the pressure, then an isobaric process that...
An ideal gas starts with pressure p 1 and volume V 1 . Draw a pV diagram showing the process in which the gas undergoes an isothermal process during which the volume is halved, then an isochoric...
On a cool morning, when the temperature is 15C, you measure the pressure in your car tires to be 30 psi. After driving 20 mi on the freeway, the temperature of your tires is 45C. What pressure will...
10,000 cm3 of 200C steam at a pressure of 20 atm is cooled until it condenses. What is the volume of the liquid water? Give your answer in cm 3 .
The 50 kg circular piston shown in FIGURE P18.58 floats on 0.12 mol of compressed air.a. What is the piston height h if the temperature is 30?C?b. How far does the piston move if the temperature is...
FIGURE P18.61 shows two different processes by which 1.0 g of nitrogen gas moves from state 1 to state 2. The temperature of state 1 is 25?C. What are (a) Pressure p 1 (b) Temperatures (in ?C) T 2 ,...
4.0 g of oxygen gas, starting at 820°C, follow the process 1 2 shown in FIGURE P18.63. What is temperature T 2 (in °C)? P1 P2 2 0+ V2 V1 FIGURE P18.63
You are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a pV diagram. c. Finish the...
The cylinder in FIGURE CP18.72 has a moveable piston attached to a spring. The cylinders cross-section area is 10 cm 2 , it contains 0.0040 mol of gas, and the spring constant is 1500 N/m. At...
When strong winds rapidly carry air down from mountains to a lower elevation, the air has no time to exchange heat with its surroundings. The air is compressed as the pressure rises, and its...
Most stars are main-sequence stars, a group of stars for which size, mass, surface temperature, and radiated power are closely related. The sun, for instance, is a yellow main sequence star with a...
A satellite to reflect radar is a 2.0-m-diameter, 2.0-mm-thick spherical copper shell. While orbiting the earth, the satellite absorbs sunlight and is warmed to 50C. When it passes into the earths...
0.020 mol of a diatomic gas, with initial temperature 20C, are compressed from 1500 cm 3 to 500 cm 3 in a process in which pV 2 = constant. How much heat energy is added during this process?
Physicians use high-frequency (f = 195 MHz) sound waves, called ultrasound, to image internal organs. The speed of these ultrasound waves is 1480 m/s in muscle and 344 m/s in air. We define the index...
The professor once again returns the apparatus to its original setting, but now she adjusts the oscillator to produce sound waves of half the original frequency. What happens? (a) The students who...
A lottery machine uses blowing air to keep 2000 Ping-Pong balls bouncing around inside a 1.0 m 1.0 m 1.0 m box. The diameter of a Ping-Pong ball is 3.0 cm. What is the mean free path between...
For a monatomic gas, what is the ratio of the volume per atom (V/N) to the volume of an atom when the mean free path is ten times the atomic diameter?
The molecules in a six-particle gas have velocities Calculate (a) v avg , (b) v avg , (c) v rms . V1 = (20 30) m/s V2 = (40 + 70) m/s V3 = (-80 + 20) m/s V = 30 m/s Vs = (40 407) m/s 36 = (-50 ...
FIGURE EX20.10 is a histogram showing the speeds of the molecules in a very small gas. What are (a) The most probable speed, (b) The average speed, (c) The rms speed? N In. 3- 2- -v (m/s) FIGURE...
A cylinder contains gas at a pressure of 2.0 atm and a number density of 4.2 1025 m -3 . The rms speed of the atoms is 660 m/s. Identify the gas.
Atoms can be cooled to incredibly low temperatures by letting them interact with a laser beam. Various novel quantum phenomena appear at these temperatures. What is the rms speed of cesium atoms that...
During a physics experiment, helium gas is cooled to a temperature of 10 K at a pressure of 0.10 atm. What are (a) The mean free path in the gas, (b) The rms speed of the atoms, (c) The average...
The thermal energy of 1.0 mol of a substance is increased by 1.0 J. What is the temperature change if the system is (a) A monatomic gas, (b) A diatomic gas, (c) A solid?
4.0 mol of monatomic gas A interacts with 3.0 mol of monatomic gas B. Gas A initially has 9000 J of thermal energy, but in the process of coming to thermal equilibrium it transfers 1000 J of heat...
Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. After a long time has passed, you record the number of balls in each...
Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H 2 ). The number density is about 1 atom/cm 3 and the temperature is about 3 K. a. Estimate the...
a. Find an expression for the v rms of gas molecules in terms of p, V, and the total mass of the gas M. b. A gas cylinder has a piston at one end that is moving outward at speed v piston during an...
A monatomic gas is adiabatically compressed to 1/8 of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not? a....
An experiment youre designing needs a gas with = 1.50. You recall from your physics class that no individual gas has this value, but it occurs to you that you could produce a gas with = 1.50 by...
Rank in order, from largest to smallest, the thermal efficiencies 1 to 4 of the four heat engines in FIGURE Q21.5. Explain. Hot reservoir Hot reservoir 10 J 100 J 4 J 2 40 J 6J 60 J Cold reservoir...
A heat engine uses a diatomic gas in a Brayton cycle. What is the engines thermal efficiency if the gas volume is halved during the adiabatic compression?
The electric output of a power plant is 750 MW. Cooling water flows through the power plant at the rate 1.0 10 8 L/h. The cooling water enters the plant at 16C and exits at 27C. What is the power...
A heat engine with 0.20 mol of a monatomic ideal gas initially fills a 2000 cm 3 cylinder at 600 K. The gas goes through the following closed cycle: Isothermal expansion to 4000 cm 3 . Isochoric...
FIGURE P21.57 shows the cycle for a heat engine that uses a gas having Ï = 1.25. The initial temperature is T 1 = 300 K, and this engine operates at 20 cycles per second. a. What is the power...
The heat engine shown in FIGURE P21.62 uses 2.0 mol of a monatomic gas as the working substance. a. Determine T 1 , T 2 , and T 3 . b. Make a table that shows ÎE th , W s , and Q for each of...
A heat engine using a diatomic ideal gas goes through the following closed cycle: Isothermal compression until the volume is halved. Isobaric expansion until the volume is restored to its initial...
The rms speed of the molecules in 1.0 g of hydrogen gas is 1800 m/s. a. What is the total translational kinetic energy of the gas molecules? b. What is the thermal energy of the gas? c. 500 J of work...
A gas of 1.0 10 20 atoms or molecules has 1.0 J of thermal energy. Its molar specific heat at constant pressure is 20.8 J/mol K. What is the temperature of the gas?
Consider a container like that shown in Figure 20.12, with n 1 moles of a monatomic gas on one side and n 2 moles of a diatomic gas on the other. The monatomic gas has initial temperature T 1i ....
A glass rod that has been charged to +12 nC touches a metal sphere. Afterward, the rods charge is +8.0 nC. a. What kind of charged particle was transferred between the rod and the sphere, and in...
What is the total charge of all the electrons in 1.0 L of liquid water?
Metal spheres A and B in FIGURE Q22.11 are initially neutral and are touching. A positively charged rod is brought near A, but not touching. Is A now positive, negative, or neutral? Use both charge...
What are the strength and direction of an electric field that will balance the weight of a 1.0 g plastic sphere that has been charged to -3.0 nC?
A Van de Graaff generator is a device that accumulates electrons on a large metal sphere until the large amount of charge causes sparks. As youll learn in Chapter 23, the electric field of a charged...
What is the force F on the 1.0 nC charge at the bottom in FIGURE P22.46? Give your answer in component form. -6.0 nC 2.0 nC, 2.0 nC 5.0 cm 45 45 , 5.0 cm +, 1.0 nC FIGURE P22.46
A positive point charge Q is located at x = a and a negative point charge -Q is at x = -a. A positive charge q can be placed anywhere on the y-axis. Find an expression for (F net ) x , the x...
FIGURE P22.51 shows four charges at the corners of a square of side L. What is the magnitude of the net force on q? +, FIGURE P22.51 +. -0
Two equal point charges 2.5 cm apart, both initially neutral, are being charged at the rate of 5.0 nC/s. At what rate (N/s) is the force between them increasing 1.0 s after charging begins?
You have a lightweight spring whose un-stretched length is 4.0 cm. First, you attach one end of the spring to the ceiling and hang a 1.0 g mass from it. This stretches the spring to a length of 5.0...
Two 5.0 g point charges on 1.0-m-long threads repel each other after being charged to +100 nC, as shown in FIGURE P22.62. What is the angle θ? You can assume that θ is a...
An electric field E = 100,000 in N/C causes the 5.0 g point charge in FIGURE P22.67 to hang at a 20° angle. What is the charge on the ball? 120 5.0 g FIGURE P22.67
You are given the equation(s) used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem. (9.0 10 Nm/C)...
The force on the -1.0 nC charge is as shown in FIGURE CP22.76. What is the magnitude of this force? -1.0 nC 60 30 +. 5.0 cm FIGURE CP22.76 10 nC
An electric dipole is formed from two charges, q, spaced 1.0 cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point (x, y) = (0 cm, 10 cm) is 360...
An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment 1.0 10 -7 C m is 25...
A sphere of radius R has charge Q. The electric field strength at distance r > R is E i . What is the ratio E f /E i of the final to initial electric field strengths if (a) Q is halved, (b) R is...
Rank in order, from largest to smallest, the electric field strengths E 1 to E 5 at the five points in FIGURE Q23.11. Explain. 5. 2 3 FIGURE Q23.11 1 1 1 + + + + + + + + + +
A small object is released at point 3 in the center of the capacitor in FIGURE Q23.11. For each situation, does the object move to the right, to the left, or remain in place? If it moves, does it...
Two 10-cm-diameter charged rings face each other, 20 cm apart. The left ring is charged to -20 nC and the right ring is charged to +20 nC. a. What is the electric field E, both magnitude and...
A 20 cm 20 cm horizontal metal electrode is uniformly charged to +80 nC. What is the electric field strength 2.0 mm above the center of the electrode?
An electron is launched at a 45? angle and a speed of 5.0 10 6 m/s from the positive plate of the parallel-plate capacitor shown in FIGURE P23.52. The electron lands 4.0 cm away. a. What is the...
The two parallel plates in FIGURE P23.53 are 2.0 cm apart and the electric field strength between them is 1.0 Ã 10 4 N/C. An electron is launched at a 45° angle from the positive plate....
The ozone molecule O 3 has a permanent dipole moment of 1.8 10 -30 C m. Although the molecule is very slightly bentwhich is why it has a dipole momentit can be modeled as a uniform rod of length 2.5...
A thin cylindrical shell of radius R and length L, like a soda straw, is uniformly charged with surface charge density . What is the electric field strength at the center of one end of the cylinder?
A proton orbits a long charged wire, making 1.0 10 6 revolutions per second. The radius of the orbit is 1.0 cm. What is the wires linear charge density?
FIGURE EX24.1 shows two cross sections of two infinitely long coaxial cylinders. The inner cylinder has a positive charge, the outer cylinder has an equal negative charge. Draw this figure on your...
What is the electric flux through each of the surfaces A to E in FIGURE Q24.6? Give each answer as a multiple of q/ 0 . D E A + ) 3q C -)-3 FIGURE Q24.6
A small, metal sphere hangs by an insulating thread within the larger, hollow conducting sphere of FIGURE Q24.10. A conducting wire extends from the small sphere through, but not touching, a small...
A 2.0 cm 3.0 cm rectangle lies in the xy-plane. What is the magnitude of the electric flux through the rectangle if a. E = (100i - 200k) N/C? b. E = (100i- 200j) N/C?
FIGURE EX24.27 shows a hollow cavity within a neutral conductor. A point charge Q is inside the cavity. What is the net electric flux through the closed surface that surrounds the conductor? Closed...
A tetrahedron has an equilateral triangle base with 20-cm long edges and three equilateral triangle sides. The base is parallel to the ground, and a vertical uniform electric field of strength 200...
A spherically symmetric charge distribution produces the electric field E = (5000r 2 )r N/C, where r is in m. a. What is the electric field strength at r = 20 cm? b. What is the electric flux through...
A hollow metal sphere has inner radius a and outer radius b.The hollow sphere has charge + 2Q. A point charge + Q sits at thecenter of the hollow sphere. a. Determine the electric fields in the three...
An infinite slab of charge of thickness 2z 0 lies in the xy plane between z = -z 0 and z = +z 0 . The volume charge density (C/m 3 ) is a constant. a. Use Gausss law to find an expression for the...
The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gausss law to a Gaussian surface that is entirely...
An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nucleus) at the center of a sphere of radius R with uniformly...
All examples of Gausss law have used highly symmetric surfaces where the flux integral is either zero or EA. Yet weve claimed that the net Φ e = Q in /Ñ 0 is independent of the...