A force F in the positive direction of an x axis acts on an object moving along the axis. If the magnitude of the force is F = 10ex/2.0 N, with x in meters, find the work done by F as the object...
A signal in air (z ? 0) with the electric field component E = 10 sin ( w t +?3z) a x V/m hits normally the ocean surface at z =?0 as in figure. Assuming that the ocean surface is smooth and that ? =...
A rope of total mass m and length L is suspended vertically. Show that a transverse pulse travels the length of the rope in a time interval t = 2Lig. (Suggestion: First find an expression for the...
A wagon wheel is constructed as shown in Fig. 9.30. The radius of the wheel is 0.300 m, and the rim has mass 1.40 kg. Each of the eight spokes that lie along a diameter and are 0.300 m long has mass...
Use the results of Example 12.5 (Section 12.3) to calculate the escape speed for a spacecraft (a) From the surface of Mars; and (b) From the surface of Jupiter. Use the data in Appendix F. (c) Why is...
During the launch from a board, a diver's angular speed about her center of mass changes from zero to 6.20 rad/s in 220ms. Her rotational inertia about her center of mass is 12.0 kg-m2. During the...
A stone of mass m is thrown upward at an angle above the horizontal and feels no appreciable air resistance. Use conservation of energy to show that at its highest point, it is a distance V02 (sin2...
For a lightly damped oscillator, show that Q w0/w (Equation 3.65).
Compute the line integral of v = (r cos2 ) r ?? (r cos sin ) + 3r around the path shown in Fig. 1.50 (the points are labeled by their Cartesian coordinates). Do it either in cylindrical or in...
A solid copper sphere whose radius is 1.0 cm has a very thin surface coating of nickel. Some of the nickel atoms are radioactive, each atom emitting an electron as it decays. Half of these electrons...
The potential difference between the cloud and ground in a typical lightning discharge may be up to 100 MV (million volts). What is the gain in kinetic energy of an electron accelerated through this...
A pendulum is made of a uniform solid sphere with mass M and radius R suspended from the end of a light rod. The distance from the pivot at the upper end of the rod to the center of the sphere is L....
Don't Miss the Boal While on a visit to Minnesota ("Land of 10,000 Lakes''), you sign up to take an excursion around one of the larger lakes. When you go to the dock where the 1500- kg boat is tied,...
A 15 kg block is accelerated at 2.0m/s2 along a horizontal frictionless surface, with the speed increasing from 10 m/s to 30 m/s. What are? (a) The change in the block's mechanical energy and (b) The...
A block weighing 10.0 N is attached to the lower end of a vertical spring (k = 200.0 N/m), the other end of which is attached to a ceiling. The block oscillates vertically and has a kinetic energy of...
A cat rides a merry-go-round turning with uniform circular motion. At time t1 = 2.00 s, the cat's velocity is v1 = (3.00 m/s) i + (4.00 m/s) j, measured on a horizontal xy coordinate system. At t2 =...
A tightly stretched high wire is 46 m long. It sags 2.2m when a 60.0-kg tightrope walker stands at its center. What is the tension in the wire? Is it possible to increase the tension in the wire so...
A curve of radius 30 m is banked so that a 950- kg car traveling 40 km/h can round it even if the road is so icy that the coefficient of static friction is approximately zero. Find the range of...
Physicists, mathematicians, and others often deal with large numbers. The number 10100 has been given the whimsical name googol by mathematicians. Let us compare some large numbers in physics with...
A high-speed railway car goes around a flat, horizontal circle of radius 470 m at a constant speed. The magnitudes of the horizontal and vertical components of the force of the car on a 51.0 kg...
A vertical cylinder with a heavy piston contains air at a temperature of 300 K. The initial pressure is 200 kPa, and the initial volume is 0.350 m3. Take the molar mass of air as 28.9 g/mol and...
A police car at rest, passed by a speeder traveling at a constant 120km/h takes off in hot pursuit. The police officer catches up to the speeder in 750m, maintaining a constant acceleration. (a)...
A tuning fork is set into vibration above a vertical open tube filled with water (Fig. 12-35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is...
The chocolate crumb mystery this story begins with Problem 56 in Chapter 23 and continues through Chapters 24 and 25. The chocolate crumb powder moved to the silo through a pipe of radius R with...
The car-in-the-garage problem, car man has just purchased the world's longest stretch limo, which has a proper length of Lc = 30.5 m. In Figure a, it is shown parked in front of a garage with a...
A 1.00-mol sample of air (a diatomic ideal gas) at 300 K, confined in a cylinder under a heavy piston, occupies a volume of 5.00 L. Compute the final volume of the gas after 4.40 kJ of energy is...
A heat engine takes in 360 J of energy from a hot reservoir and performs 25.0 J of work in each cycle. Find (a) The efficiency of the engine and (b) The energy expelled to the cold reservoir in each...
A quarterback throws a football straight toward a receiver with an initial speed of 20.0 m/s, at an angle of 30.0 above the horizontal. At that instant, the receiver is 20.0 m from the quarterback....
Consider a damped oscillator as illustrated in Figures 15.21 and 15.22. Assume the mass is 375 g, the spring constant is 100 N/m, and b = 0.100 N4 s/m. (a) How long does it takes for the amplitude to...
A bellow, t bin-walled sphere of mass 12.0 kg and diameter 48.0 cm is rotating about an axle through its center. The angle (in radians) through which it turns as a function of time (in seconds) is...
The hay bale of Problem 11.77 is dragged along a horizontal surface with constant speed by a force F (Fig. 11.58). The coefficient of kinetic friction is 0.35. (a) Find the magnitude of the force F....
(a) Using the Bohr model, calculate the speed of the electron in a hydrogen atom in the n = 1,2 and 3 levels. (b) Calculate the orbital period in each of these levels. (c) The average lifetime of the...
Write down the (real) electric and magnetic fields for a monochromatic plane wave of amplitude E0, frequency co, and phase angle zero that is (a) Traveling in the negative x direction and polarized...
An iceboat has a constant velocity toward the east when a sudden gust of wind causes the iceboat to have a constant acceleration toward the east for a period of 3.0 s. A plot of x versus / is shown...
A train with proper length L moves at speed c/2 with respect to the ground. A ball is thrown from the back to the front, at speed c/3 with respect to the train. How much time does this take, and what...
1. A 10.0-kg mass has a potential energy of 10.0 J when it is at what height? 2. A 10.0-lb weight has a potential energy of 20.0 ft lb at what height? 3. At what speed does a 1.00-kg mass have a...
If the air pressure at a particular place in the mountains is 0.72atm, estimate the temperature at which water boils.
A mirror at an amusement park shows and upright image of any person who stand 1.4 m in front of it if the image is three times the persons height, what is the radius of curvature?
Derive the expression for the phase paths of the plane pendulum if the total energy is E > 2mgl. Note that this is just the case of a particle moving in a periodic potential U () = mgl (1 - cos ).
Use conservation of angular momentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20km, from a star whose radius was equal to that of our Sun (7 x 108m), of...
The planet Uranus has a radius of 25,560 km and a surface acceleration due to gravity of11.1 rn/s2 at its poles. Its moon Miranda (discovered by Kniper in 1948) is in a circular orbit about Uranus at...
A Constant-Volume Gas Thermometer An experimenter using a gas thermometer found the pressure at the triple point of water (0.01C) to be 4.80 X l04Pa and the pressure at the normal boiling point...
The critical density for closure of the universe is pc 10 26 kg/m3 state pc in terms of the average number of nucleons per cubic meter.
In an experiment, two protons are shot directly toward each other, each moving at half the speed of light relative to the laboratory. (a) What speed does one proton measure for the other proton? (b)...
A spring is suspended vertically from the ceiling of a room. When a mass is attached to the bottom of the spring, the amount of stretch is recorded. A plot of stretch versus mass is given in FIGURE...
If a particle is projected vertically upward to a height h above a point on Earths surface at a northern latitude , show that it strikes the ground at a point 4/3 w cos 8h3/g to the west (Neglect air...
An object lying on Earth's equator is accelerated (a) Toward the center of Earth because Earth rotates, (b) Toward the Sun because Earth revolves around the Sun in an almost circular orbit, and (c)...
Two points A and B on the surface of the Earth are at the same longitude and 60.0 apart in latitude. Suppose that an earthquake at point A creates a P wave that reaches point B by traveling straight...
Two circular loops are parallel, coaxial, and almost in contact, 1.00 mm apart (Fig. P30.59). Each loop is 10.0 cm in radius. The top loop carries a clockwise current of 140 A. The bottom loop...
A horizontal, uniform, copper rod has an original length 10, cross-sectional area A, Young's modulus Y, and mass m. It is supported by a frictionless pivot at its right end and by a cable at its left...
Find the dimension of the parallelepiped of maximum volume circumscribed by (a) A sphere of radius R; (b) An ellipsoid with semi axes a, b, c.
A cyclotron with a radius of 1.0m is to accelerate deuterons (2/1H) to an energy of 12MeV. (a) What is the required magnetic field? (b) What frequency is needed for the voltage between the dees? (c)...
When a certain photoelectric surface is illuminated with light of different wavelengths, the following stopping potentials are observed:Plot the stopping potential on the vertical axis against the...
In Figure, initially unpolarized light is sent into a system of three polarizing sheets whose polarizing directions make angles of 1 = 2 = 3 = 50? with the direction of the y axis. What percentage of...
(a) Where is the near point of an eye for which a contact lens with a power of + 2.75 diopters is prescribed? (b) Where is the far point of an eye for which a contact lens with a power of -1.30...
Ricardo, of mass 80 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 30 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.0 m apart and...
Two blocks, of masses M = 2.0 kg and 2M, are connected to a spring of spring constant k = 200 N/m that has one end fixed, as shown in Figure. The horizontal surface and the pulley are frictionless,...
A solar cooker consists of a curved reflecting surface that concentrates sunlight onto the object to be warmed (Fig. P20.63), the solar power per unit area reaching the Earths surface at the location...
Air in a thundercloud expands as it rises. If its initial temperature is 300 K and no energy is lost by thermal conduction on expansion, what is its temperature when the initial volume has doubled?
An R-C circuit has a time constant RC. (a) If the circuit is discharging, how long will it take for its stored energy to be reduced to 1/e of its initial value? (b) If it is charging, how long will...
A Charged Dielectric Disk. A thin disk of dielectric material with radius a has a total charge + Q distributed uniformly over its surface. It rotates n times per second about an axis perpendicular to...
In Figure two speakers separated by distance dt = 2.00 m are in phase. Assume the amplitudes of the sound waves from the speakers are approximately the same at the listener's ear at distance d2 =...
Consider a thin disk composed of two homogeneous halves connected along a diameter of the disk. If one half has density p and the other has density 2p, find the expression for the Lagrangian when the...
A particle of mass m at the end of a light string wraps itself about a fixed vertical cylinder of radius a (Figure 9-F). All the motion is in the horizontal plane (disregard gravity). The angular...
An atomic spectrum contains a line with a wavelength centered at 488nm. Careful measurements show the line is really spread out between 487and 489 nm. Estimate the lifetime of the excited state that...
Stars located in a certain cluster are assumed to be about the same distance from us. Two such stars have spectra that peak at 1 = 500 nm and 2 = 700nm, and the ratio of their apparent brightness is...
The coefficient of static friction between a rubber tire and the road surface is 0.85. What is the maximum acceleration of a 1000-kg four-wheel-drive truck if the road makes an angle of 12 with the...
Accelerometer the system shown in Fig. 5.76 can be used to measure 1he acceleration of 1he system. An observer riding on the platform measures the angle θ that the 1hread supporting the light...
(a) Show that the lens equation can be written in the Newtonian form xx` = f2, where x is the distance of the object from the focal point on the front side of the lens, and x` is the distance of the...
Show that the standing wave f(z, t) = A sin(kz) cos(kvt) satisfies the wave equation, and express it as the sum of a wave traveling to the left and a wave traveling to the right (Eq. 9.6).
A 6090 kg space probe moving nose-first toward Jupiter at 105 m/s relative to the Sun fires its rocket engine, ejecting 80.0 kg of exhaust at a speed of 253 m/s relative to the space probe. What is...
Figure shows a spherical shell with uniform volume charge density p = 1.84nC/m3, inner radius a = 10.0 cm, and outer radius b = 2.00a.What is the magnitude of the electric field at radial distances...
In basketball, hang is an illusion in which a player seems to weaken the gravitational acceleration while in midair. The illusion depends much on a skilled player's ability to rapidly shift the ball...
Two loudspeakers, A and B, radiate sound uniformly in all directions in air at 20°C. The acoustic power output from A is 8.00 X 10-4 W, and from B it is 6.00 X 10-5 W. Both loudspeakers are...
A beat engine takes 0.350 mol of a diatomic ideal gas around the cycle shown in the pV-diagram of fig. 20.24. Process I 2 is at constant volume, process 23 is adiabatic, and process 3 1 is at a...
An L-R-C series circuit is connected to a 120-Hz ac source that has Vrms = 80.0 V. The circuit has a resistance of 75.0 and an impedance at this frequency of 105. What average power is delivered to...
Over a certain region of space, the electric potential is V = 5x - 3x2y + 2yz2. Find the expressions for the x, y, and z components of the electric field over this region. What is the magnitude of...
A person is working near the secondary of a transformer, as shown in Figure P33.25. The primary voltage is 120 V at 60.0 Hz. The capacitance Cs, which is the stray capacitance between the hand and...
A uniform, solid metal disk of mass 6.50 kg and diameter 24.0 cm bangs in a horizontal plane, supported at its center by a vertical metal wire. You find that it requires a horizontal force of 4.23 N...
Hydraulic Lift L the hydraulic lift shown in Fig. 14.8, what must be the ratio of the diameter of the vessel at the car to the diameter of the vessel where the force F, is applied so that a 1520-kg...
The wire semicircles shown in Fig. have radii a and b. Calculate the net magnetic field (magnitude and direction) that the current in the wires produces at point P. b' Ca
Two long, parallel conductors, separated by 10.0 cm, carry currents in the same direction. The first wire carries current I1 = 5.00 A and the second carries I 2 = 8.00 A. (a) What is the magnitude of...
A brass lid screws tightly onto a glass jar at 20oC. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 60oC. The...
Quantum Effects in Daily Life a 1.25-mg insect flies through a 4.00-mm-diameter hole in an ordinary window screen. The thickness of the screen is 0.500 mm. (a) What should be the approximate...
The temperature and pressure in the Sun's atmosphere are 2.00 x 106 K and 0.0300 Pa. Calculate the rms speed of free electrons (mass 9.11 x 10-31 kg) there, assuming they are an ideal gas.
Suppose 200 J of work is done on a system and 70.0 cal is extracted from the system as heat. In the sense of the first law of thermodynamics, what are the values (including algebraic signs) of (a) W,...
A cantilever beam of rectangular cross section is subjected to a concentrated load P = 17 k acting at the free end (see figure). The beam has width b = 3 in. and height h = 12 in. Point A is located...
At what temperature would the average speed of helium atoms equal? (a) The escape speed from Earth, 1.12 X 104 m/s and (b) The escape speed from the Moon, 2.37 X 103 m/s? (See Chapter 13 for a...
Suppose a current is given by the equation l = 1.80sin 210r, where l is in amperes and t in seconds. (a) What is the frequency? (b) What is the rms value of the current? (c) If this is the current...
Consider a hot automotive engine, which can be approximated as a 0.5-m-high, 0.40-m-wide, and 0.8-m-long rectangular block. The bottom surface of the block is at a temperature of 80C and has an...
Calculate the wavelength of a 0.23-kg ball traveling at 0.10m/s.
Suppose that the electric average power consumption, day and night, in a typical house is 950W. What initial mass of 235/92U would have to undergo fission to supply the electrical needs of such a...
Calculate the wavelength of 35-GeV electrons.
The quarter-car weight of a certain vehicle is 625 lb and the weight of the associated wheel and axle is 190 lb. The suspension stiffness is 8000 lb/ft and the tire stiffness is 10,000 lb/ft. If the...
Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one balls initial speed was 2.00m/s, and the others was 3.00m/s in the opposite direction, what will be their speeds...
Estimate the total mass of the Earths atmosphere, using the known value of atmospheric pressure at sea level.
Samples of copper, aluminum, and water experience the same temperature rise when they absorb the same amount of heat. What is the ratio of their masses?
A typical banana contains 400mg of potassium, of which a small fraction is the radioactive isotope 40/19K (see Appendix B). Estimate the activity of an average banana due to 40/19K.
(a) Let F1 = x2 z and F2 = x x + y y + z z. Calculate the divergence and curl of F1 and F2. Which one can be written as the gradient of a scalar? Find a scalar potential that does the job. Which one...
It may have occurred to you that since parallel currents attract, the current within a single wire should contract into a tiny concentrated stream along the axis. Yet in practice the current...