The point of support of a simple pendulum of mass m and length b is driven horizontally by x = a sin wt. Find the pendulums equation of motion.

The method by which the massive lintels (top stones) were lifted to the top of the upright stones at Stonehenge has long been debated. One possible method was tested in a small Czech town. A concrete...

Two atmospheric sound sources A and B emit isotropically at constant power. The sound levels F of their emissions are plotted in Figure versus the radial distance r from the sources. The vertical...

The magnitude of the force vector F is 82.3 new tons. The x component of this vector is directed along the +x-axis and has a magnitude of 74.6 new tons. The y component points along the +y-axis. (a)...

Two gases in a mixture diffuse through a filter at rates proportional to the gases rms speeds. (a) Find the ratio of speeds for the two isotopes of chlorine, 35Cl and 37Cl, as they diffuse through...

In a certain series RLC circuit, Irms = 9.00 A, Vrms = 180 V, and the current leads the voltage by 37.0. (a) What is the total resistance of the circuit? (b) Calculate the reactance of the circuit...

An organ pipe has two successive harmonics with frequencies 1372 and 1764 Hz. (a) Is this an open or a stopped pipe? Explain. (b) What two harmonics are these? (c) What is the length of the pipe?

The block of mass m sliding without friction along the looped track shown in Fig. 6-39 is to remain on the track at all times, even at the very top of the loop of radius r. (a) In terms of the given...

A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the planes altitude?

One of the beams of an interferometer (Fig. 24-59) passes through a small glass container containing a cavity 1.30cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark...

Monochromatic electromagnetic radiation with wavelength A from a distant source passes through a slit. The diffraction pattern is observed on a screen 2.50 m from the slit. If the width of the...

When a hypothetical diatomic molecule having atoms 0.8860 nm apart undergoes a rotational transition from the l = 2 state to the next lower state, it gives up a photon having energy 8.841 x 10-4eV....

A point charge Q is located on the axis of a disk of radius R at a distance b from the plane of the disk (Fig. P24.68). Show that if one fourth of the electric flux from the charge passes through the...

A budding electronics hobbyist wants to make a simple 1.0-nF capacitor for tuning her crystal radio, using two sheets of aluminum foil as plates, with a few sheets of paper between them as a...

Stellar system Q1 moves away from us at a speed of 0.800c. Stellar system Q2, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c...

An ice tray contains 500 g of liquid water at 0C. Calculate the change in entropy of the water as it freezes slowly and completely at 0C.

Determine the current in each branch of the circuit shown in Figure P28.21. 3.00 5.00 1.00 8.00 1.00 12.0 V 4.00 V

Figure P30.23 is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, which is surrounded by an outer conductor, which is surrounded by another rubber...

Calculate the net torque about point 0 for the two forces applied as in Fig. 10.38. The rod and both forces are in the plane of the page. F2 120N F1 8.00N 30.0 K-2.00 m 3.00 m>

A fisherman notices that wave crests pass the bow of his anchored boat every 3.0s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?

As a new electrical engineer for the local power company, you are assigned the project of designing a generator of sinusoidal ac voltage with a maximum voltage of 120 V. Besides plenty of wire, you...

De Haas-van Alphen period of potassium (a) Calculate the period (1/B) expected for potassium on the free electron model. (b) What is the area in real space of the external orbit, for B 10kG = 1 T?...

A rock is thrown vertically upward from ground level at time t = 0. At t = 1.5 s it passes the top of a tall tower, and 1.0 s later it reaches its maximum height. What is the height of the tower?

A lossy material has = 5o, = 2o. If at 5 MHz, the phase constant is 10rad/m, calculate (a) The loss tangent (b) The conductivity of the material (c) The complex permittivity (d) The attenuation...

A stiff uniform wire of mass Mo and length La is cut, bent, and the parts soldered together so that it forms a circular wheel having four identical spokes coming out from the center. None of the wire...

(1). Formulate an appropriate boundary condition, to replace Eq. 9.27, for the case of two strings under tension T joined by a knot of mass m. (2). Find the amplitude and phase of the reflected and...

An airport terminal has a moving sidewalk to speed passengers through a long corridor. Larry does not use the moving sidewalk; he takes 150 s to walk through the corridor. Curly, who simply stands on...

Find the Thevenin equivalent looking into terminals a-b of the circuit in Fig. 4.110 and solve for ix? 10 a6 b 20V (+ 1012 5 2 A

The coefficient of static friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?

Let A be vector from the origin to point P fixed in space. Let r be a vector from the origin to a variable point Q (x1, x2, x3). Show that A r = A2 is the equation of a plane perpendicular to A and...

What is the angular speed of? (a) The second hand, (b) The minute hand, and (c) The hour hand of a smoothly running analog watch, answer in radians per second.

A horizontal vinyl record of mass 0.10 kg and radius 0.10 m rotates freely about a vertical axis through its center with an angular speed of 4.7 rad/s. The rotational inertia of the record about its...

Figure shows an "autotransformer." It consists of a single coil (with an iron core). Three taps Ti are provided. Between taps T1 and T2 there are 200 turns, and between taps T2 and T3 there are 800...

The magnetic field 40.0 cm away from a long, straight wire carrying current 2.00 A is 1.00 T. (a) At what distance is it 0.100 T? (b) At one instant, the two conductors in a long household extension...

An aluminum pipe, 0.655 m long at 20.0C and open at both ends, is used as a flute. The pipe is cooled to a low temperature but then is filled with air at 20.0C as soon as you start to play it. After...

In the situation described in Problem 20 and illustrated in Figure P12.20, the lift cable suddenly breaks! The hinge between the castle wall and the bridge is frictionless, and the bridge swings...

A current pulse is fed to the partial circuit shown in Figure P32.25. The current begins at zero, then becomes 10.0 A between t = 0 and t = 200 μs, and then is zero once again. Determine the...

A lightning flash transfers 4.0 C of charge and 4.2 MJ of energy to the Earth. (a) Across what potential difference did it travel? (b) How much water could this boil and vaporize, starting from room...

Suppose that f is a function of two variables (y and z) only. Show that the gradient f = (f/y)y + (f/z)z transforms as a vector under rotations, Eq. 1.29.

In Figure a rectangular slab of slate rests on a bedrock surface inclined at angle = 26. The slab has length L = 43 m, thickness Z = 2.5 m, and width 17 = 12 m, and 1.0 cm3 of it has a mass of 3.2...

The data shown in the accompanying table were obtained from a tensile test of high-strength steel. The test specimen had a diameter of 0.505 in. and a gage length of 2.00 in. (see figure for Prob....

Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.0 X 10 m/s when at a distance of 2.5 X 1011 m from the center of the sun, what is its speed when at...

Corrective Lenses determine the power of the corrective contact lenses required by (a) A hyperopic eye whose near point is at 60.0 cm and (b) A myopic eye whose far point is at 60.0cm.

A box of canned goods slides down a ramp from street level into the basement of a grocery store with acceleration 0.15 m/s 2 directed down the ramp. The ramp makes an angle of 40 with the horizontal....

In the arrangement of Figure we gradually pull the block from x = 0 to x = +3.0 cm, where it is stationary. Figure gives the work that our force does on the block. The scale of the figure's vertical...

A particle is confined to the one-dimensional infinite potential well of figure. If the particle is in its ground state, what is its probability of detection between?(a) x = 0 and x = 025L,(b) x =...

What is the difference in blood pressure (mm-Hg) between the top of the head and bottom of the feet of a 1.60-m-tall person standing vertically?

A free neutron is unstable and decays into a proton and an electron. How much energy other than the rest energies of the proton and electron is available if a neutron at rest decays? This is an...

A disk of radius 2.5 cm has a surface charge density of 5.3C/m2 on its upper face. What is the magnitude of the electric field produced by the disk at a point on its central axis at distance z = 12cm...

A baseball is hit at ground level. The ball reaches its maximum height above ground level 3.0 s after being hit. Then 2.5 s after reaching its maximum height, the ball barely clears a fence that is...

A certain storm cloud has a potential of 1.00 x 108 V relative to a tree. If, during a lightning storm, 50.0 C of charge is transferred through this potential difference and 1.00% of the energy is...

How many joules of energy does a 100-watt light bulb use per hour? How fast would a 70-kg person have to run to have that amount of kinetic energy?

A 3.0-g copper penny has a positive charge of 38C. What fraction of its electrons has it lost?

Two charges are placed as shown in Fig. 17-35 with q1 = 1.5μC and Q2 = 3.3μC. Find the potential difference between points A and B. 91 0.10 m 13 0.10 m

A power supply has a fixed output voltage of 12.0 V, but you need VT = 3.0V for an experiment. (a) Using the voltage divider shown in Fig. 19-66, what should R2 be if R1 is 10.0? (b) What will the...

Electromagnetic radiation is emitted by accelerating charges. The rate at which energy is emitted from an accelerating charge that has charge q and acceleration a is given by where c is the speed of...

A laser used to weld detached retinas puts out 28-ms-long pulses of 640-nm light which average 0.68-W output during a pulse. How much energy can be deposited per pulse and how many photons does each...

In Figure a crate slides down an inclined right-angled trough. The coefficient of kinetic friction between the crate and the trough ir ? k .What is the acceleration of the crate in terrns of ? k , ,...

A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed,...

In Figure, the four particles form a square of edge length a = 5.00 cm and have charges q 1 = + 10.0 nC, q 2 = 20.0 nC , q 3 = +20.0 nC, and q 4 = 10.0 nC. In unit-vector notation, what net electric...

An archer needs to hit a bulls eye on a target at eye level 60.0 ft away. If the archer fires the arrow from eye level with a speed of 47.0 ft/s at an angle of 25.0 above the horizontal, will the...

To an Earth observer, meter sticks on three spaceships are seen to have these lengths. Rank the speeds of the spaceships relative to Earth from highest to lowest. B C

Two blocks, one with mass m1 = 0.050 kg and one with mass m 2 = 0.030 kg, are connected to one another by a string. The inner block is connected to a central pole by another string as shown in the...

Two solid cylinders connected along their common axis by a short, light rod have radius R and total mass M and rest on a horizontal tabletop. A spring with force constant k has one end attached to a...

A typical cost for electric power is 12.0 per kilowatt-hour. (a) Some people leave their porch light on all the time. What is the yearly cost to keep a 75-W bulb burning day and night? (b) Suppose...

An infinite non-conducting sheet has a surface charge density = +5.80pC/m2. (a) How much work is done by the electric field due to the sheet if a particle of charge q = + 1.60 x 10-19 C is moved...

Calculate (a) The Fermi temperature and (b) The Fermi energy at T = 0 for iron.

Roads going up mountains are formed into switchbacks, with the road weaving back and forth along the face of the slope such that there is only a gentle rise on any portion of the roadway. Does this...

Vector A is in the negative y direction, and vector B is in the negative x direction. What are the directions of? (a) A X B (b) B X A?

A point charge q is imbedded at the center of a sphere of linear dielectric material (with susceptibility Xe and radius R). Find the electric field, the polarization, and the bound charge densities,...

In Figure a uniform beam of length 12.0 m is supported by a horizontal cable and a hinge at angle = 50.0?. The tension in the cable is 400 N. In unit-vector notation, what are?. (a) The...

The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during the...

How much electromagnetic energy per cubic meter is contained in sunlight, if the intensity of sunlight at the Earths surface under a fairly clear sky is 1 000 W/m2?

In Fig. 9.38, the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers. A light rope is wrapped around the cylinder. passes over the pulley, and...

Given the two charges shown in Fig. 16-68, at what position (s) x is the electric field zero? Is the field zero at my other points, not on the x axis? -Q2 d x-

A particle moves in a plane under the influence of a force f = Ara-1 directed toward the origin; A and a (> 0) are constants. Choose appropriate generalized coordinates, and let the potential energy...

Resolution of a Microscope The image formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. The eyepiece has a focal length of 26.0 mm. (a) What is the...

Coherent light with wavelength 400nm passes through two very narrow slits that are separated by 0.200 mm and the interference pattern is observed on a screen 4.00 m from the slits. (a) What is the...

A single slit is illuminated by light of wavelengths a and b chosen so that the first diffraction minimum of the ab component coincides with the second minimum of the b component. (a) If b = 350nm,...

A 12.0-m-long steel beam is accidentally dropped by a construction crane from a height of 9.00 m. The horizontal component of the Earths magnetic field over the region is 18.0 T. What is the induced...

A nurse needs to draw 20.0 cc of blood from a patient and deposit it into a small plastic container whose interior is at atmospheric pressure. He inserts the needle end of a long tube into a vein...

What is the thermal efficiency of an engine that operates by taking n moles of diatomic ideal gas through the cycle 1→2 → 3→4 →1 shown in Fig.20.27? 2po Po V. 2Vo Vo

A stone is dropped at t - 0. A second stone, with twice the mass of the first, is dropped from the same point at t = 100ms. (a) How far below the release point is the center of mass of the two stones...

A particle moves under the influence of a central force given by F(r) = k/rn, If the particles orbit is circular and passes through the force center, show that n = 5.

In Figure, wheel A of radius rA = 10 cm is coupled by belt B to wheel C of radius rc = 25 cm. The angular speed of wheel A is increased from rest at a constant rate of I.6 rad/s2. Find the time...

A rectangular cast-iron column 16.0 cm x 16.0 cm x 4.50 m supports a weight of 7.95 x 106 N. Find the stress on the top of the column.

In Figure two blocks are connected over a pulley. The mass of block A is 10 kg, and the coefficient of kinetic friction between A and the incline is 0.20. Angle of the incline is 30 o . Block 4...

A uniform, spherical, l000.0-kg shell has a radius of 5.00 m. (a) Find the gravitational force this shell exerts on a 2.00-kg point mass placed at the following distances from the center of the...

The rubidium isotope 87/37Rb, a emitter with a half-life of 4.75 X 1010 yr, is used to determine the age of rocks and fossils. Rocks containing fossils of ancient animals contain a ratio of 87/38Sr...

Para-magnetism of S = 1 system. (a) Find the magnetization as a function of magnetic field and temperature for a system of spins with S = 1, moment and concentration n. (b) Show that in the limit B...

What are? (a) The speed and (b) The period of a 220 kg satellite in an approximately circular orbit 640 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average...

A 1.2-m plank with a mass of 3 kg rests on two joists. Knowing that the coefficient of static friction between the plank and the joists is 0.30, determine the magnitude of the horizontal force...

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A Coil spring of mass m rests upright on a table. If you compress the spring by pressing down with your hand and then release it, can the spring leave table? Explain, using the law of conservation of...

Unpolarized light falls on two polarizer sheets whose transmission axes are at right angles. A third polarizer is placed between the first two so that its axis makes a 62o angle with the axis of the...

To pull a 50 kg crate across a horizontal frictionless floor, a worker applies a force of 210 N, directed 20o above the horizontal. As the crate moves 3.0 m, what work is done on the crate by (a) The...

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 5.0 s, it rotates 25 rad. During that time, what are the magnitudes of (a) The angular acceleration...

Party hearing as the number of people at a party increases you must raise your voice for a listener to hear you against the background noise of the other partygoers. However, once you reach the level...

(a) Find the speed of waves on a violin string of mass 800 mg and length 22.0 cm if the fundamental frequency is 920 Hz. (b) What is the tension in the string? For the fundamental, what is the...

A block is sliding on a frictionless surface along a loop-the-loop, as in Figure (a). The block is moving fast enough that it never loses contact with the track. Match the points along the track to...