Figure 35.25 shows an interferometer known as Fresnel's biprism. The magnitude of the prism angle A is extremely small.(a) If S0 is a very narrow source slit, show that the separation of the two...

(a) Carbon nanotubes are one of the stiffest and strongest materials known to scientists and engineers. Carbon nanotubes have an elastic modulus of 1.1 TPa (1 TPa = 1012 Pa). If a carbon nanotube has...

An excited hydrogen atom could, in principle, have a radius of 1.00mm. What would be the value of n for a Bohr orbit of this size? What would its energy be?

An object in the shape of a thin ring has radius a and mass M. A uniform sphere with mass m and radius R is placed with its center at a distance x to the right of the center of the ring, along a line...

A glass sphere has radius R = 5.0cm and index of refraction 1.6. A paperweight is constructed by slicing through the sphere along a plane that is 2.0cm from the center of the sphere, leaving height h...

Figure P2.17 shows a graph of vx versus t for the motion of a motorcyclist as he starts from rest and moves along the road in a straight line. (a) Find the average acceleration for the time interval...

Neutron Star Glitches Occasionally, a rotating neutron star (see Exercise 10.39) undergoes a sudden and unexpected speedup called a glitch. One explanation is that a glitch occurs when the crust of...

If the field vector is independent of the radial distance within a sphere, find the function describing the density p = p(T) of the sphere.

When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 76 cm and for rotation less than 1 rev, what are the (a)...

A constant potential difference of 12 V is maintained between the terminals of a 0.25-F, parallel-plate, air capacitor. (a) A sheet of Mylar is inserted between the plates of the capacitor,...

A dive bomber has a velocity of 280 m/s at an angle below the horizontal. When the altitude of the aircraft is 2.15 km, it releases a bomb, which subsequently hits a target on the ground. The...

A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 2.50 s. You may ignore air resistance, so the brick is in free fall. (a) How tall, in meters, is...

The earth, which is not a uniform sphere, has a moment of inertia of 0.3308MR2 about an axis through its north and south poles. It takes the earth 86,164 s to spin once about this axis. Use Appendix...

An inextensible cable with a tension force f = 500 N is used to pull a two-wheeled cart on a horizontal surface. The wheels roll without slipping. The cart has a mass mc = 120 kg. Each wheel has a...

A 1500-kg rocket is to be launched with an initial upward speed of 50.0 m/s. In order to assist its engines, the engineers will start it from rest on a ramp that rises 53° above the horizontal...

A 1.8-m3 rigid tank contains steam at 220oC. One-third of the volume is in the liquid phase and the rest is in the vapor form. Determine (a) The pressure of the steam, (b) The quality of the...

(a) Determine the work done on a fluid that expands from i to f as indicated in Figure P20.24. (b) What If? How much work is performed on the fluid if it is compressed from f to i along the same path?

An object with mass m initially at rest is acted on by a force F = kli, + k2t3j, where kl and k2 are constants. Calculate the velocity v(t) of the object as a function of time.

(a) Two protons in a molecule are separated by 3.80 x 1010 m. Find the electric force exerted by one proton on the other. (b) How does the magnitude of this force compare to the magnitude of the...

A 5.00-kg block is moving at Vo = 6.00 m/s along a frictionless, horizontal surface toward a spring with force constant k = 500 N/m that is attached to a wall (Fig. 6.36). The spring has negligible...

Two very large horizontal sheets are 4.25 cm apart and carry equal but opposite uniform surface charge densities of magnitude . You want to use these sheets to hold stationary in the region between...

For no apparent reason, a poodle is running at a constant speed of v ~ 5.00 m/s in a circle with radius R = 2.50 m. Let VI be the velocity vector at time t" and let V2 be the velocity vector at time...

A hockey puck with mass 0.160 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of the rink. At time t = 0 a player applies a force of 0.250 N to the puck, parallel to the...

Calculate the gravitational potential due to a thin rod of length l and mass M at a distance R from the center of the rod and in a direction perpendicular to the rod.

Two masses m1 = 100 g and m2 = 200g slide freely in a horizontal frictionless track and are connected by a spring whose force constant is k = 0.5 N/m. Find the frequency of oscillatory motion for...

An object of mass m starts from rest and slides a distance d down a frictionless incline of angle &. While sliding, it contacts an unstressed spring of negligible mass as shown in Figure P8.10. The...

A violin string has a length of 0.350 m and is tuned to concert G, with fG = 392 Hz. Where must the violinist place her finger to play concert A, with fA = 440 Hz? If this position is to remain...

In Figure a 0.250 kg block of cheese lies on the floor of a 900 kg elevator cab that is being pulled upward by a cable through distance d1 = 2.40 m and then through distance d2 = 10.5 m. (a) Through...

A circular coil 16.0cm in diameter and containing nine loops lies flat on the ground. The Earths magnetic field at this location has magnitude 5.50 X 10-5 T and Points into the Earth at an angle of...

An electron's position is given by r = 3.00ti 4.00t 2 j + 2.00k, with t in seconds and r in meters. (a) In unit vector notation, what is the electron's velocity v (t)? At t = 2.00 s, what is v (b)...

A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each...

Figure P2.24 represents part of the performance data of a car owned by a proud physics student. (a) Calculate from the graph the total distance traveled. (b) What distance does the car travel between...

A Ball Rolling Uphill, A bowling ball rolls without slipping up a ramp that slopes upward at an angle p to the horizontal (see Example 10.7 in Section 10.3). Treat the ball as a uniform, solid...

A 2.40-kg, 50.0-cm-Iong uniform bar has a small 1.l0-kg mass glued to its left end and a small 2.20-kg mass glued to the other end. You want to balance this system horizontally on a fulcrum placed...

In a game of pool, the cue ball strikes another ball of the same mass and initially at rest. After the collision, the cue ball moves at 3.50 m/s along a line making an angle of 22.0o with the cue...

In Figure a block slides along a path that is without friction until the block reaches the section of length L = 0.75m, which begins at height h = 2.0m on a ramp of angle = 30 o . In that section,...

Two concentric spherical shells with uniformly distributed masses M1 and M2 are situated as shown in Figure. Find the magnitude of the net gravitational force on a particle of mass m, due to the...

A thin lens with a focal length of 6.00 cm is used as a simple magnifier. (a) What angular magnification is obtainable with the lens if the object is at the focal point? (b) When an object is...

A bag of cement of weight 325 N hangs from three wires as suggested in Figure P5.18. Two of the wires make angles θ1 = 60.0° and θ1 = 25.0° with the horizontal. If the system is...

A child having a mass of 50 kg holds her legs up as shown as she swings downward from rest at 01 = 30o. Her center of mass is located at point G1. When she is at the bottom position θ = 0o, she...

Light with wavelength 648nm in air is incident perpendicularly from air on a film 8.76m thick and with refractive index 1.35. Part of the light is reflected from the first surface of the film, and...

Figure 12-32 shows various positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position a through E, will the child hear the...

Spheres A (mass 0.020 kg), B (massO.030kg) and C (mass 0.050 kg) are approaching the origin as they slide on a frictionless air table (Fig. 8.41). The initial velocities of A and B are given in the...

(a) Determine the wavelength of the second Balmer line (n = 4 to n = 2 transition) using Fig. 27-27. Determine likewise (b) The wavelength of the second Lyman line and (c) The wavelength of the third...

Barium has a work function of 2.48eV. What is the maximum kinetic energy of electrons if the metal is illuminated by UV light of wavelength 365nm? What is their speed?

Coherent light of frequency 6.32 x 1014 Hz passes through two thin slits and falls on a screen 85.0 cm away. You observe that the third bright fringe occurs at 3.11 cm on either side of the central...

A cannon located 60.0 m from the base of a vertical 25.O-mtall cliff, shoots a 15-kg shell at 43.0 o above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the shell...

A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare (a) The average kinetic energies of the three types of atoms and; (b) The root-mean-square speeds. (Hint: The...

A cockroach of mass m lies on the rim of a uniform disk of mass 4.00m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular...

A 2.00-nF capacitor with an initial charge of 5.10 C is discharged through a 1.30-k resistor. (a) Calculate the current in the resistor 9.00 s after the resistor is connected across the terminals of...

You are testing a new amusement park roller coaster with an empty car with mass 120 kg. One part of the track is a vertical loop with radius 12.0 m. At the bottom of the loop (point A) the car has...

A wire with mass 40.0 g is stretched so that its ends are tied down at points 80.0 cm apart. The wire vibrates in its fundamental mode with frequency 60.0 Hz and with amplitude at the antinodes of...

Particles of charge + 75 + 48, and 85μC are placed in a line (Fig. 16-49). The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two. -85 C +48...

SHM of a Floating Object An object with height h, mass M, and a uniform cross-sectional area A floats upright in a liquid with density p. (a) Calculate the vertical distance from the surface of the...

A house at the bottom of a hill is fed by a full tank of water 5.0 m deep and connected to the house by a pipe that is 110m long at an angle of 58o from the horizontal (Fig. 10-50). (a) Determine the...

The three balls each have the same mass m. if A has a speed v just before a direct collision with Bv determine the speed of C after collision. The coefficient of restitution between each ball is e....

What is the average zenith angle given the following direct and reversed readings? Direct: 94o 23' 48'', 94 o 23' 42'', 94 o 23' 44'' Reversed: 265 o 36' 20'', 265 o 36' 24'', 265 o 36' 22'' In...

Use the work-energy' theorem to solve each of these problems. You can use Newton's laws to check your answers. Neglect air resistance in sell cases. (a) A branch falls from the top of a 95.0.m-tall...

In the Bainbridge mass spectrometer (see Fig.), the magnetic Field magnitude in the velocity selector is 0.650 T, and ions having a speed of 1.82 X 106 m/s pass through undeflected. (a) What is the...

A beam of polarized light passes through a polarizing filter. When the angle between the polarizing axis of the filter and the direction of polarization of the light is , the intensity of the...

Figure is an idealized schematic drawing of a rail gun. Projectile P sits between two wide rails of circular cross section; a source of current sends current through the rails and through the...

A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x( t) = SO.O cm + (2.00...

The summit of a mountain, 2450m above base camp, is measured on a map to be 4580m horizontally from the camp in a direction 32.4o west of north. What are the components of the displacement vector...

The spool, which has a mass of 4 kg, slides along the rotating rod. At the instant shown, the angular rate of rotation of the rod is θ = 6 rad/s and this rotation is increasing at θ = 2...

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. But she does have devices to measure distance and time accurately. She knows her own mass is 78.4 kg,...

Coherent light from a sodium-vapor lamp is passed through a filter that blocks everything except light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting...

In the circuit shown in Fig. 30.30, neither the battery nor the inductors have any appreciable resistance, the capacitors are initially uncharged, and the switch S has been in position 1 for a very...

A rocket fires two engines simultaneously. One produces a thrust of 725 N directly forward, while the other gives a 513-N thrust at 3240 above the forward direction. Find the magnitude and direction...

If a loop of chain is spun at high speed, it can roll along the ground like a circular hoop without slipping or collapsing. Consider a chain of uniform linear mass density whose center of mass...

A 0.45-kg ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75N, what...

A worker pours 1.250 kg of molten lead at a temperature of 365.0oC into 0.5000 kg of water at a temperature of 75.00oC in an insulated bucket of negligible mass. Assuming no heat loss to the...

If you put a uniform block at the edge of a table the center of the block must be over the table for the block not to fall off. (a) If you stack two identical blocks at the table edge, the center of...

Refer to Example 4.1. If each of the springs must be stretched a distance d to attach the particle at the equilibrium position (i.e., in its equilibrium position, the particle is subject to two equal...

A 750.0-kg boulder is raised from a quarry 125 m deep by a long uniform chain having a mass of 575 kg. This chain is of uniform strength, but at any point it can support a maximum tension no greater...

Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in grams. The atomic masses of these atoms are 4.00 u, 55.9 u, and 207 u, respectively.

Figure shows three forces applied to a trunk that moves leftward by 3.00 m over a frictionless floor. The force magnitudes ate F1 = 5.00N, F2 = 9.00N, and F3 = 3.00 N, and the indicated angle is ? =...

Consider the fusion reaction 21H + 21 H 32He + 10n (a) Estimate the barrier energy by calculating the repulsive electrostatic potential energy of the two 21H nuclei when they touch. (b) Compute the...

A very light rigid rod with a length of 0.500 m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation. (a)...

A uniformly charged disk of radius 35.0 cm carries charge with a density of 7.90 & 10"3 C/m2. Calculate the electric field on the axis of the disk at (a) 5.00 cm, (b) 10.0 cm, (c) 50.0 cm, and (d)...

A jet fighter pilot knows he is able to withstand an acceleration of 9g before blacking out. The pilot points his plane vertically down while traveling at Mach 3 speed and intends to pull up in a...

Blood pressure in Argentinosaurus. (a) If this long-necked, gigantic sauropod had a head height of 21 m and a heart height of 9.0 m, what (hydrostatic) gauge pressure in its blood was required at the...

An infinitely long conductor is bent into an L shape as shown in figure. If a direct current of 5 A flows in the current, find the magnetic field intensity at? (a) (2, 2, 0), (b) (0, ? 2, 0), and?...

(a) Find to three significant digits the charge and the mass of an ionized hydrogen atom, represented as H+. Suggestion: Begin by looking up the mass of a neutral atom on the periodic table of the...

A 10 kg brick moves along an x axis. Its acceleration as a function of its position is shown in Fig. 7-40.The scale of the figure's vertical axis is set by as = 20.0 m/s2. What is the net work...

Using the data of Example 10-11, calculate the average speed of blood flow in the major arteries of the body, which have a total cross-sectional area of about 2.0cm2.

Form factor of atomic hydrogen for the hydrogen atom is its ground state, the number density is n(r) = (a 0 3 ) 1 exp ( 2r/a 0 ), where a0 is the Bohr radius. Show that the form factor is f G = 16/...

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 1014 times as great as that of...

A car starts rolling down a 1-in-4 hill (1-in-r mean that for each 4m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55m? (a)...

A piece of material, suspected of being a stolen diamond (n = 2.42), is submerged in oil of refractive index 1.43 and illuminated by Unpolarized light. It is found that the reflected light is...

An ice puck of mass m revolves on an icy surface in a circle at speed v at the end of a horizontal string of length L. The tension in the string is T. a. Write the equation for centripetal force, and...

In Figure sound of wavelength 0.850 m is emitted isotropically by point source S. Sound ray I extends directly to detector D, at distance L = 10.0 m. Sound ray 2 extends to D via a reflection...

You will find in Chapter 39 that electrons cannot move in definite orbits within atoms, like the planets in our solar system. To see why, let us try to "observe" such an orbiting electron by using a...

Four point charges are at the corners of a square of side a as shown in Figure P23.21. (a) Determine the magnitude and direction of the electric field at the location of charge q. (b) What is the...

A solid, insulating sphere of radius a has a uniform charge density 1 and a total charge Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and...

A crate of 45.0-kg tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it and observe that the crate just begins to move when your force exceeds 313 N. After that...

How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is incident normally? What if the glass is to appear dark?

In an L-R-C series circuit, L = 0.280 H and C = 4.00F. The voltage amplitude of the source is 120 V. (a) What is the resonance angular frequency of the circuit? (b) When the source operates at the...

In Figure sound waves A and B, both of wavelength , are initially in phase and traveling rightward, as indicated by the two rays. Wave A is reflected from four surfaces but ends up traveling in its...

Volume of Brillouin zone show that the volume of the first Brillouin zone is (2) 3 /V c , where V c is the volume of a crystal primitive cell. Recall the vector identity (e x a) x (a x b) = (e a x...

Two long, parallel transmission lines, 40.0 cm apart, carry 25.0-A and 75.0-A currents. Find all locations where the net magnetic field of the two wires is zero if these currents are in (a) The same...