Continuation of Problems 2 and 39, another explanation is that the stones move only when the water dumped on the playa during a storm freezes into a large, thin sheet of ice. The stones are trapped...

A golf ball is launched at an angle of 20 to the horizontal, with a speed of 60 m/s and a rotation rate of 90 rad/s. Neglecting air drag, determine the number of revolutions the ball makes by the...

Wave Equation and Standing Waves. (a) Prove by direct substitution that y(x, t) = (Aswsinkx) sin wt is a solution of the wave equation, Eq. (I5.12), for u = w/k. (b) Explain why the relationship u =...

An object with mass 3.0 kg is attached to a spring with spring stiffness constant k = 280N/m and is executing simple harmonic motion. When the object is executing simple harmonic motion, it is moving...

Estimate the range of the strong force if the mediating particle were the kaon instead of the pion.

In Figure a 1.34kg ball is connected by means of two mass less strings, each of length L = 1.70 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.70 m and are...

A 50.0-kg stunt pilot who has been diving her all plane vertically pulls out of the dive by changing her course to a circle in a vertical plane. (a) If the plane's speed at the lowest point of the...

Singing in the Shower. A pipe closed at both ends can have standing waves inside of it, but you normally don't hear them because little of the sound can get out. But you can hear them if you are...

An object is hung from a spring balance attached to the ceiling of an elevator cab. The balance reads 65 N when the cab is standing still. What is the reading when the cab is moving upward? (a) With...

At time t = 0, a ball is struck at ground level and sent over level ground. Figure gives momentum p versus t during the flight (p0 = 6.0 kg m/s and p1 = 4.0 kg m/s). At what initial angle is the ball...

A potential difference V is applied to a wire of cross-sectional area A, length L, and resistivity p. You want to change the applied potential difference and stretch the wire so that the energy...

An aluminum wire is clamped at each end under zero tension at room temperature. The tension in the wire is increased by reducing the temperature, which results in a decrease in the wires equilibrium...

Springs in Series two mass less springs are connected in series when they are attached one after the other, head to tail. (a) Show that the effective force constant (see Problem 6.63) of a series...

(a) What is the energy of a photon that has wavelength 0.10m? (b) Through approximately what potential difference must electrons be accelerated so that they will exhibit wave nature in passing...

Find the potential outside a charged metal sphere (charge Q, radius R) placed in an otherwise uniform electric field E 0. Explain clearly where you are setting the zero of potential.

If the phase angle for a block-spring system in SHM is /6 rad and the block's position is given by x = xm cos (wt + ), what is the ratio of the kinetic energy to the potential energy at time t = 0?

In the first stage of a two-stage Carnot engine, energy is absorbed as heat Q1 at temperature T1, work W1 is done, and energy is expelled as heat Q2 at a lower temperature T2. The second stage...

Use mesh analysis to find i1, i2, and i3 in the circuit of Fig. 3.97? Figure 3.97 6) 8 3 A 121. i3

One conductor of an overhead electric transmission line is a long aluminum wire 2.40 cm in radius. Suppose that at a particular moment it carries charge per length 1.40 C/m and is at potential 345...

When a liquid is introduced into the air space between the lens and the plate in a Newtons-rings apparatus, the diameter of the tenth ring changes from 1.50 to 1.31 cm, find the index of refraction...

Estimate your own moment of inertia about a vertical axis through the center of the top of your head when you are standing up straight with your arms outstretched. Make reasonable approximations and...

Archimedes principle can be used not only to determine the specific gravity of a solid using a known liquid (Example 10-8); the reverse can be done as well. (a) As an example, a 3.40-kg aluminum ball...

A rectangular block, with face lengths a = 35 cm and b = 45 cm, is to be suspended on a thin horizontal rod running through a narrow hole in the block. The block is then to be set swinging about the...

Niobium forms a substitutional solid solution with vanadium. Compute the weight percent of niobium that must be added to vanadium to yield an alloy that contains 1.55 1022 Nb atoms per cubic...

Food Intake of a Hamster. The energy output of an animal engaged in an activity is called the basal metabolic rate (BMR) and is a measure of the conversion of food energy into other forms of energy....

A shunt-wound dc motor with the field coils and rotor connected in parallel (Fig) operates from a 120-V dc power line. The resistance of the field windings, RI , is 218 .n. The resistance of the...

Perform the integration of Equation 8.38 to obtain Equation 8.39.

Suppose V = 0 and A = A0 sin(kx wt) y, where A0, w, and k are constants. Find E and B, and check that they satisfy Maxwell's equations in vacuum. What condition must you impose on w and k?

Two students with vibrating 440-Hz tuning forks walk away from each other with equal speeds. How fast must they walk so that they each hear a frequency of 438 Hz from the other fork?

(a) Show that the partition function of a photon gas is given by Where the product is over the modes n (b) The Helmholtz free energy is found directly from (53) as Transform the sum to an integral;...

A rectangular parallelepiped has dimensions a, b, and c, as in Figure P3.64. (a) Obtain a vector expression for the face diagonal vector R1. What is the magnitude of this vector? (b) Obtain a vector...

An infinitely long line charge having a uniform charge per unit length A lies a distance d from point O as shown in Figure P24.19. Determine the total electric flux through the surface of a sphere of...

A betatron accelerates electrons to energies in the MeV range by means of electromagnetic induction. Electrons in a vacuum chamber are held in a circular orbit by a magnetic field perpendicular to...

Consider the hemispherical closed surface in Figure P30.34. The hemisphere is in a uniform magnetic field that makes an angle θ with the vertical. Calculate the magnetic flux through (a) The...

A 100-W lightbulb generates 95 W of heat, which is dissipated through a glass bulb that has a radius of 3.0cm and is 1.0 mm thick. What is the difference in temperature between the inner and outer...

In Figure particle 1 of charge + q and particle 2 of charge + 4.00q are held at separation L = 9.00 cm on an x axis. If particle 3 of charge q3 rs to be located such that the three particles remain...

(a) What total (excess) charge q must the disk in Figure have for the electric field on the surface of the disk at its center to have magnitude 3.0 x 106 N/C, the E value at which air breaks down...

A 1.8-kg block slides on a horizontal surface with a speed of v = 0.80 m/s and an acceleration of magnitude a = 2.8 m/s2, as shown in FIGURE 6-30. (a) What is the coefficient of kinetic friction...

Square lattice, free electron energies (a) Show for a simple square lattice (two dimensions) that the kinetic energy of a free electron at a corner of the first zone is higher than that of an...

You must push a crate across a floor to a docking bay. The crate weighs 165 N. The coefficient of static friction between crate and floor is 0.510, and the coefficient of kinetic friction is 0.32....

The accompanying figure shows three different crystallographic planes for a unit cell of a hypothetical metal. The circles represent atoms: (a) To what crystal system does the unit cell belong? (b)...

A uniform pole is propped between the floor and the ceiling of a room. The height of the room is 7.80 ft, and the coefficient of static friction between the pole and the ceiling is 0.576. The...

Two boxes A and B, each having a weight of 160 lb, sit on the 500-lb conveyor which is free to roll on the ground. If the belt starts from rest and begins to run with a speed of 3 ft/s, determine the...

A cyclotron is to accelerate protons to an energy of 5.4 MeV. The superconducting electromagnet of the cyclotron produces a 3.5-T magnetic field perpendicular to the proton orbits. (a) When the...

What minimum horizontal force F is needed to pull wheel of radius R and mass M over a step of height h as shown in Fig. 9-72 ( R > h)? (a) Assume the force is applied at the top edge as shown. (b)...

Show that the energy of an ideal dipole p in an electric field E is given by U = p E. (4.6)

An ideal gas undergoes an adiabatic compression from p = 1.0 atm, V = 1.0 x 106L, T = 0.0oC to p = 1.0 x 105 atm, V = l0 x 103 L. (a) Is the gas monatomic, diatomic, or polyatomic? (b) What is its...

A 4-kg object is subjected to two forces, F 1 = 2 N i - 3 N j and F 2 = 4 n i - 11 N j . The object is at rest at the origin at time t = 0. (a) What is the objects acceleration? (b) What is its...

A railroad train is traveling at 30.0 m/s in still air. The frequency of the note emitted by the train whistle is 262 Hz. What frequency is heard by a passenger on a train moving in the opposite...

In Figure a 3.2 kg box of running shoes slides on a horizontal frictionless table and collides with a 2.0 kg box of ballet slippers initially at rest on the edge of the table, at height h = 0.40 m....

(a) What is the magnitude of an electron's acceleration in a uniform electric field of magnitude 1.40 x 106 N/C? (b) How long would the electron take, starting from rest, to attain one tenth the...

(a) A proton of kinetic energy 4.80MeV travels head-on toward a lead nucleus. Assuming that the proton does not penetrate the nucleus and that the only force between proton and nucleus is the Coulomb...

Manufacturers of wire (and other objects of small dimension) sometimes use a laser to continually monitor the thickness of the product. The wire intercepts the laser beam, producing a diffraction...

A physics student drops a vibrating 440-Hz tuning fork down the elevator shaft of a tall building. When the student hears a frequency of 400 Hz, how far has the tuning fork fallen?

The l0.00-V battery in Fig. is removed from the circuit and reinserted with the opposite polarity, so that its positive terminal is now next to point a. The rest of the circuit is as shown in the...

The smiling face of Figure consists of three items: 1. A thin rod of charge ?? 3.0C that forms a full circle of radius 6.0 cm; 2. A second thin rod of charge 2.0C that forms a circular arc of radius...

A decade before Einstein published his theory of relativity, J. J. Thomson proposed that the electron might consist of small parts and attributed the electron's mass m to the electric potential...

A proton moves perpendicular to a uniform magnetic field B at 1.00 % 107 m/s and experiences an acceleration of 2.00 x 1013 m/s2 in the 'x direction when its velocity is in the + z direction....

Figure 36.36 diagrams a cross section of a camera. It has a single lens of focal length 65.0 mm, which is to form an image on the film at the back of the camera. Suppose the position of the lens has...

An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a 10-s interval. What are the magnitude,...

Paleoclimate. Climatologists can determine the past temperature of the earth by comparing the ratio of the isotope oxygen-18 to the isotope oxygen-16 in air trapped in ancient ice sheets, such as...

Wearing a metal bracelet in a region of strong magnetic field could be hazardous. Explain.

A free neutron (m = 1.67 x 10 27kg) has a mean life of 900s. What is the uncertainty in its mass (in kg)?

Suppose J(r) is constant in time but p (r, t) is not---conditions that might prevail, for instance, during the charging of a capacitor. (a) Show that the charge density at any particular point is a...

On a clear, sunny day, a vertical electric field of about 130 N/C points down over flat ground. What is the surface charge density on the ground for these conditions?

In a region of free space the electric field at an instant of time is E = (80.0i + 32.0j) 64.0k) N/C and the magnetic field is B = (0.200i + 0.080 0j + 0.290k) T. (a) Show that the two fields are...

For 589-nm light, calculate the critical angle for the following materials surrounded by air: (a) Diamond, (b) Flint glass, and (c) Ice.

A weight W is supported by attaching it to a vertical uniform metal pole by a thin cord passing over a pulley having negligible mass and friction. The cord is attached to the pole 40.0 cm below the...

(a) How long did it take for a message sent from Earth to reach the first astronauts on the Moon? (b) How long will it take for a message from Earth to reach the first astronauts who arrive on Mars;...

What is the energy range (in joules and eV) of photons in the visible spectrum, of wavelength 400nm to 750nm?

A nucleus of mass 238u, initially at rest, emits an particle with a KE of 5.0MeV. What is the KE of the recoiling daughter nucleus?

A force Fa is applied to a bead as the bead is moved along a straight wire through displacement + 5.0cm. The magnitude of Fa is set at a certain value, but the angle ? between Fa and the bead??s...

(a) A circular diaphragm 60 cm in diameter oscillates at a frequency of 25 kHz as an underwater source of sound used for submarine detection. Far from the source, the sound intensity is distributed...

The 20-lb cart B is supported on rollers of negligible size, if a 10-lb suitcase A is thrown horizontally on it at 10ft/s, determine the length of time that A slides relative to B, and the final...

A subway train starts from rest at a station and accelerates at a rate of 1.60 m/s2 for 14.0 s. It runs at constant speed for 70.0 s and slows down at a rate of 3.50 m/s2 until it stops at the next...

Use two different techniques, (a) A ray diagram, and (b) The mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of...

Figure shows a thin rod, of length L = 2.00 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A ball of mass m = 5.00 kg is attached to the other end. The rod is...

In Figure, a 1.0 g bullet is fired into a 0.50 kg block attached to the end of a 0.60 m non uniform rod of mass 0.50 kg. The block-rod-bullet system then rotates in the plane of the figure, about a...

In Figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d1 = 360 m from the station and at angle 1 = 40o above the...

A particle with a charge of - 1.24 X l0-8 C is moving with instantaneous velocity U = (4.19 X 104m/s)i + (-3.85 X l04 m/s)J. What is the force exerted on this particle by a magnetic field (a) B =...

In the electron gun of a TV picture tube the electrons (charge -e, mass m) are accelerated by a voltage V. After leaving the electron gun, the electron beam travels a distance D to the screen; in...

Electric energy units are often expressed in the form of kilowatt-hours. (a) Show that one kilowatt-hour (kWh) is equal to 3.6 x 10oJ. (b) If a typical family of four uses electric energy at an...

A concrete highway is built of slabs 12m long (20oC). How wide should the expansion cracks between the slabs be (at 20oC) to prevent buckling if the range of temperature is -30oC to + 50oC?

A 2000-kg block is lifted at a constant speed of 8 cm/s by a steel cable that passes over a massless pulley to a motor-driven winch (Figure). The radius of the winch drum is 30 cm. (a) What force...

Evangelista Torricelli was the first person to realize that we live at the bottom of an ocean of air. He correctly surmised that the pressure of our atmosphere is attributable to the weight of the...

An object located 32.0 cm in front of a lens forms an image on a screen 8.00 cm behind the lens. (a) Find the focal length of the lens. (b) Determine the magnification. (c) Is the lens converging or...

A hydrogen atom (with the Bohr radius of half an angstrom) is situated between two metal plates 1 mm apart, which are connected to opposite terminals of a 500 V battery. What fraction of the atomic...

Four bricks of length L, identical and uniform, are stacked on a table in two ways, as shown in Figure. We seek to maximize the overhang distance h in both arrangements. Find the optimum distances...

At what initial speed must the basketball player in Figure throw the ball, at angle 0 = 55o above the horizontal, to make the foul shot? The horizontal distances are 0 = 1.0 ft and d2 = 14 ft, and...

A 30-m steel tape measured 29.991 m when standardized fully supported under a 5.500-kg pull at a temperature of 20C. The tape weighed 1.22 kg and had a cross-sectional area of 0.016 cm2. What is the...

How much energy is released when tritium, 3/1H, decays by emission?

(a) A tank containing methanol has walls 2.50cm thick made of glass of refractive index 1.550. Light from the outside air strikes the glass at a 413o angle wills the normal to the glass. Find the...

Sally, who weighs 125 lb, knows that getting out of a 65.5-lb canoe can be a difficult experience. (a) What happens to the canoes velocity if she attempts to step out of the canoe and onto the dock...

A satellite moves around the Earth in a circular orbit of radius r. (a) What is the speed v0 of the satellite? Suddenly, an explosion breaks the satellite into two pieces, with masses m and 4m....

A car is parked on a steep incline overlooking the ocean, where the incline makes an angle of 37.0 below the horizontal. The negligent driver leaves the car in neutral, and the parking brakes are...

The 10-Mg helicopter carries a bucket containing 500 kg of water, which is used to fight fires, if is hovers over the land in a fixed position and then releases 50 kg/s of water at 10m/s, measured...

Applying Gauss's Law for Gravitation Using Gauss's law for gravitation (derived in part (b) of Problem 22.59), show that the following statements are true: (a) For any spherically symmetric mass...

A point charge q1 = 4.00 nC is placed at the origin, and a second point charge q2 = -3.00 nC is placed on the x-axis at x = + 20.0 cm. A third point charge q3 = 2.00 nC is to be placed on the x-axis...

In a double-slit experiment, the third-order maximum for light of wavelength 500nm is located 12mm from the central bright spot on a screen 1.6m from the slits. Light of wavelength 650nm is then...

In Figure, a metal wire of mass m = 24.1 mg can slide with negligible friction on two horizontal parallel rails separated by distance d = 2.56 cm. The track lies in a vertical uniform magnetic field...