A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10 rev/s; 60 revolutions later, its angular speed is 15...

A75 kg window cleaner uses a 10 kg ladder that is 5.0 m long. He places one end on the ground 2.5 m from a wall, rests the upper end against a cracked window, and climbs the ladder. He is 3.0 m up...

A combination of 0.250 kg of water at 20.0C, 0.400 kg of aluminum at 26.0C, and 0.100 kg of copper at 100C is mixed in an insulated container and allowed to come to thermal equilibrium. Ignore any...

A toaster is rated at 600 W when connected to a 120-V source. What current does the toaster carry, and what is its resistance?

Combining Standing Waves. A guitar string of length L is plucked in such a way that the total wave produced is the sum of the fundamental and the second harmonic. That is, the standing wave is given...

Focus of the Eye. The cornea of the eye has a radius of curvature of approximately 0.50 cm, and the aqueous humor behind it has an index of refraction of 1.35. The thickness of the cornea itself is...

An Object at an Angle A 16.0-cm-long pencil is placed at a 45.0? angle, with its center 15.0 cm above the optic axis and 45.0 cm from a lens with a 20.0-cm focal length as shown in Fig. 34.65. (Note...

Two perfectly black surfaces are constructed so that all the radiant energy leaving a surface at 800C reaches the other surface. The temperature of the other surface is maintained at 250C. Calculate...

Binary Star-Equal Masses Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius R, so that the two stars are always on opposite sides of the circle....

A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity w. You can ignore the force of gravity on the rope. Find the time required for a...

A spaceship and its occupant have a total mass of 150,000kg. The occupant would like to travels to a star that is 25 light-years away at a speed of 0.60c. to accelerated, the engine of the spaceship...

Steam at 100C is added to ice at 0C. (a) Find the amount of ice melted and the final temperature when the mass of steam is 1.0 g and the mass of ice is 50.0 g. (b) What If? Repeat when the mass of...

A professional golfer hits her 5-iron 155 m (170 yd). A 46.0-g golf ball experiences a drag force of magnitude R = Cv2, and has a terminal speed of 44.0 m/s. (a) Calculate the drag constant C for the...

An observer to the right of the mirrorlens combination shown in Figure P36.68 sees two real images that are the same size and in the same location. One image is upright and the other is inverted....

The atmosphere of the planet Mars is 95.3% carbon dioxide (CO2) and about 0.03% water vapor. The atmospheric pressure is only about 600 Pa, and the surface temperature varies from 30oC to -100oC....

Pressure on Venus. At the surface of Venus the average temperature is a balmy 460oC due to the greenhouse effect (global warming!), the pressure is 92 Earth-atmospheres, and the acceleration due to...

A raft is made of 10 logos lashed together. Each is 56cm in diameter and has a length of 6.1 m. How many people can the raft hold before they start getting their feet wet, assuming the average person...

An air-filled parallel-plate capacitor has capacitance C0. If two identically sized dielectric slabs of dielectric constants K1 and K2 are inserted as shown in Fig. 19-64, what is the new capacitance?

For both converging and diverging lenses, discuss how the focal length for red light differs from that for violet light.

The cube in Figure has edge length 1.40 m and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field, in Newton?s per coulomb,...

In Figure four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 8.50 cm. Each wire carries 15.0 A, and all the currents are out of the...

An emf of 24.0 mV is induced in a 500-turn coil at an instant when the current is 4.00 A and is changing at the rate of 10.0 A/s. What is the magnetic flux through each turn of the coil?

A large cylindrical tank contains 0.750 m3 of nitrogen gas at 27C and 1.50 X 105 Pa (absolute pressure). The tank has a tight fitting piston that allows the volume to be changed. What will be the...

(An ideal gas expands at a constant total pressure of 3.0atm from 400mL to 660mL. Heat then flows out of the gas at constant volume, and the pressure and temperature are allowed to drop until the...

How much energy would the person of Example 15-8 transform if instead of working 11.0 h she took a noon-time break and ran for 1.0h?

An inductor is connected to the terminals of a battery that has an emf of 120 V and negligible internal resistance. The current is 4.86 rnA at 0.725 ms after the connection is completed. After a long...

Milwaukee is 121 mi (air miles) due west of Grand Rapids. Maria drives 255 mi in 4.75 h from Grand Rapids to Milwaukee around Lake Michigan. Find (a) Her average driving speed (b) Her average travel...

An incompressible, nonviscous fluid is initially at rest in the vertical portion of the pipe shown in Figure P14.69a, where L = 2.00 m. When the valve is opened, the fluid flows into the horizontal...

A uniformly solid sphere of mass M and radius R is fixed a distance h above a thin infinite sheet of mass density ps (mass/area). With what force does the sphere attract the sheet?

Two stretched cables both experience the same stress. The first cable has a radius of 3.5 10-3 m and is subject to a stretching force of 270 N. The radius of the second cable is 5.1 10-3 m....

A 25.0-kg block is initially at rest on a horizontal surface. A horizontal force of 75.0 N is required to set the block in motion. After it is in motion, a horizontal force of 60.0 N is required to...

Two fun-loving otters are sliding toward each other on a muddy (and hence Iiictioo1ess) horizontal surface. One of them, of mass 7.so kg, is sliding to the left at 5.00 m/s, while the other, of mass...

If the coefficient of kinetic friction between a 35-kg crate and the floor is 0.30, what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is...

What are the largest and smallest possible values for the angular momentum L of an electron in the n = 5 shell?

Male Rana catesbeiana bullfrogs are known for their loud mating call. The call is emitted not by the frog's mouth but by its eardrums, which lie on the surface of the head. And, surprisingly, the...

The van der Waals equation of state, an approximate representation of the behavior of gases at high pressure, is given by Where a and b are constants having different values for different gases. (In...

(a) Suppose you imbedded some free charge in a piece of glass. About how long would it take for the charge to flow to the surface? (b) Silver is an excellent conductor, but it's expensive. Suppose...

Structure of a vortex? (a) Find a solution to the London equation that has cylindrical symmetry and applies outside a line core. In cylindrical polar coordinates, we want a solution of B ? ? 2 ? 2 B...

Two concentric conducting spheres of inner and outer radii a and b, respectively, carry charges ?Q. The empty space between the spheres is half-filled by a hemispherical shell of dielectric (of...

A uniform magnetic field of magnitude 0.150 T is directed along the positive x axis. A positron moving at 5.00 x 106 m/s enters the field along a direction that makes an angle of 85.0° with the x...

Figure 34.10 shows a Hertz antenna (also known as a half wave antenna, because its length is A/2). The antenna is located far enough from the ground that reflections do not significantly affect its...

The energy of an RLC circuit decreases by 1.00% during each oscillation when R = 2.00 . If this resistance is removed, the resulting LC circuit oscillates at a frequency of 1.00 kHz. Find the values...

What will be the equilibrium temperature when a 245-g block of copper at 285oC is placed in a 145-g aluminum calorimeter cup containing 825 g of water at 12.0oC?

X is an unknown vector satisfying the following relations involving the known vectors A and B and the scalar . A x X = B, A X = . Express X in terms of A, B, , and the magnitude of A.

A batter hits a pitched ball when the center of the ball is 1.22 m above the ground. The ball leaves the bat at an angle of 45o with the ground. With that launch, the ball should have a horizontal...

A 45 kg block of ice slides down a frictionless incline l.5 m long and 0.91 m high, a worker pushes up against the ice, parallel to the incline, so that the block slides down at constant speed. (a)...

A uniform solid sphere of radius R produces a gravitational acceleration of ar on its surface. At what distance from the sphere's center are there points (a) Inside and (b) Outside the sphere where...

The coil in Figure 21.19a contains 410 turns and has an area per turn of 3.1 Ã 10-3 m2. The magnetic field is 0.23 T, and the current in the coil is 0.26 A. A brake shoe is pressed...

A hawk flies in a horizontal arc of radius 12.0m at a constant speed of 4.00 m/s. (a) Find its centripetal acceleration. (b) It continues to fly along the same horizontal arc but increases its speed...

In two dimensions, show that the divergence transforms as a scalar under rotations.

Initially the system of objects shown in Figure P5.61 is held motionless. All surfaces, pulley, and wheels are frictionless. Let the force F is zero and assume that m2 can move only vertically. At...

Figure P36.72 shows a thin converging lens for which the radii of curvature are R1 = 9.00 cm and R2 = -11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R =...

In an L-R-C series circuit, R = 300, L = 0.400 H, and C = 6.00 X 10-8 F. When the ac source operates at the resonance frequency of the circuit, the current amplitude is 0.500 A. (a) What is the...

(a) The uncertainty in the y-component of a proton's position is 2.0 x 10-12m. What is the minimum uncertainty in a simultaneous measurement of the y-component of the proton's velocity? (b) The...

In Prob. 2.25 you found the potential on the axis of a uniformly charged disk: (a) Use this, together with the fact that Pl(1) = 1, to evaluate the first three terms in the expansion (3.72) for the...

The position vector for an electron is R = (5.0 m)i (3.0 m)j + (2.0 m)k. (a) Find the magnitude of 7. (b) Sketch the vector on a right-handed coordinate system.

Heather in her Corvette accelerates at the rate of (3.00i 2.00j) m/s2, while Jill in her Jaguar accelerates at (1.00i + 3.00j) m/s2. They both start from rest at the origin of an xy coordinate...

In about 1965, engineers at the Toro Company invented a gasoline gauge for small engines, diagrammed in Figure P35.43. The gauge has no moving parts. It consists of a flat slab of transparent plastic...

A long, straight wire lies along the y-axis and carries a current I = 8.00 A in the -y-direction (Fig). In addition to the magnetic field due to the current in the wire, a uniform magnetic field B0...

A solenoid is designed to produce a magnetic field of 0.0270 T at its center. It has radius 1.40 cm and length 40.0 cm, and the wire can carry a maximum current of 12.0 A. (a) What minimum number of...

A particle is attached between two identical springs on a horizontal frictionless table. Both springs have spring constant k and are initially unstressed. (a) If the particle is pulled a distance x...

(a) Show that the rate of change of the free-fall acceleration with distance above the Earths surface is dg/dr = 2GME/RE3 This rate of change over distance is called a gradient. (b) If h is small in...

Simple Machines Ramps for the disabled are used because a large weight w can be raised by a relatively small force equal to w sin a plus the small friction force. Such inclined planes are an example...

The orbit of Earth around the Sun is almost circular: The closest and farthest distances are 1.47 x 108 km and 1.52 x 108 km respectively. Determine the corresponding variations in (a) Total energy,...

A plano-convex lens having a radius of curvature of r = 4.00m is placed on a concave glass surface whose radius of curvature is R= 12.0 m, as shown in Figure P37.65. Determine the radius of the 100th...

In Fig. 19-53, If C1 = C2 = 2C3 = 22.6F, how much charge is stored on each capacitor when V = 45.0V?

Use the conservation of energy to explain why the temperature of a gas increases when it is quickly compressed, whereas the temperature decreases when the gas expands.

An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1100 N. The coefficient of static friction between the box and the floor...

The mean diameters of Mars and Earth are 6.9 x 103 km and 1.3 x 104 km, respectively. The mass of Mars is 0.11 times Earth's mass (a) What is the ratio of the mean density (mass per unit volume) of...

A 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Figure P22.62. The process A B is a reversible isothermal expansion. Calculate (a) the net work done by the gas, (b)...

Due to a gravitational torque exerted by the Moon on the Earth, our planets rotation period slows at a rate on the order of 1 ms/century. (a) Determine the order of magnitude of the Earths angular...

A 2.00-kg particle has a velocity (2.00i 3.00j) m/s, and a 3.00-kg particle has a velocity (1.00i + 6.00j) m/s. Find (a) the velocity of the center of mass and (b) the total momentum of the system.

When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude I max of the current without disconnecting the wire to shunt the current in a meter....

A series RL circuit with L = 3.00 H and a series RC circuit with C = 3.00 'F have equal time constants. If the two circuits contain the same resistance R, (a) What is the value of R and (b) What is...

A 180-kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a physical pendulum. 1be period for small-angle oscillations is 0940 s. (a) What is the moment of inertia of...

Normalization of the Wave Function Consider a particle moving in one dimension which we shall call the x-axis. (a) What does it mean for the wave function of this particle to be normalized? (b) Is...

A short cylinder, of radius a and length L, carries a "frozen-in" uniform polarization P, parallel to its axis. Find the bound charge, and sketch the electric field (i) for L >> a. (ii) for L < < a,...

An aluminum-alloy rod has a length of 10.000 cm at 20.000oC and a length of 10.015 cm at the boiling point of water. (a) What is the length of the rod at the freezing point of water? (b) What is the...

A small piece of Styrofoam packing material is dropped from a height of 2.00 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g bv. After falling...

A laboratory technician drops a 0.0850-kg sample of unknown material, at a temperature of l00.0C, into a calorimeter. The calorimeter can, initially at 19.0C, is made of 0.150 kg of copper and...

A box is separated by a partition into two parts of equal volume. The left side of the box contains 500 molecules of nitrogen gas; the right side contains 100 molecules of oxygen gas. The two gases...

A banked circular highway curve is designed for traffic moving at 60 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a rainy day. What is the minimum...

In Figure four particles form a square. The charges q1 = + Q, q2 = q3 = q, and q4 = -2.00Q. What is q/Q if the net electrostatic force on particle 1 is zero? t (2 $ 2) 1

Consider two identical conducting spheres whose surfaces are separated by a small distance. One sphere is given a large net positive charge while the other is given a small net positive charge. It is...

A capacitor has parallel plates of area 12 cm' separated by 2.0 mm. The space between the plates is filled with polystyrene (see Table 24.2). (a) Find the permittivity of polystyrene. (b) Find the...

A 3.00-m length of copper wire at 20oC has a 1.20-m-long section with diameter 1.60 mm and a 1.80-m-long section with diameter 0.80 mm. There is a current of 2.5 m A in the 1.60-mm diameter section....

A string oscillates according to the equation what are the(a) Amplitude and(b) Speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation?(c) What is...

You have a stopped pipe of adjustable length close to a taut 85.0-cm, 7.25-g wire under a tension of 4110 N. You want to adjust the length of the pipe so that, when it produces sound at its...

A nonmagnetic medium has an intrinsic impedance 240 <30 . Find its (a) Loss tangent (b) Dielectric constant (c) Complex permittivity (d) Attenuation constant at 1 MHz

A telephone line has the following parameters: R = 40 /m, G = 400S/m, L = 0.2H/m, C = 0.5nF/m (a) If the line operates at 10 MHz, calculate the characteristic impedance Zo and velocity u. (b) After...

Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 100 km above the surface of the Moon, where the acceleration...

The blade divides the jet of water having a diameter of 3 in. If one-fourth of the water flows downward while the other three-fourths flows upwards, and the total flow is Q = 0.5 ft3/s, determine the...

A gyroscope is processing about a vertical axis. Describe what happens to the precession angular speed if the following changes in the variables are made, with all other variables remaining the same:...

In a physics laboratory you do the following ballistic pendulum experiment: You shoot a ball of mass m horizontally from a spring gun with a speed v. The hall is immediately caught a distance below a...

Obtain Eq. 9.20 directly from the wave equation, by separation of variables.

How much work is required to turn an electric dipole 180o in a uniform electric field of magnitude E = 46.0 N/C if p = 3.02 x 10-25 C m and the initial angle is 64o?

Figure shows the kinetic energy K of a simple harmonic oscillator versus its position x. The vertical axis scale is set by Ks = 4.0 J. What is the spring constant? K (J) K, 8 12 -12 -8 -4 x (cm)

In a 30.0-s interval, 500 hailstones strike a glass window of area 0.600 m2 at an angle of 45.0 to the window surface. Each hailstone has a mass of 5.00 g and moves with a speed of 8.00 m/s. Assuming...

When high-energy charged particles move through a transparent medium with a speed greater than the speed of light in that medium, a shock wave, or bow wave, of light is produced. This phenomenon is...

If an object on a horizontal, frictionless surface is attached to a spring, displaced, and then released, it will oscillate. If it is displaced 0.120 m from its equilibrium position and released with...