A van accelerates down a hill (Fig. P5.69), going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy (m =0.100 kg) hangs by a string from the vans ceiling. The acceleration is such that...
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?
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...
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...
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...
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...
The p-V diagram in Figure shows two paths along which a sample of gas can be taken from state a to state 4 where Vb = 3.0V1. Path 1 requires that energy equal to 5.0p1V1 be transferred to the gas as...
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...
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...
Consider a long cylindrical charge distribution of radius R with a uniform charge density 1. Find the electric field at distance r from the axis where r < R.
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...
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 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...
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,...
Hovering over the pit of hell, the devil observes that as a student falls past (with terminal velocity), the frequency of his scream decreases from 842 to 820 Hz. (a) Find the speed of descent of the...
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...
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....
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 =...
What are the largest and smallest possible values for the angular momentum L of an electron in the n = 5 shell?
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...
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...
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...
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 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?
(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...
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...
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...
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...
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) 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...
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)...
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...
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...
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...
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...
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 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 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 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 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...
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.
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....
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?
In Fig. 19-53, If C1 = C2 = 2C3 = 22.6F, how much charge is stored on each capacitor when V = 45.0V?
In two dimensions, show that the divergence transforms as a scalar under rotations.
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) 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...
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 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.
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 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,...
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...
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 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...
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...
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 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...
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...
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.
Obtain Eq. 9.20 directly from the wave equation, by separation of variables.
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)...
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...
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 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....
Figure is an overhead view of a thin uniform rod of length 0.600 m and mass M rotating horizontally at 80.0 rad/s counterclockwise about an axis through its center. A particle of mass M/3.00 and...
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?
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
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...
For the vectors shown in Fig. 3-32, determine (a) B 2A, (b) 2A 3B + 2C
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...
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...
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...
Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see the first part of the figure). Thus, beam ABC may be represented as a propped cantilever beam with an overhang...
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...
In about A.D. 150, Claudius Ptolemy gave the following measured values for the angle of incidence 1 and the angle of refraction 2 for a light beam passing from air to water: Assuming these data are...
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:...
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)A deuteron, 2/1H1 is the nucleus of a hydrogen isotope and consists of one proton and one neutron. The plasma of deuterons in a nuclear fusion reactor must be heated to about 300 million K. What...
In Figure the pulley has negligible mass, and both it and the inclined plane are frictionless. Block A has a mass of 1.0 kg, block B has a mass of 2.0 kg, and angle ? is 30o. If the blocks are...
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)
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....
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 charge of 170 %C is at the center of a cube of edge 80.0 cm. (a) Find the total flux through each face of the cube. (b) Find the flux through the whole surface of the cube. (c) What If? Would your...
A resistor is constructed of a carbon rod that has a uniform cross-sectional area of 5.00 mm2. When a potential difference of 15.0 V is applied across the ends of the rod, the rod carries a current...
Equation (5.10) applies to the case where the initial velocity is zero. (a) Derive the corresponding equation for v,(t) when the falling object has an initial downward velocity with magnitude vo. (b)...
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...
In mechanics, mass less strings are often assumed. Why is this not a good assumption when discussing waves on strings?
A point source emits 30.0 W of sound isotropically. A small microphone intercepts the sound in an area of 0.750 cm2, 200 m from the source. Calculate (a) The sound intensity there and (b) The power...
A laser beam with vacuum wavelength 632.8 nm is incident from air onto a block of Lucite as shown in Figure 35.10b. The line of sight of the photograph is perpendicular to the plane in which the...
In Figure sound with a 40.0 cm wavelength travels rightward from a source and through a tube that consists of a straight portion and a half-circle. Part of the sound wave travels through the...
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)...
An astronaut on the surface of the Moon fires a cannon to launch an experiment package, which leaves the barrel moving horizontally. (a) What must be the muzzle speed of the package so that it...
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...