A 12.0-g wad of sticky clay is hurled horizontally at a 100-g wooden block initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides 7.50 m before coming...

A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (Fig. P15.59). Find the frequency of vibration of the system for small...

A thin disk with a circular hole at its center, called an annulus, has inner radius R 1 and outer radius R2 (Fig. 21.51). The disk has a uniform positive surface charge density σ on its...

(a) The tube of a mercury thermometer has an inside diameter of 0.140mm. The bulb has a volume of 0.255cm3. How far will the thread of mercury move when the temperature changes from 11.5oC to 33.0oC?...

Effect of a Window in a Door. A carpenter builds a solid wood door with dimensions 2.00 m X 0.95 m X 5.0 cm. Its thermal conductivity is k = 0.120 W/m K. The air films on the inner and outer surfaces...

Reflective Coatings and Herring. Herring and related fish have a brilliant silvery appearance that camouflages them while they are swimming in a sunlit ocean. The silveriness is due to platelets...

A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. You...

Two uniform 75.0-g marbles 2.00 cm in diameter are stacked as shown in Fig. 11.55 in a container that is 3.00 cm wide. (a) Find the force that the container exerts on the marbles at the points of...

A 20-kg sphere rests between two smooth planes as shown in Fig. 9-85. Determine the magnitude of the force acting on the sphere exerted by each plane. 20 kg 70 30

(a) An insulating sphere with radius a has a uniform charge density p. The sphere is not centered at the origin but at r = b. Show that the electric field inside the sphere is given by E = p (r -...

What fraction of the volume of an iceberg (density 917 kg/m3) would be visible if the iceberg floats? (a) In the ocean (salt water, density 1024 kg/m3) and (b) In a river (fresh water, density 1000...

The nucleus of 21'PO decays radioactively by emitting an alpha particle (mass 6.65 X 10-27 kg) with kinetic energy 1.23 X 10-12 J, as measured in the laboratory reference frame. Assuming that the Po...

Linear ionic crystal Consider a line of 2N ions of alternating charge q with a repulsive potential energy A/R n between nearest neighbors. (a) Show that at the equilibrium separation (CGS) U (R 0 )...

A 20.0-m-long uniform beam weighing 550 N rests on walls A and B, as shown in Fig 9-80 (a) Find the maximum weight of a person who can walk to the extreme end D without tipping the beam. Find the...

Until his seventies, Henri LaMothe (Figure) excited audiences by belly-flopping from a height of 12 m into 30 cm of water. Assuming that he stops just as he reaches the bottom of the water and...

Find the position of the center of mass of the system of the sun and Jupiter. (Since Jupiter is more massive than the rest of the planets combined, this is essentially the position of the center of...

We have two equal-size boxes, A and B. Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box A is at a temperature of 50C while the...

A computer disk drive is turned on starting from rest and has constant angular acceleration. If it took 0.750 s for the drive to make its second complete revolution, (a) How long did it take to make...

(a) Calculate the difference in blood pressure between the feet and top of the head for a person who is 1.65 m tall. (b) Consider a cylindrical segment of a blood vessel 2.00 cm long and 1.50 nun in...

At a temperature of 10C the percent relative humidity is R10, and at 40C it is R40. At each of these temperatures, the partial pressure of water vapor in the air is the same. Using the vapor pressure...

A 3.00-m-long, 240-N, uniform rod at the zoo is held in a horizontal position by two ropes at its ends (Fig. 11.30). The left rope makes an angle of 150° with the rod and the right rope makes an...

A particle of mass 1.18 kg is attached between two identical springs on a horizontal frictionless tabletop. The springs have force constant k and each is initially unstressed. (a) If the particle is...

An oil tanker's engines have broken down, and the wind is blowing the tanker straight toward a reef at a constant speed of 1.5 m/s (Fig. 4.37). When the tanker is 500 m from the reef, the wind dies...

Two coils are wrapped around each other as shown in Fig. 30.3. The current travels in the same sense around each coil. One coil has self-inductance L.. and the other coil has selfinductance L2?? The...

A pendulum with a cord of length r = 1.00 m swings in a vertical plane (Fig. P4.53). When the pendulum is in the two horizontal positions θ = 90.0° and θ = 270°, its speed is 5.00...

An isolated spherical capacitor has charge + Q on its inner conductor (radius ra and charge -Q on its outer conductor (radius rb) Half of the volume between the two conductors is then filled with a...

The cartoon shown in Figure lies on a plane tilted at and angle θ = 22.0o to the horizontal, with μk = 0.12. (a) Determine the acceleration of the carton as it slides down the plane. (b) If...

In Section 8.5 we calculated the center of mass by considering objects composed of ajinite number of point masses or objects that, by symmetry, could be represented by a finite number of point...

(a) When a 0.750-kg mass oscillates on an ideal spring, the frequency is 1.33 Hz. What will the frequency be if 0.220 kg are added to the original mass, and (b) Subtracted from the original mass? Try...

A solid cube of uniform density and sides of b is in equilibrium on top of a cylinder of radius R (Figure 2-C). The planes of four sides of the cube are parallel to the axis of the cylinder. The...

Two crates, one with mass 4.00 kg and the other with mass 6.00 kg, sit on the frictionless surface of a frozen pond, connected by a light rope (Fig. 4.38). A woman wearing golf shoes (so she can get...

A pendulum is suspended from the cusp of a cycloid* cut in a rigid support (Figure 3-A). The path described by the pendulum bob is cycloidal and is given by x = a (Ã - sin Ã), y = a...

At the intersection of Texas Avenue and University Drive, a yellow subcompact car with mass 950 kg traveling east on University collides with a red pickup truck with mass 1900 kg that is traveling...

A 15.0-kg stone slides down a snow-covered hill (Fig. 7.34), leaving point A with a speed of 10.0 m/s. There is no friction on the hill between points A and B, but there is friction on the level...

Potential energy in the diamond structure (a) Show that for the diamond structure the Fourier component UG of the crystal potential seen by an electron is equal to zero for G = 2A, where A is a basis...

A certain volcano on earth can eject rocks vertically to a maximum height H. (a) How high (in terms of If) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The...

(a) A massless string of length 2? connects two hockey pucks that lie on frictionless ice. A constant horizontal force F is applied to the midpoint of the string, perpendicular to it (see Fig.). How...

Three uniform spheres are fixed at the positions shown in Fig. 12.36. (a) What are the magnitude and direction of the force on a 0.0150-kg particle placed at P? (b) If the spheres are in deep outer...

In Fig. 5.41 each of the suspended blocks has weight w. The pulleys are frictionless and the ropes have negligible weight. Calculate, in each case, the tension T in the rope in terms of the weight w....

A ring placed along y2 + z2 = 4, x = 0 carries a uniform charge of 5C/m. (a) Find D at P(3,0, 0). (b) If two identical point charges Q are placed at (0, 3, 0) and (0, 3, 0) in addition to the ring,...

Engineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum (Fig....

In all three cases, A, B, and C, the crate is in equilibrium (no acceleration). From greatest to least, rank the amount of friction between the crate and the floor. v 1 m/s

According to the U.S. National Electrical Code, copper wire used for interior wiring of houses, hotels, office buildings, and industrial plants is permitted to carry no more than a specified maximum...

In Figure a small 50 g block slides down a frictionless surface through height h = 20 cm and then sticks to a uniform rod of mass 100 g and length 40 cm. The rod pivots about point O through angle ?...

A 280-g wood block is firmly attached to a very light horizontal spring. Fig 6-40. The block can slide along a table where the coefficient of friction is 0.30.. Af force of 22N compresses the spring...

In Figure where V23 = 3.00V1, n moles of a diatomic ideal gas are taken through the cycle with the molecules rotating but not oscillating. What are? (a) p2/p1 (b) p3/p1 and (c) T3/T1 For path 1 ?? 2,...

Consider the system shown in Fig. 5.54. Block A weighs 45.0 N and block B weighs 25.0 N. Once block B is set into downward motion, it descends at a constant speed. (a) Calculate the coefficient of...

A 44-kg chandelier is suspended 1.5 m below a ceiling by three wires, each of which has the same tension and the same length of 2.0 m (see the drawing). Find the tension in eachwire. 1.5 m 2.0 m

(a) Show that a projectile with mass m can escape from the surface of a planet if it is launched vertically upward with a kinetic energy greater than mgRp, where g is the acceleration due to gravity...

A 300-g mass vibrates according to the equation x = 0.38 sin 6.50 t, where x is in meters and t is in seconds. Determine (a) The amplitude, (b) The frequency, (c) The period, (d) The total energy,...

Number of Fringes in a Diffraction Maximum In Fig. 36.12c the central diffraction maximum contains exactly seven interference fringes, and in this case d/a = 4. (a) What must the ratio d/a be if the...

A 2.00-kg object is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 20.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium...

7/4Be decays with a half-life of about 53d. It is produced in the upper atmosphere, and filters down onto the Earths surface. If a plant leaf is detected to have 450 decays/s of 7/4Be, (a) How long...

Zero point lattice displacement and strain (a) In the Debye approximation, show that the mean square displacement of an atom at absolute zero is R) = 3hw 2 D /8 2 pv 3 , where v is the velocity of...

Visitors at an amusement park watch divers step off a platform 21.3 m (70 ft) above a pool of water. According to the announcer, the divers enter the water at a speed of 56 mi/h (25 m/s). Air...

A large tank is filled with methane gas at a concentration of 0.650 kg/m3. The valve of a 1.50-m pipe connecting the tank to the atmosphere is inadvertently left open for twelve hours. During this...

A very long straight wire carries current I. In the middle of the wire a right-angle bend is made. The bend forms an arc of a circle of radius r, as shown in Figure P30.10. Determine the magnetic...

Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 60 minutes, reaching a point 2.0 km farther upstream....

Suppose that you can lift no more than 650 N (around 150lb) unaided. (a) How much can you lift using a 1.4-m-long wheelbarrow that weighs 80.0 N and whose center of gravity is 0.50 m from the center...

A Truck on a Drawbridge A loaded cement mixer drives onto an old drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help,...

The force on an object, acting along the x axis, varies as shown in Fig. 6-37. Determine the work done by this force to move the object (a) From x = 0.0 to x = 10.00m, and (b) From x = 0.0 to x =...

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 12.0 cm, giving it a charge of -15.0 C. Find the electric field (a) Just inside the paint...

The 800-lb roller-coaster car starts from rest on the track having the shape of a cylindrical helix. If the helix descends 8ft for every one revolution, determine the speed of the car in t = 4s....

A long, rigid conductor, lying along an x axis, carries a current of 5.0 A in the negative x direction. A magnetic field B is present, given B = 3.0i + 8.0 x2j, with x in meters and F in milliteslas....

A sphere of radius 2a is made of a non-conducting material that has a uniform volume charge density 1. (Assume that the material does not affect the electric field.) A spherical cavity of radius a is...

A long, straight wire containing a semicircular region of radius 0.95 m is placed in a uniform magnetic field of magnitude 2.20 T as shown in Fig. What is the net magnetic force acting on the wire...

Construct a Table indicating the position x of the mass if Fig. 11-2 at times t = 0, T, T, T, and 5/2 T, where T is the period of oscillation. On a graph of x vs, t plot these six points now...

A 1.00-kg object is attached to a horizontal spring. The spring is initially stretched by 0.100 m, and the object is released from rest there. It proceeds to move without friction. The next time the...

A solid cube of wood of side 2a and mass M is resting on a horizontal surface. The cube is constrained to rotate about an axis AB (Fig. P11.54). A bullet of mass m and speed v is shot at the face...

A 172-cm-tall person lies on a light (mass less) board which is supported by two scales, one under the top of her head and one beneath the bottom of her feet (Fig. 9-53). The two scales read,...

Suppose that the force acting on a particle is factorable into one of the following forms; (a) F(xi, t) = f(xi) g(t) (b) F(xi, t) = f(xi) g(t) (c) F(xi, xi) = f(xi) g(xi) for which cases are the...

A man is riding on a flatcar traveling at a constant speed of 9.10 m/s (Fig. 3.54). He wishes to throw a ball through a stationary hoop 4.90 m above the height of his hands in such a manner that the...

A plank with a mass M = 6.00 kg rides on top of two identical solid cylindrical rollers that have R = 5.00 cm and m = 2.00 kg (Fig. P10.86). The plank is pulled by a constant horizontal force F of...

Consider the network of resistor shown in Fig. 19-40. Answer qualitatively: (a) What happens to the voltage across each resistor when the switch S is closed? (b) What happens to the current through...

When a gas in taken from a to c along the curved path in Fig. 15-24, the work done by the gas is W = 35J and the heat added to the gas is Q = 63 J. Along path abc, the work done is W = 48 J. (a) What...

The Electromagnetic Pump Magnetic forces acting on conducting fluids provide a convenient means of pumping these fluids. For example, this method can be used to pump blood without the damage to the...

The conducting rod ab shown in Fig. 29.38 makes contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure(a) Find the...

Many machines employ cams for various purposes, such as opening and closing valves. In Figure P10.29, the cam is a circular disk rotating on a shaft that does not pass through the center of the disk....

A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a mass less string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. These...

A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 k/n above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed...

When Babe Ruth hit a homer over the 7.5 m-light right-field fence 95m from home plate, roughly what was the minimum speed of the ball when it left the bat? Assume the ball was hit 1.0m above the...

A loud factory machine produces sound having a displacement amplitude of 1.00 m. but the frequency of this sound can be adjusted. In order to prevent ear damage to the workers, the maximum pressure...

Pancake collapse of a tall building. In the section of a tall building shown in Figure a, the infrastructure of any given floor K must support the weight W of all higher floors. Normally the...

Evaluate the equivalent capacitance of the configuration shown in Figure P26.18. All the capacitors are identical, and each has capacitance C. C C C

An inventive child named Pat wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley (Fig. P5.51), Pat pulls on the...

A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 160 N. The coefficient of static friction between the foot of the...

For your cabin in the wilderness, you decide to build a primitive refrigerator out of Styrofoam, planning to keep the interior cool with a block of ice that has an initial mass of24.0 kg. The box has...

A brass ring with triangular cross section encircles a very long straight wire concentrically as in figure. If the wire carries a current I, show that the total number of magnetic flux lines in the...

A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (Fig. 3.51). The takeoff ramp was inclined at 53.0", the river was...

Two identical spheres with mass m are hung from silk threads of length L, as shown in Fig. 21.44. Each sphere has the same charge, so q1 = q2 = q. The radius of each sphere is very small compared to...

(a) Derive an expression for the total shift in photon wavelength after two successive Compton scatterings from electrons at rest. The photon is scattered by an angle 1, in the first scattering and...

Designers of todays cars have built 5mi/h (8km/h) bumpers that are designed to compress and rebound elastically without any physical damage at speeds below 8km/h. IF the material of the bumpers...

A long horizontal wire carries a current a of 48 A.A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. 20-58). (a)...

A swimming pool is 5.0 m long, 4.0 m wide and 3.0 m deep. Compute the force exerted by the water against (a) The bottom; and (b) Either end. (Hint: Calculate the force on a thin, horizontal strip at...

A skilled skier knows to jump upward before reaching a downward slope. Consider a jump in which the launch speed is v0 = 10m/s, the launch angle is 0 = 9.0o, the initial course is approximately flat,...

A small particle of mass m is pulled to the top of a frictionless half-cylinder (of radius R) by a cord that passes over the top of the cylinder, as illustrated in Figure P7.20. (a) If the particle...

(a) What is the minimum index of refraction for a glass or plastic prism to be used in binoculars (Fig. 23-26) so that total internal reflection occurs at 45o? (b) Will binoculars work if its prisms...

Figure shows a red car and a green car that move toward each other. Figure is a graph of their motion, showing the positions xg0 = 270 m and xr0 = ?? 35.0 m at time t = 0. The green car has a...

A cylindrical bucket, open at the top, is 25.0 cm high and 10.0 cm in diameter. A circular hole with a cross-sectional area 1.50 cm2 is cut in the center of the bottom of the bucket. Water flows into...

A very simplified schematic of the rain drainage system for a home is shown in Figure. Rain falling on the slanted roof runs off into gutters around the roof edge; it then drains through downspouts...