A marble of mass m and radius r rolls along the looped rough track of Fig. 8-58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of...

(a) Find the electric field (magnitude and direction) a distance z above the midpoint between two equal charges, q, a distance d apart (Fig. 2.4). Check that your result is consistent with what you'd...

A major leaguer hits a baseball so that it leaves the bat at a speed of30.0 m/s and at an angle of36.9" above the horizontal. You can ignore air resistance. (a) At what two times is the baseball at a...

An electron is shot into one end of a solenoid. As it enters the uniform magnetic field within the solenoid, its speed is 800 m/s and its velocity vector makes an angle of 30 with the central axis of...

A Multirange Ammeter The resistance of the moving coil of the galvanometer G in Fig. is 48.0 Ω, and the galvanometer deflects full scale with a current of 0.0200 A. When the meter is connected...

A uniform hollow disk has two pieces of thin light wire wrapped around its outer rim and is supported from the cei1ing (Fig. 10.51). Suddenly one of the wires breaks and the remaining wire does not...

Tarzan, who weighs 820 N, swings from a cliff at the end of a 20.0 m vine that hangs from a high tree limb and initially makes an angle of 22.0o with the vertical assume that an x axis extends...

A 20.0 kg body is moving through space in the positive direction of an x axis with a speed of 200 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 10.0 kg,...

A 500-turn solenoid, 25 cm long, has a diameter of 2.5 cm. A 10-turn coil is wound tightly around the center of the solenoid. If the current in the solenoid increased uniformly from 0 to 5.0A in 0.60...

A uniform rod of mass M and length L can pivot freely (i.e. we ignore friction) about a hinge attached to a wall, as in Fig. 8-54. The rod is held horizontally and then released. AT the moment of...

Compute the voltage drop along a 26-m length of household no. 14 copper wire (used in 15-A circuits). The wire has diameter 1.628 mm and carries a 12-A current.

At a point high in the Earths atmosphere, He 2+ ions in a concentration of 2.8 X 1012/m3 are moving due north at a speed of 2.0 X 105 m/s. Also, a 7.0 X 1011/m3 concentration of O2 ions is moving due...

A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At that point on the earths surface, the dip angle of the earths magnetic field makes an angle of 38o to the wire. Estimate...

Two stiff parallel wires a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), Fig 20-66, A magnetic field B, directed vertically...

Figure gives the one-dimensional potential energy well for a 2.0 kg particle (the function U(x) has the form bx2 and the vertical axis scale is set by us = 2.0 J). (a) If the particle passes through...

A 0.200-A current is charging a capacitor that has circular plates 10.0 cm in radius. If the plate separation is 4.00 mm, (a) What is the time rate of increase of electric field between the plates?...

A rock with mass m slides with initial velocity Vo on a horizontal surface. A retarding force FR that the surface exerts on the rock is proportional to the square root of the instantaneous velocity...

In the ohmmeter in Fig. M is a 2.50-rnA meter of resistance 65.0 Ω. (A 2.50-. mA meter deflects full scale when the current through it is 2.50 mA.) The battery B has an emf of 1.52 V and...

(a) Find the potential of point a with respect to point b in Fig. (b) If points a and b are connected by a wire with negligible resistance, find the current in the 12.0-V battery. 1.00n 12.0 V wtli...

Figure shows Atwood's machine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pulley (also of negligible mass). At time t = 0, container 1 has mass...

A horse pulls a cart with a force of 40 lb at an angle of 30o above the horizontal and moves along at a speed of 6.0 mi/h. (a) How much work does the force do in 10 min? (b) What is the average power...

When a click beetle is upside down on its back, it jumps upward by suddenly arching its back, transferring energy stored in a muscle to mechanical energy. This launching mechanism produces an audible...

Figure shows a rigid assembly of a thin hoop (of mass m and radius R = 0.150 m) and a thin radial rod (of mass m and length L = 2.00R). The assembly is upright, but if we give it a slight nudge, it...

(a) Show that a black hole attracts an object of mass m with a force of mc'Rs/ (2r'), where r is the distance between the object and the center of the black hole. (b) Calculate the magnitude of the...

A particle of mass m slides down a smooth circular wedge of mass M as shown in Figure 7-C. The wedge rests on a smooth horizontal table. Find (a) The equation of motion of m and M and (b) The...

A deuteron (nucleus of deuterium atom consisting of a proton and a neutron) with speed 14.9 km/s collides elastically with a neutron at rest. Use the approximation that the deuteron is twice the mass...

An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through one of the slots at the outside edge of the wheel, as in Figure, travels to a...

In Figure four particles form a square. The charges are q1 = q4 = Q and q2 = q3 = q. (a) What is Q/q if the net electrostatic force on particles 1 and 4 is zero? (b) Is there any value of q that...

A frame-by-frame analysis of slow-motion video shows that a hovering dragonfly takes 7 frames to complete one wing beat. If the video is shot at 240 frames per second, (a) What is the period of the...

A proton with mass m moves in one dimension. The potential-energy function is U(x) = alx2- B/x, where a and p are positive constants. The proton is released from rest at Xo = alp. (a) Show that U(x)...

Figure shows, not to scale, a cross section through the interior of Earth. Rather than being uniform throughout, Earth is divided into three zones: an outer crust, a mantle, and an inner core. The...

You are designing a delivery ramp for crates containing exercise equipment The l470-N crates will move at 1.8 m/s at the top of a ramp that slopes downward at 22.0. The ramp exerts a 550-N kinetic...

Two balls, of masses mA = 40 g and mB = 60 g, are suspended as shown in Fig. 7-44. The lighter ball is pulled away to a 60o angle with the vertical and released. (a) What is the velocity of the...

(a) By whatever means you can think of (short of looking it up), find the vector potential a distance s from an infinite straight wire carrying a current I. Check that A = 0 and x A = B. (b) Find...

A 5.00-g bullet moving with an initial speed of 400 m/s is fired into and passes through a 1.00-kg block, as in Figure P9.67. The block, initially at rest on a frictionless, horizontal surface, is...

A 5.00-kg ball is dropped from a height of 12.0 m above one end of a uniform bar that pivots at its center. The bar has mass 8.00 kg and is 4.00 m in length. At the oilier end of the bar sits another...

Consider a sound wave in air that has displacement amplitude 0.0200 mm. Calculate the pressure amplitude for frequencies of (a) 150 Hz; (b) 1500 Hz; (c) 15,000 Hz. In each case compare the result to...

Two moles of an ideal monatomic gas go through the cycle abc. For the complete cycle, 800 J of heat flows out of the gas. Process ab is at constant pressure, and process bc is at constant volume....

A swimmer is capable of swimming 0.45 m/s in still water. (a) If she aims her body directly across a 75-m-wide river whose current is 0.40m/s, how far downstream (from a point opposite her starting...

A box of mass m 2 = 3.5 kg rests on a frictionless horizontal shelf and is attached by strings to boxes of masses m 1 = 1.5 kg and m 3 = 2.5 kg, which hang freely, as shown in Figure 4-39. Both...

A 0.500-kg sphere moving with a velocity (2.00i 3.00j + 1.00k) m/s strikes another sphere of mass 1.50 kg moving with a velocity (1.00i + 2.00j 3.00k) m/s. (a) If the velocity of the 0.500-kg sphere...

A copper calorimeter can with mass 0.100 kg contains 0.160 kg of water and 0.0180 kg of ice in thermal equilibrium at atmospheric pressure. H 0.750 kg of lead at a temperature of 255C is dropped into...

Strength of the Electric Force Imagine two 1.0-g bags of protons, one at the earth's North Pole and the other at the South Pole. (a) How many protons are in each bag? (b) Calculate the gravitational...

A thin insulating rod is bent into a semicircular arc of radius a, and a total electric charge Q is distributed uniformly along the rod. Calculate the potential at the center of curvature of the arc...

(a) Find the total power radiated into space by the Sun, assuming it to be a perfect emitter at T = 5500 K. The Suns radius is 7.0 X 108 m. (b) From this, determine the power per unit area arriving...

The following data apply to a closed link traverse [like that of Figure 9.1(b)]. Compute preliminary azimuths, adjust them, and calculate departures and latitudes, misclosures in departure and...

A wheel 2.00 m in diameter lies in a vertical plane and rotates with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on...

Barry Bonds hits a home run so that the baseball just clears the top row of bleachers, 21.0 m high, located 130 m from home plate. The ball is hit at an angle of 35.0 to the horizontal, and air...

A 2.00-kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150 m, to a hanging hook with mass 3.00 kg. The system is released...

Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of...

Free electron energies in reduced zone. Consider the free electron energy bands of an fcc crystal lattice in the approximation of an empty lattice, hut in the reduced zone scheme in which all k s are...

A rock is suspended by a light string. When the rock is in air, the tension in the string is 39.2 N. When the rock is totally inunersed in water, the tension is 28.4 N. When the rock is totally...

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karens rope is more elastic, called a dynamic rope by climbers Bill has a static rope, not recommended for safety purposes in...

A slender rod, 0.240 m long, rotates with an angular speed of 8.80 rad/s about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform...

An aluminum calorimeter with a mass of 100 g contains 250 g of water. The calorimeter and water are in thermal equilibrium at 10.0C. Two metallic blocks are placed into the water. One is a 50.0-g...

Three forces acting on an object are given by F1 = (2.00i + 2.00j) N, F2 = (5.00i 3.00j) N, and F3 = (45.0i) N. The object experiences an acceleration of magnitude 3.75 m/s2. (a) What is the...

A lobstermans buoy is a solid wooden cylinder of radius r and mass M. It is weighted at one end so that it floats upright in calm sea water, having density 6. A passing shark tugs on the slack rope...

Use Lenzs law to answer the following questions concerning the direction of induced currents. (a) What is the direction of the induced current in resistor R in Figure P31.28a when the bar magnet is...

A Ferris wheel 24.0m in diameter rotates once every 15.5s (see Fig. 5-9). What is the ratio of a persons apparent weight to her real weight? (a) At the top, and (b) At the bottom?

1. A gardener pushes a mower a distance of 900 m in mowing a yard. The handle of the mower makes an angle of 40.0° with the ground. The gardener exerts a force of 35.0 N along the handle of the...

At the Fermilab accelerator in Batavia, Illinois, protons having momentum 4.80 x 10-16 kg #m/s are held in a circular orbit of radius 1.00 km by an upward magnetic field. What is the magnitude of...

A pump is required to lift 800 kg of water (about 210 gallons) per minute from a well 14.0 m deep and eject it with a speed of 18.0 m/s. (a) How much work is done per minute in lifting the water? (b)...

Size of a Light Bulb Filament. The operating \temperature of a tungsten filament in an incandescent light bulb is 2450 K, and its emissivity is 0.350. Find the surface area of the filament of a 150-W...

A 2200-kg trailer is attached to a stationary truck at point B, Fig. 9-86. Determine the normal force exerted by the road on the rear tires at A, and the vertical force exerted on the trailer by the...

A science museum has a display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. (a) If the pipes have lengths of 3.0m, 2.5m, 2.0m, 1.5m...

A tunnel of length L = 150 m, height H = 7.2 m, and width 5.8 m (with a flat roof) is to be constructed at distance d = 60 m beneath the ground. (See Figure) The tunnel roof is to be supported...

A torsional pendulum is formed by taking a meter stick of mass 2.00 kg, and attaching to its center a wire. With its upper end clamped, the vertical wire supports the stick as the stick turns in a...

Two identical conducting small spheres are placed with their centers 0.300m apart. One is given a charge of 12.0 nC and the other a charge of 18.0 nC. (a) Find the electric force exerted by one...

A lightweight, rigid beam 10.0 m long is supported by a cable attached to a spring of force constant k = 8.25 kN/m as shown in Figure P12.38. When no load is hung on the beam (Fg = 0), the length L...

SHM of a Butcher's Scale A spring of negligible mass and force constant k = 400 N/m is hung vertically, and a 0.200-kg pan is suspended from its lower end. A butcher drops a 2.2-kg steak onto the pan...

You need to siphon water from a clogged sink. The sink has an area of 0.48m2 and is filled to a height of 4.0cm. Your siphon tube rises 50 cm above the bottom of the sink and then descends 100cm to a...

In Figure, initially unpolarized light is sent into a system of three polarizing sheets whose polarizing directions make angles of ?1 = 40?, ?2 = 20?, and ?3 = 40? with the direction of the y axis....

A glass window pane has an area of 3.00 m2 and a thickness of 0.600 cm. If the temperature difference between its faces is 25.0C, what is the rate of energy transfer by conduction through the window?

A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg m2 and is rotating at 10.0 rev/min about a frictionless vertical axle. Facing the axle, a 25.0-kg child hops onto...

A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 2.00 m. A 6.00-kg object is dropped...

A particle having charge q = +2.00 μC and mass m = 0.010 0 kg is connected to a string that is L = 1.50 m long and is tied to the pivot point P in Figure P25.14. The particle, string and pivot...

Bulk Modulus of an Ideal Gas the equation of state (the equation relating pressure, volume, and temperature) for an ideal gas is pV = nRT, where n and R are constants. (a) Show that if the gas is...

Suppose a 50-kW radio station emits EM waves uniformly in all directions (a) How much energy per second crosses a 1.0-m2 area 100 m from the transmitting antenna? (b) What is the rms magnitude of the...

If two firecrackers produce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded?

A gas is compressed at a constant pressure of 0.800 atm from 9.00 L to 2.00 L. In the process, 400 J of energy leaves the gas by heat. (a) What is the work done on the gas? (b) What is the change in...

Figure shows a spherical hollow inside a lead sphere of radius R = 4.00 cm; the surface of the hollow passes through the center of the sphere and "touches" the right side of the sphere. The mass of...

A billiard ball initially at rest is given a sharp blow by a cue stick. The force is horizontal and is applied at a distance 2R/3 below the centerline, as shown in Figure. The initial speed of the...

Two cars, A and B, move along the x-axis. Figure 2.39 is a graph of the positions of A 25 x (m) and B versus time. (a) In motion diagrams (like Figs. 2.13b and 2.14b), show the position, velocity,...

Automotive Thermodynamics A Volkswagen Passat has a six-cylinder Otto cycle engine with compression ratio r = 10.6. The diameter of each cylinder, called the bore of the engine, is 82.5 mm. The...

Two horizontal forces F1 and F2 act on a 4.0 kg disk that slides over frictionless ice, on which an xy coordinate system is laid out. Force F1 is in the positive direction of the x axis and has a...

Two pulses traveling on the same string are described by y1 = 5 / (3x 4t)2 + 2 And y2 = 5 / (3x + 4t 6)2 + 2 (a) In which direction does each pulse travel? (b) At what time do the two cancel...

Certain streets in San Francisco make an angle of 17.5 with the horizontal. What force parallel to the street surface is required to keep a loaded 1967 Corvette of mass 1390 kg from rolling down such...

A very long uniform line of charge has charge per unit length 4.80 C/m and lies along the x-axis. A second long uniform line of charge has charge per unit length - 2.40 C/m and is parallel to the...

A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much...

A flat, rectangular coil consisting of 50 turns measures 25.0 cm by 30.0 cm. It is in a uniform, 1.20-T, magnetic field, with the plane of the coil parallel to the field. In 0.222 s, it is rotated so...

A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 14-18). The copper end is placed in a furnace maintained at a constant temperature of 250oC....

An ordinary glass is filled to the brim with 350.0mL of water at 100.0oC. If the temperature decreased to 20.0oC, how much water could be added to the glass?

A solid metal sphere of radius 3.00 m carries a total charge of -3.50C. What is the magnitude of the electric field at a distance from the spheres center of? (a) 0.15m, (b) 2.90m, (c) 3.10m, (d)...

A ring of matter is a familiar structure in planetary and stellar astronomy. Examples include Saturns rings and a ring nebula. Consider a uniform ring of mass 2.36 X 1020 kg and radius 1.00 X 108 m....

In a materials testing laboratory, a metal wire made from a new alloy is found to break when a tensile force of 90.8 N is applied perpendicular to each end. If the diameter of the wire is 1.84 cm,...

(a) At a distance of 0.200 cm from the center of a charged conducting sphere with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the center of the sphere?...

In an electric shaver, the blade moves back and forth over a distance of 2.0 mm in simple harmonic motion with frequency 120Hz find? (a) The amplitude, (b) The maximum blade speed, and (c) The...

A uniform solid cylinder Figure of mass M is supported on a ramp that rises at an angle θ T above the horizontal by a wire that is wrapped around its rim and pulls on it tangentially parallel...

A projectile is fired up an incline (incline angle ) with an initial speed vi at an angle i with respect to the horizontal (i > ), as shown in Figure P4.50. (a) Show that the projectile travels a...

A 1 200-N uniform boom is supported by a cable as in Figure P12.46. The boom is pivoted at the bottom, and a 2 000-N object hangs from its top. Find the tension in the cable and the components of the...