Two astronauts (Fig P11.51), each having a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.00 m/s....

An electron and a proton are each placed at rest in an electric field of 520 N/C. Calculate the speed of each particle 48.0 ns after being released.

A certain electronic device needs to be protected against sudden surges in current. In particular, after the power is turned on the current should rise no more than 7.5mA in the first 120s. The...

(a) Through what potential difference does an electron have to be accelerated, starting from rest, to achieve a speed of 0.980c? (b) What is the kinetic energy of the electron at this speed? Express...

Consider the wave packet defined by Let B(k) = e a2k2 (a) The function B(k) has its maximum value at k = 0. Let kh, be the value of k at which B(k) bas fallen to half its maximum value, and define...

A borosilicate glass (82% SiO2, 2% Al2O3, 4% Na2O, 12% B2O3) has a density of 2.23 g/cm3, while a fused silica glass (assume 100% SiO2) has a density of g/cm3. Explain why the density of the...

Weather Forecasting, A radar installation used for monitoring thunderstorms emits radio waves at a frequency of2800 MHz. A line of thunderstorms is approaching the installation at 42.0 km/h. (a) In...

A 1.50-m cylindrical rod of diameter 0500 cm is connected to a power supply that maintains a constant potential difference of 15.0 V across its ends, while an ammeter measures the current through it....

Describe the path of a moving body in the event that its acceleration is constant in magnitude at all times and (a) perpendicular to the velocity; (b) parallel to the velocity.

If a negatively charged particle enters a region of uniform magnetic field which is perpendicular to the particles velocity, will the kinetic energy of the particles increase, decrease, or stay the...

Babinet's principle, a monochromatic beam of parallel light is incident on a "collimating" hole of diameter x >> A. Point P lies in the geometrical shadow region on a distant screen (Figure a) Two...

The creation and study of new elementary particles is an important part of contemporary physics. Especially interesting is the discovery of a very massive particle. To create a particle of mass M...

Given three lightbulbs and a battery, sketch as many different electric circuits as you can.

Thin lenses Object O stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for...

How much work is done on the steam when 1.00 mol of water at 100C boils and becomes 1.00 mol of steam at 100C at 1.00 atm pressure? Assuming the steam to behave as an ideal gas, determine the change...

A plano-concave lens having index of refraction 1.50 is placed on a flat glass plate, as shown in Figure P37.64. Its curved surface, with radius of curvature 8.00 m, is on the bottom. The lens is...

You throw a baseball straight up. The drag force is proportional to v2. In terms of g, what is the y-component of the ball's acceleration when its speed is half its terminal speed and (a) it is...

A small block with mass m rests on a frictionless horizontal tabletop a distance r from a hole in the center of the table (Fig. 5.79). A string tied to the small block passes down through the hole,...

A deep-sea diver is suspended beneath the surface of Loch Ness by a l00-m-Iong cable that is attached to a boat on the surface (Fig. 15.40). The diver and his suit have a total mass of 120 kg and a...

A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it sinks 4.0cm deeper into the water. When the steps off, the raft vibrates for a while. (a) What is the frequency of...

Projectile Motion on an Incline IL Refer to Challenge Problem 3.89. (a) An archer on ground that has a constant upward slope of 30.00 aims at a target 60.0 m farther up the incline. The arrow in the...

You connect a light string to a point on the edge of a uniform vertical disk with radius R and mass M. The disk is free to rotate without friction about a stationary horizontal axis through its...

A wave pulse on a string has the dimensions showninFig.15.31 at t = 0. The wave speed is 40 cm/s. (a) If point o is a fixed end, draw the total wave on the string at t = 15 ms, 20ms, 25 ms, 30 ms, 35...

Hot Air in a Physics Leeture (a) A typical student listening attentively to a physics lecture has a heat output of 100 W. How much heat energy does a class of 90 physics students release into a...

Make a Generator? You are shipwrecked on a deserted tropical island. You have some electrical devices that you could operate using a generator but you have no magnets. The earth's magnetic field at...

An electron moves through a uniform magnetic field given by B = Bx i + (3.0Bx) j. At a particular instant, the electron has velocity v = (2.0i + 4.0) j m/s and the magnetic force acting on it is (6.4...

An electron is placed in an xy plane where the electric potential depends on x and y as shown in Figure (the potential does not depend on z). The scale of the vertical axis is set by Vs = 500 V. In...

Proton in a well figure shows electric potential V along an x axis. The scale of the vertical axis is set by Vs = 10.0 V. A proton is to be released at x = 3.5 cm with initial kinetic energy 4.00eV....

At time t = 0, the operator of the road roller disengages the transmission so that the vehicle rolls down the incline (see Figure). Determine an expression for the vehicle's speed as a function of...

The particle P travels with a constant speed of 300 mm/s along the curve. Determine its acceleration when it is located at point (200 mm, 100 mm). y (mm) 2010) 9 x (mm)

A cyclist is coasting at a steady speed of 12 m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to...

In a constant-volume process, 209 J of energy is transferred by heat to 1.00 mol of an ideal monatomic gas initially at 300 K. Find (a) The increase in internal energy of the gas, (b) The work done...

A 125-kg (including all the contents) rocket bas an engine that produces a constant vertical force (the thrust) of 1720 N. Inside this rocket, a 15.5-N electrical power supply rests on the floor. (a)...

One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates the rope transversely at 120 Hz. The other end passes over a pulley and supports a 1.5D-kg...

Light with a frequency of 5.80 x 1014 Hz travels in a block of glass that bas an index of refraction of 1.52. What is the wavelength of the light? (a) In vacuum and (b) In the glass?

A solenoid has 120 turns uniformly wrapped around a wooden core, which has a diameter of 10.0 mm and a length of 9.00 cm. (a) Calculate the inductance of the solenoid. (b) What If? The wooden core is...

A thin hoop of radius R and mass M oscillates in its own plane hanging from a single fixed point. Attached to the hoop is a small mass M constrained to move (in a frictionless manner) along the hoop....

A horizontal boom is supported at its left end by a frictionless pivot. It is held in place by a cable attached to the right-hand end of the boom. A chain and crate of total weight w hang from...

A liquid is irregularly stirred in a well-insulated container and thereby undergoes a rise in temperature. Regard the liquid as the system. (a) Has heat been transferred? How can you tell? (b) Has...

Leiden frost effect a water drop that is slung onto a skillet with a temperature between 100oC and about 200oC will last about 1 s. However, if the skillet is much hotter, the drop can last several...

Figure represents an insect caught at the midpoint of a spider-web thread. The thread breaks under a stress of 8.20 x 108 N/m2 and a strain of 2.00. Initially, it was horizontal and had a length of...

An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as where p0, a, and b are positive constants and r is the distance from the axis of the...

A mixing beater consists of three thin rods, each 10.0 cm long. The rods diverge from a central hub, separated from each other by 120, and all turn in the same plane. A ball is attached to the end of...

The electric field along the axis of a uniformly charged disk of radius R and total charge Q was calculated in Example 23.9. Show that the electric field at distances x that are large compared with R...

A wire carrying a current I is bent into the shape of an exponential spiral, r = eθ, from θ = 0 to θ = 2π as suggested in Figure P30.69. To complete a loop, the ends of the...

A certain copper wire has a resistance of 10.0. At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the...

A grating has 8300 lines/cm. How many complete spectral orders can be seen (400nm to 700nm) when it is illuminated by white light?

A plate of glass 9.00cm long is placed in contact with a second plate and is held at a small angle with it by a metal strip 0.0800 mm thick placed under one end. The space between the plates is...

A woman is draining her fish tank by siphoning the water into an outdoor drain, as shown in Figure P14.74. The rectangular tank has footprint area A and depth h. The drain is located a distance d...

A baseball player hits a foul ball straight up into the air. It leaves the bat with a speed of 120 km/h. In the absence of air resistance, how fast will the ball be travelling when the catcher...

Figure shows three crates being pushed over a concrete floor by a horizontal force F of magnitude 440N. The masses of the crates are m 1 = 30.0kg, m 2 = 10.0kg, and m 3 = 20.0kg. The coefficient of...

Two identical tuning forks can oscillate at 440Hz. A person is located somewhere on the line between them. Calculate the beat frequency as measured by this individual if (a) She is standing still and...

In a test of a "g-suit," a volunteer is rotated in a horizontal circle of radius 7.0 m. What must the period of rotation be so that the centripetal acceleration has a magnitude of (a) 3.0g? (b) 109?

A ball is held at rest at position A in Fig. 5.87 by two light strings. The horizontal string is cut and the ball starts swinging as a pendulum. Point B is the farthest to the right the ball goes as...

The total consumption of electrical energy in the United States is about 1.0 X IOt9 J per year. (a) What is the average rate of electrical energy consumption in watts? (b) The population of the...

(a) Show that the flow velocity measured by a century meter (see Fig. 10.30) is given by the relation (b) A venturi tube is measuring the flow of water; it has a main diameter of 3.0cm tapering down...

A passenger sitting in the rear of a bus claims that she was injured as the driver slammed on the brakes, causing a suitcase to come flying toward her from the front of the bus. If you were the judge...

What would be the sound level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13mm at 300 Hz?

Find the ratio of the radius R to the height H or a right-circular cylinder of fixed volume V that minimizes the surface area A.

Monochromatic light with wavelength 620 nm passes through a circular aperture with diameter 7.4 ",m. The resulting diffraction pattern is observed on a screen that is 4.5 m from the aperture. What is...

Everyday Time Dilation two atomic clocks are carefully synchronized. One remains in New York, and the other is loaded on an airliner that travels at an average speed of 250m/s and then returns to New...

The position vector for a proton is initially r = 5.0i 6.0j + 2.0k and then later is r = 2.0i + 6.0i + 2.0k, all in meters. (a) What is the proton's displacement vector, and (b) To what plane is...

The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a free-body diagram of the bird. How much...

A particle with a mass of 0.500 kg is attached to a spring with a force constant of 50.0 N/m. At time t = 0 the particle has its maximum speed of 20.0 m/s and is moving to the left. (a) Determine the...

The weight of a king's solid crown is w. When the crown is suspended by a light rope and completely immersed in water, the tension in the rope (the crowns apparent weight) is fw. (a) Prove that the...

Time Needed for a Lake to Freeze over. (a) When the air temperature is below 0oC, the water at the surface of a lake freezes to form an ice sheet. Why doesn't freezing occur throughout the entire...

Tarzan, who weighs 688N, swings from a cliff at the end of a vine 18m long (Figure). From the top of the cliff to the bottom of the swing, he descends by 3.2m. The vine will break if the force on it...

Course AB of a five-sided traverse runs due north. From the given balanced interior angles to the right, compute and tabulate the bearings and azimuths from north for each side of the traverses in...

Two friends are carrying a 200-kg crate up a flight of stairs. The crate is 1.25 m long and 0.500 m high, and its center of gravity is at its center. The stairs make a 45.0° angle with respect to...

Three charged particles are placed at the corners of an equilateral triangle of side 1.20m (Fig. 16-53). The charges are + 4.0μC, - 8.0μC, and 6.0μC. Calculate the magnitude and direction of...

An automobile drag racer drives a car with acceleration a and instantaneous velocity v. The tires (of radius r0) are not slipping Find which point on the tire has the greatest acceleration relative...

The radius Rh and mass Mh of a black hole are related by Rh = 2GMh/c2, where c is the speed of light. Assume that the gravitational acceleration ar of an object at a distance ro = 1.001Rh, from the...

A beam contains 2.0 x 108 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.0 x 105 m/s. What are the (a) Magnitude and (b) Direction of the current...

In Figure, a ball is shot directly upward from the ground with an initial speed of v0 =7.00 m/s, simultaneously a construction elevator cab begins to move upward from the ground with a constant speed...

A thin, uniform rod is hinged at its midpoint. To begin with, one-half of the rod is bent upward and is perpendicular to the other half. This bent object is rotating at an angular velocity of 9.0...

A straight cylindrical wire lying along the x axis has a length L and a diameter d. It is made of a material that obeys Ohms law with a resistivity %. Assume that potential V is maintained at x = 0,...

A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this solar sail. Suppose a sail of area...

An object is placed against the center of a spherical mirror and then moved 70 cm from it along the central axis as the image distance i is measured. Figure gives i versus object distance p out to...

An automobile accident causes both the driver and passenger front airbags to deploy. (a) If the vehicle was traveling at a speed of 88.6 km/h and is now at rest, find the change in momentum for both...

Falling Baseball You drop a baseball from the roof of a tall building. As the ball falls, the air exerts a drag force proportional to the square of the ball's speed (f= Dv2). (a) In a diagram, show...

In her hand a softball pitcher swings a ball of mass 0.250 kg around a vertical circular path of radius 60.0 cm before releasing it from her hand. The pitcher maintains a component of force on the...

Imagine that a hole is drilled through the center of the Earth to the other side. An object of mass m at a distance r from the center of the Earth is pulled toward the center of the Earth only by the...

Batteries are rated in terms of ampere-hours (A h). For example, a battery that can produce a current of 2.00 A for 3.00 h is rated at 6.00 A h. (a) What is the total energy, in kilowatt-hours,...

Doppler Radar. A giant thunderstorm is moving toward a weather station at 45.0mi/h (20.1 m/s). If the station sends a radar beam of frequency 200.0 MHz toward the storm, what is the difference in...

A parallel-plate capacitor has plates with area 0.0225 m2 separated by 1.00 mm of Teflon. (a) Calculate the charge on the plates when they are charged to a potential difference of 12.0 V. (b) Use...

The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A h). A 50- A h battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h,...

(a) In Problem, remove sphere A and calculate the gravitational potential energy of the remaining three-particle system. (b) Lt A is then put back in place, is the potential energy of the...

A certain electric dipole is placed in a uniform electric field E of magnitude 40 N/C. Figure gives the magnitude of the torque on the dipole not versus the angle between field E and the dipole...

A cube is placed so that one comer is at the origin and three edges are along the x-, y-, and z-axes of a coordinate system (Fig. 1.43). Use vectors to compute (a) The angle between the edge along...

(a) Derive Eq. (9.12) by combining Eqs. (9.7) and (9.11) to eliminate f (b) The angular velocity of an airplane propeller increases from 12.0 rad/s to 16.0 rad/s while turning through 7.00 rad. What...

A block of mass M, supported by a string, rests on an incline making an angle θ with the horizontal. The string's length is L and its mass is m

An Earth satellite has a perigee of 300 km and an apogee of 3,500 km above Earths surface. How far is the satellite above Earth when (a) It has rotated 90o around Earth from perigee and (b) It has...

An electromagnetic wave has a magnetic field given by B(x, t) = (8.25 x 10-9 T)j sin[(1.38 x 104rad/m)x + wt]. (a) In which direction is the wave traveling? (b) What is the frequency f of the wave?...

An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.190 s. The first officer on the spacecraft measures that the...

Hexagonal emit-packed structure Consider first Brillouin zone of a crystal with a simple hexagonal lattice in three dimensions with lattice constants a and c. Let G c denote the shortest reciprocal...

The flywheel of an engine is rotating at 25-A rad/s. When the engine is turned off, the flywheel slows at a constant rate and stops in 20.0 s. Calculate (a) The angular acceleration of the flywheel,...

(a) Explain what happens to the balls of Problem 54 if one of them is discharged (loses its charge q to, say, the ground).(b) Find the new equilibrium separation x, using the given values of L and m...

A crate of eggs is located in the middle of the flat bed of a pickup truck as the truck negotiates an un-banked curve in the road. The curve may be regarded as an arc of a circle of radius 35.0 m. If...

A charge + q is at the origin. A charge -2q is at x = 2.00 m on the x axis. For what finite value(s) of x is (a) The electric field zero? (b) The electric potential zero?

A rocket is launched vertically from rest with a constant upward acceleration of 1.75 m/s'. Suddenly 220 s after launch, an unneeded fuel tank is jettisoned by shooting it away from the rocket. A...