Using nodal analysis, find current io in the circuit of Fig. 3.66? Figure 3.66 4 2 10 8 60 V 3i,

The active element of a certain laser is made of a glass rod 30.0 cm long by 1.50 cm in diameter. If the temperature of the rod increases by 65.0C, what is the increase in (a) Its length, (b) Its...

The plane of a 5.0 cm X 8.0 cm rectangular loop of wire is parallel to a 0.19-T magnetic field. The loop carries a current of 6.2 A. (a) What torque acts on the loop? (b) What is the magnetic moment...

An asteroid of mass 1.0 x 105 kg, traveling at a speed of 30 km/s relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earths rotation. Use angular momentum to...

A 20.0 g copper ring at 0.000oC has an inner diameter of D = 2.54000 cm. An aluminum sphere at 100.0oC has a diameter of d = 2.545 08 cm. The sphere is placed on top of the ring (Figure), and the two...

Figure shows, in cross section, three infinitely large non-conducting sheets on which charge is uniformly spread. The surface charge densities are ? 1 = +2.00pC/m 2 ? 2 = +4.00pC/m 2 , and ? 3 = ?...

A traveling wave propagates according to the expression y = (4.0 cm) sin (2.0x 3.0t), where x is in centimeters and t is in seconds. Determine (a) The amplitude, (b) The wavelength, (c) The...

A 50.0-m length of coaxial cable has an inner conductor that has a diameter of 2.58 mm and carries a charge of 8.10 C. The surrounding conductor has an inner diameter of 7.27 mm and a charge of -8.10...

An astronaut is tethered by a strong cable to a spacecraft. The astronaut and her space snit have a total mass of 105 kg, while the mass of the cable is negligible. The mass of the spacecraft is 9.05...

The sound source of a ship's sonar system operates at a frequency of 22.0 kHz. The speed of sound in water (assumed to be at a uniform 20C) is 1482 m/s. (a) What is the wavelength of the waves...

If a 1500-kg car can accelerate from 35 km/h to 55km/g in 3.2s, how long will it take to accelerate from 55 km/g to 75 km/h? Assume the power stays the same, and neglect frictional losses.

A heart pacemaker is designed to operate at 72 beats/min using a 7.5-F capacitor in a simple RC circuit what value of resistance should be used if the pacemaker is to fire (capacitor discharge) when...

A rod of length rotates about the z-axis with an angular velocity w. If B = Boaz, calculate the voltage induced on the conductor.

Consider a science fiction universe in which the number of photons N is constant, at a concentration of 1020 cm3. The number of thermally excited photons we assume is given by the result of Problem...

Estimate the density of the water 6.0 km deep in the sea. (Se Table9-1 and Section 9-5 regarding bulk modulus.) By what fraction does it differ from the density at the surface?

How fast does water flow from a hole at the bottom of a very wide, 4.6-m-deep storage tank filled with water? Ignore viscosity.

A cart is propelled over an xy plane with acceleration components ax = 4.0m/ 2 and a y = 2.0m/s 2 . Its initial velocity has components v 0x = 8.0 m/s and v 0y = 12m/s. In unit-vector notation, what...

A cube of wood having an edge dimension of 20.0 cm and a density of 650 kg/m3 floats on water. (a) What is the distance from the horizontal top surface of the cube to the water level? (b) How much...

Two-Dimensional Waves. A stretched string lies along the x-axis. The string is displaced along both the y- and z-directions, so that the transverse displacement of the string is given by Y(x, t) =...

Electronic devices found in integrated circuits are composed of very high purity silicon to which has been added small and very controlled concentrations of elements found in Groups IIIA and VA of...

Boiling Water at High Pressure When water is boiled at a pressure of 2.00 atm, the heat of vaporization is 2.20 X 106 I/kg and the boiling point is 120C. At this pressure, 1.00 kg of water has a...

Interplanetary space contains many small particles referred to as interplanetary dust. Radiation pressure from the sun sets a lower limit on the size of such dust particles. To see the origin of this...

The three spheres in Figure with masses mA = 80 g, mB = 10 g, and mC = 20 g, have their centers on a common line, with L = 12 cm and d = 4.0 cm. You move sphere B along the line until its...

A bar is used to lift a 100-kg block of concrete. The pivot is 1.00 m from the block. (a) If the worker pushes down on the other end of the bar a distance of 2.50 m from the pivot, what force (in N)...

A circular pizza of radius R has a circular piece of radius R/2 removed from one side as shown in Figure P12.4. The center of gravity has moved from C to C` along the x axis. Show that the distance...

Figure 34.3 shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose that the wavelength is 50.0 m, and the electric field vibrates in the xy plane with amplitude of 22.0...

A ball with mass M, moving horizontally at 5.00 m/s, collides elastically with a block with mass 3M that is initially hanging at rest from the ceiling on the end of a 50.G-cm wire. Find the maximum...

A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.3m/s. Calculate its total kinetic energy.

A circular loop of wire with a radius of 12.0 cm and oriented in the horizontal xy-plane is located in a region of uniform magnetic field. A field of 1.5 T is directed along the positive z-direction,...

One 110-kg football lineman is running to the right at 2.75 m/s while another 125-kg lineman is running directly toward him at 2.60 m/s. What are? (a) The magnitude and direction of the net momentum...

A plumber steps out of his truck, walk 50m east and 25m south, and then takes an elevator 10m down into the subbasement of a building where a bad leak is occurring. What is the displacement of the...

A very long cylinder, of radius a, carries a uniform polarization P perpendicular to its axis. Find the electric field inside the cylinder. Show that the field outside the cylinder can be expressed...

A ice block floating in a river is pushed through a displacement d = (15 m)i - (12 m)j along a straight embankment by rushing water, which exerts a force F = (210 N)i - (150 N)j on the block. How...

Show that the geodesic on the surface of a right circular cylinder is a segment of a helix.

A piece of wire bent into a loop, as shown in Fig. 10.5, carries a current that increases linearly with time: I (t) = kt. Calculate the retarded vector potential A at the center. Find the electric...

For the wire arrangement in Figure, a = 12.0 cm and b = 16.0 cm. The current in the long straight wire is given by i = 4.50t2 - 10.0t, where i is in amperes and r is in seconds. (a) Find the emf in...

In Figure a, a particle of elementary charge +e is initially at coordinate z = 20 nm on the dipole axis (here a z axis) through an electric dipole, on the positive side of the dipole. (The origin of...

Banked Cone I A curve with a 120-m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s. what is the minimum coefficient of static...

At what distance above the surface of the earth is the acceleration due to the earth's gravity 0.980 m/s2 if the acceleration due to gravity at the surface has magnitude 9.80 mls2?

If an ohmmeter is connected between points a and b in each of the circuits shown in Fig, what will it read? (a) (b) a 100.0N b 7.00 N a 10.006 60.00 50.0N 75.0 N 25,00 30.0 0 20.00 40.0 0 50.0 (n...

Fusion Reactor If two deuterium nuclei (charge +e, mass 3.34 X 10-27 kg) get close enough together, the attraction of the strong nuclear force will fuse them to make an isotope of helium, releasing...

In Figure water flows through a horizontal pipe and then out into the atmosphere at a speed v1 = 15 m/s. The diameters of the left and right sections of the pipe are 5.0 cm and 3.0 cm. (a) What...

A conducting bar is connected via flexible leads to a pair of rails in a magnetic field B = 6 cos 10t ax mWb/m2 as in figure. If the z-axis is the equilibrium position of the bar and its velocity is...

A 1.20-kg ball is projected straight upward with an initial speed of 18.5 m/s and reaches a maximum height of 14.7 m. (a) Show numerically that total mechanical energy is not conserved during this...

A particle moves along the x axis from x = 12.8 m to x = 23.7 m under the influence of a force F= 375/x3 +3.75x Where F is in newtons and x is in meters. Using numerical integration, determine the...

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude...

A factory worker pushes a 30.O-kg crate a distance of 4.5 m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor...

Archimedes is said to have burned the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with huge spherical mirror. Is this reasonable?

The eyepiece of a refracting telescope (see Fig. 34.53) has a focal length of 9.00 cm. The distance between objective and eyepiece is 1.80 m, and the final image is at infinity. What is the angular...

Longitudinal wave velocity, show that the velocity of a longitudinal wave in the [111] direction of a cubic crystal is given by v s = [1/3(C 11 + 2C 12 + 4C 44 )/p] 1/2 .

Figure P1.14 shows a frustum of a cone. Of the following mensuration (geometrical) expressions, this describes (a) The total circumference of the flat circular faces (b) The volume (c) The area of...

(a)An electron is to be accelerated from 3.00 X 106 m/s to 8.00 X 106 m/s. Through what potential difference must the electron pass to accomplish this? (b)Through what potential difference must the...

A bolt is dropped from a bridge under construction, falling 90 m to the valley below the bridge. (a) In how much time does it pass through the last 20% of its fall? What is its speed? (b) When it...

An infinitely long cylindrical insulating shell of inner radius a and outer radius b has a uniform volume charge density 1. A line of uniform linear charge density A is placed along the axis of the...

Example 16.1 (Section 16.1) showed that for sound waves in air with frequency 1000 Hz, a displacement amplitude of 1.2 X 10-8 m produces a pressure amplitude of 3.0 X 10-2 Pa Water at 20C has a bulk...

A straight wire caries a 10.0-A current (Fig) ABCD is a rectangle with point D the middle of a 1.10-mm segment of the wire and point C in the wire. Find the magnitude and direction of the magnetic...

A student builds and calibrates an accelerometer, which she uses to determine the speed of her car around a certain unbanked highway curve. The accelerometer is a plumb bob with a protractor that she...

(a) Calculate the speed of a proton that is accelerated from rest through a potential difference of 120 V. (b) Calculate the speed of an electron that is accelerated through the same potential...

A spy satellite can consist essentially of a large-diameter concave mirror forming an image on a digital-camera detector and sending the picture to a ground receiver by radio waves. In effect, it is...

A rocket carrying a satellite is accelerating straight up from the earth's surface. At 1.15 s after liftoff, the rocket clears the top of its launch platform, 63 m above the ground. After an...

Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Hz (A). (a) What are the frequencies of the first two overtones for each string? (b) If the two strings have the same...

A three-particle system consists of masses mi and coordinates (x1, x2, x3) as follows: Find the inertia tensor, principal axes, and principal moments of inertia. , (, 0, b) , 4m, (b, , -6) 2m,...

A positron (charge + e, mass equal to the electron mass) is moving at 1.0 x 107 m/s in the positive direction of an x axis when, at x = 0, it encounters an electric field directed along the x axis....

The magnetic vector potential of a current distribution in free space is given by A = 15ep sin az Wb/m Find H at (3, /4, 10). Calculate the flux through = 5, 0 < < /2, 0 < z < 10.

Four resistors are connected to a battery as shown in Figure P28.19. The current in the battery is I, the battery emf is , and the resistor values are R1 = R, R2 = 2R, R3 = 4R, R4 = 3R. (a) Rank the...

A weightlifter stands on a bathroom scale. He pumps a barbell up and down. What happens to the reading on the bathroom scale as this is done? What if he is strong enough to actually throw the barbell...

At the interface between one linear dielectric and another the electric field lines bend (see Fig. 4.34). Show that tan ? 2 /tan ? 1 = ? 2 / ? 1 , (4.68) assuming there is no free charge at the...

In Figure a two identical rectangular rods of metal are welded end to end, with temperature of T1 = 0oC on the left side and a temperature of T2 = 100oC on the right side. In 2.0 min, 10J is...

A penny of mass 3.10 g rests on a small 20.0-g block supported by a spinning disk (Fig. P6.60). The coefficients of friction between block and disk are 0.750 (static) and 0.640 (kinetic) while those...

A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density p (r} is given by Here a is a positive constant having units of C/m3. (a)...

An elevator in a tall building is allowed to reach a maximum speed of 3.5m/s going down. What must the tension be in the cable to stop this elevator over a distance of 2.6m if the elevator has a mass...

A frictionless plane is 10.0 m long and inclined at 35.0. A sled starts at the bottom with an initial speed of 5.00 m/s up the incline. When it reaches the point at which it momentarily stops, a...

The maximum distance from the Earth to the Sun (at our aphelion) is 1.521 X 1011 m, and the distance of closest approach (at perihelion) is 1.471 X 1011 m. If the Earths orbital speed at perihelion...

Rigid rods of negligible mass lying along the y axis connect three particles (Fig. P10.20). If the system rotates about the x axis with an angular speed of 2.00 rad/s, find (a) The moment of inertia...

A capacitor has two parallel plates with area A separated by a distance d. The space between plates is filled with a material having dielectric constant K. The material is not a perfect insulator but...

Two ships, A and B, leave port at the same time. Ship A travels northwest at 24 knots, and ship B travels at 28 knots in a direction 40o west of south. (1 knot = 1 nautical mile per hour; see...

A 2-kg block is released 4 m from a massless spring with a force constant k = 100 N/m that is fixed along a frictionless plane inclined at 30, as shown in Figure. (a) Find the maximum compression of...

A 4.00-L sample of a diatomic ideal gas with specific heat ratio 1.40, confined to a cylinder, is carried through a closed cycle. The gas is initially at 1.00 atm and at 300 K. First, its pressure is...

Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is 27.0C and the pressure is constant. As part of a machine design project,...

A charge of 28.0 nC is placed in a uniform electric field that is directed vertically upward and has a magnitude of 4.00 X 104 V/m. What work is done by the electric force when the charge moves? (a)...

Critical Current Density in Superconductors One problem with some of the newer high-temperature super conductors is getting a large enough current density for practical use without causing the...

If a 6.13-g sample of an isotope having a mass number of 124 decays at a rate of 0.350Ci, what is its half-life?

In Figure, a thin uniform rod (mass 3.0 kg, length 4.0 m) rotates freely about a horizontal axis A that is perpendicular to the rod and passes through a point at distance d = 1.0 m from the end of...

At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi = (3.00i 2.00j) m/s and is at the origin. At t = 3.00 s, the particles velocity is v = (9.00i + 7.00j) m/s....

The Hydrogen Maser You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency of these waves is 1,420,405,751.786 hertz. (A hertz is another nanre for one...

A monatomic ideal gas that is initially at a pressure of 1.50 X 105 Pa and has a volume of 0.0800 m' is compressed adiabatically to a volume of 0.0400 m3. (a) What is the final pressure? (b) How much...

A particle of mass m can slide freely along a wire AB whose perpendicular distance to the origin O is h. The line OC rotates about the origin at a constant angular velocity θ = w. The position...

A particle of mass m moving along the x axis with a velocity component +u collides head-on and sticks to a particle of mass m/3 moving along the x axis with the velocity component -u. What is the...

A homogeneous slab of thickness a is placed atop a fixed cylinder of radius R whose axis is horizontal. Show that the condition for stable equilibrium of the slab, assuming no slipping, is R > a/2....

Fluid flows in pipe networks can be analyzed in a manner similar to that used for electric resistance networks. Figure (a) shows a network with three pipes, which is analogous to the electrical...

A cube of steel has a volume of 1.00 cm3 and a mass of 8.00 g when at rest on the Earth. If this cube is now given a speed u = 0.900c, what is its density as measured by a stationary observer? Note...

(a) If a flea can jump straight up to a height of 0.440 m, what is its initial speed as it leaves the ground? (b) How long is it in the air?

A softball having a mass of 0.25kg is pitched at 95km/g. By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch,...

What is the smallest thickness of a soap film (n = 1.42) that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film.

How fast must a rocket travel relative to the earth so that time in the rocket "slows down'" to half its rate as measured by earth-based observers? Do present-day jet planes approach such speeds?

A sealed tank containing seawater to a height of 11.0 m also contains air above the water at a gauge pressure of 3.00 atm. Water flows out from the bottom through a small hole. How fast is this water...

Two spherical cavities, of radii a and b, are hollowed out from the interior of a (neutral) conducting sphere of radius R (Fig. 2.49). At the center of each cavity a point charge is placed???call...

In Figure the current in resistance 6 is i 6 = 1.40 A and the resistances are R 1 = R 2 = R 3 = 2.00?, R 4 = 16.0?, R 5? = 8.00?, and R 6 = 4.00?. What is the emf of the ideal battery? R. R,

A flat-topped toy cart moves on frictionless wheels, pulled by a rope under tension T. The mass of the cart is m1. A load of mass m2 rests on top of the cart with a coefficient of static friction s....

Two stars of masses M and m, separated by a distance d, revolve in circular orbits about their center of mass (Fig. P13.69). Show that each star has a period given by T2 = 4π2d3/G (M + m) Proceed...