There are two equations from which a change it the gravitational potential energy U of the system of a mass m and the earth can be calculated. One is U = may (Eq. 7.2). The other is U = - GmEm/ r...

A vertical spring (ignore its mass). Whose spring stiffness constant is 950 N/m. (a) What upward speed can it give to a 0.30-kg ball when released? (b) How high above its original position (spring...

A sailor strikes the side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5s later. How deep is the ocean at this point? Assume...

A solid sphere of mass M and radius R rotates freely in space with an angular velocity w about a fixed diameter. A particle of mass m, initially at one pole, moves with a constant velocity v along a...

A water droplet falling in the atmosphere is spherical. Assume that as the droplet passes through a cloud, it acquires mass at a rate equal to kA where k is a constant (>0) and A its cross-sectional...

A cargo plane is flying horizontally at an altitude of 12 km with a speed of 900 km/h when a battle tank falls out of the rear loading ramp. (a) How long does it take the tank to hit the ground? (b)...

Calculate the potential difference between points a and b in Figure P28.54 and identify which point is at the higher potential. 4.00 V 2.00 4.00 T120 V 10.0

An antelope moving with constant acceleration covers the distance between two points 70.0 m apart in 7.00 s. Its speed as it passes the second point is 15.0 m/s. (a) What is its speed at the first...

A closely wound, circular coil with a diameter of 4.00 cm has 600 turns and carries a current of 0.500 A. What is the magnitude of the magnetic field? (a) At the center of the coil and (b) At a point...

In a hot days race a bicyclist consumes 8.0 L of water over the span of four hours. Making the approximation that all of the cyclists energy goes into evaporating this water as sweat, how much energy...

Three-Dimensional Anisotropic Harmonic Oscillator An oscillator bas the potential-energy function U(x. y. z) = k1(x2 + y2) + k2 z2 where k1 > k2. This oscillator is called anisotropic because the...

In Figure, three uniform thin rods, each of length L = 22cm, form an inverted U. The vertical rods each have a mass of 14g; the horizontal rod has a mass of 42g. What are?(a) The x coordinate and(b)...

A hand pump is used to inflate a bicycle tire to a gauge pressure of 482 kPa (about 70 lb/in2). How much work must be done if each stroke of the pump is an adiabatic process? Atmospheric pressure is...

For the circuit shown in Fig. 19-46, find the potential difference between points a and b, each resistor has R = 75Ω and each battery is 1.5V. 15 V

Determine the binding energy of the last neutron in a 40/19K nucleus.

Consider two vibrations of equal amplitude and frequency but differing in phase, one along the x-axis, x = a sin (wt - a) and the other along the y-axis, y = a sin (wt - ?) These can be written as...

At the Earths surface a projectile is launched straight up at a speed of 10.0 km/s. To what height will it rise? Ignore air resistance and the rotation of the Earth.

Angle for Minimum Force. A box with weight w is pulled at constant speed along a level floor by a force F that is at an angle 6 above the h0ri2ontal. The coefficient of kinetic friction between the...

Suppose a piece of Styrofoam, p = 180 kg/m3, is held completely submerged in water (Fig. 14.46). (a) What is the tension in the cord? Find this using Archimedes's principle. (b) Use P = Po + pgh to...

A fixed force center scatters a particle of mass m according to the force law F(r) = k/r3. If the initial velocity of the particle is u0, show that the differential scattering cross section is km (T...

How much mass of 238/92U is required to produce the same amount of energy as burning 1.0kg of coal (about 3 X 107J)?

Find the current in the 4.00- resistor in the drawing. Specify the direction of thecurrent. 2.00 8.00 6.00 V 3.00 V 9.00 v 4.00

Calculate the centrifugal acceleration, due to Earths rotation, on a particle on the surface of Earth at the equator. Compare this result with the gravitational acceleration. Compute also the...

In a physics lab, light with wavelength 490 nm travels in air from a laser to a photocell in 17.0ns. When a slab of glass 0.840 m thick is placed in the light beam, with the beam incident along the...

Find the longest and shortest wavelengths in the Lyman and Paschen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?

A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric metal shell (inner radius a, outer radius b, as in Fig. 2.48). The shell carries no net charge. (a) Find the surface...

(a) Prove that the average magnetic field, over a sphere of radius R, due to steady currents within the sphere, is where m is the total dipole moment of the sphere. Contrast the electrostatic result,...

What is the bulk modulus of oxygen if 32.0 g of oxygen occupies 22.4 L and the speed of sound in the oxygen is 317 m/s?

A boat floating in fresh water displaces water weighing 35.6kN. (a) What is the weight of the water this boat displaces when floating in salt water of density 1.10 x 103 kg/m3? (b) What is the...

The block A has a mass of 2 kg and slides into and open ended box B with a velocity of 2m/s. If the box has a mass of 3 kg and rests on top of a plate P that has a mass of 3 kg, determine the...

Torque on a Current Loop in a Nonuniform Magnetic Field. In Section 27.7 the expression for the torque on a current loop was derived assuming that the magnetic field B was uniform. But what if B is...

An earthquake P wave traveling at 8.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 47o and the angle of refraction is...

Determine the magnitudes and directions of the currents in each resistor shown if Fig. 19-48. The batteries have emfs of ε1 = 9.0 V and ε2 = 12.0 V and the resistors have values of R1...

The ends of a cylindrical rod 6.4 mm (0.25 in.) in diameter and 250 mm (10 in.) long are mounted between rigid supports. The rod is stress free at room temperature [20C (68F)]; and upon cooling to...

The following figure shows the tensile stress-strain curve for a plain-carbon steel. (1) What is this alloy's tensile strength? (A) 650 MPa (B) 300 MPa (C) 570 MPa (D) 3,000 MPa (2) What is its...

A uniform electric field is directed due east. Point B is 2.00 m west of point A, point C is 2.00 m east of point A and point D is 2.00 m south of A. For each point, B, C, and D, is the potential at...

A cannon in a fort overlooking the ocean fires a shell of mass M at an elevation angle and muzzle velocity v0. At the highest point, the shell explodes into two fragments (mass m1 + m2 = M), with an...

A billiard ball of initial velocity u1 collides with another billiard ball (same mass) initially at rest. The first ball moves off at = 45o. For an elastic collision, what are the velocities of both...

Of the charge Q on a tiny sphere, a fraction d is to be transferred to a second, nearby sphere. The spheres can be treated as particles. (a) What value of a maximizes the magnitude F of the...

A solid non-conducting sphere of radius R = 5.60 cm has a non-uniform charge distribution of volume charge density p: (14.1pC/m3)r/R, where r is radial distance from the sphere's center. (a) What is...

A 215-g sample of a substance is heated to 330oC and then plunged into a 105-g aluminum calorimeter cup containing 165g of water and 1 17-g glass thermometer at 12.5oC. The final temperature is...

A rocket starts from rest in free space by emitting mass, at what fraction of the initial mass is the momentum a maximum?

A Circuit within a Circuit Fig. 29.47 shows a small circuit within a larger one, both lying on the surface of a table. The switch is closed at t = 0 with the capacitor initially uncharged. Assume...

The radii of curvature of the surfaces of a thin converging meniscus lens are R1 = + 12.0 cm and R2 = + 28.0 cm. The index of refraction is 1.60. (a) Compute the position and size of the image of an...

Radiocarbon Dating a sample from timbers at an archeological site containing 500g of carbon provides 3070 decays/min. What is the age of the sample?

A container holds a mixture of three non reacting gases: 2.40 mol of gas 1 with Cv1 = 12.0 J/mol ?? K, 1.50 mol of gas 2 with Cv2 = 12.8 J/mol ?? K and 3.20 mol of gas 3 with Cv3 = 20.0 J/mol ?? K....

An electron with speed vo = 21.5 x 106 m/s is traveling parallel to an electric field of magnitude E = 11.4 X 103 N/C. (a) How far will the electron travel before it stops? (b) How much time will...

A wire with current i = 3.00 A is shown in Figure. Two semi-infinite straight sections, both tangents to the same circle, are connected by a circular arc that has a central angle and runs along the...

Engineers at Boeing developing specs for their next-generation 737 aircraft needed to know the acceleration of the 737-900 during a typical take-off. (a) What acceleration would they calculate given...

Cycling For a touring bicyclist the drag coefficient C(f air = 2 ) is 1.00, the frontal area A is 0.463 m2, and the coefficient of rolling friction is 0.0045. The rider has mass SO.O kg, and her bike...

(a) What are the x and y components of each vector? (b) Determine the sum V1 + V2 (magnitude and angle).

Compute the gradient and Laplacian of the function T = r (cos + sin cos ). Check the Laplacian by converting T to Cartesian coordinates and using Eq. 1.42. Test the gradient theorem for this...

A small rectangular tank 5.00 in. by 9.00 in. is filled with mercury. (a) If the total force on the bottom of the tank is 165 lb, how deep is the mercury? (Weight density of mercury = 0.490 lb/in3.)...

An airplane whose air speed is 620 km/h is supposed to fly in a straight path 35.0o north of east. But a steady 95 km/h wind is blowing from the north. In what direction should the plane head?

Evaporative cooling of beverages a cold beverage can be kept cold even on a warm day if it is slipped into a porous ceramic container that has been soaked in water. Assume that energy lost to...

(a) Determine the dc resistance of a round copper wire ( = 5.8 X 10 7 S/m, r = 1, r = 1) of radius 1.2 mm and length 600 m. (b) Find the ac resistance at 100 MHz. (c) Calculate the approximate...

Why are drag- racing tires wide and smooth, whereas passenger- car tires are narrower and have tread (Fig. 4.32)? Are there frictional and/ or safety considerations? Does this difference between the...

A 0.400-kg particle slides around a horizontal track. The track has a smooth vertical outer wall forming a circle with a radius of 1.50 m. The particle is given an initial speed of 8.00 m/s. After...

A small sphere that carries a charge q is whirled in a circle at the end of an insulating string. The angular frequency of rotation is w. What average current does this rotating charge represent?

A cubic box of volume 5.1 X 10-2 m3 is filled with air at atmospheric pressure at 20oC. The box is closed and heated to 180oC. What is the net force on each side of the box?

Vector A has a magnitude of 6.00 units, vector B has a magnitude of 7.00 units, and A B has a value of 14.0. What is the angle between the directions A and B?

A square steel tube of length L = 20 ft and width b2 = 10.0 in. is hoisted by a crane (see figure). The tube hangs from a pin of diameter d that is held by the cables at points A and B. The cross...

An electron is accelerated through 2 400 V from rest and then enters a uniform 1.70-T magnetic field. What are? (a) The maximum and (b) The minimum values of the magnetic force this charge can...

As a result of his observations, Roemer concluded that eclipses of Io by Jupiter were delayed by 22 min during a 6 month period as the Earth moved from the point in its orbit where it is closest to...

Supernova! The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. The explosion was seen on the earth on...

Steam Burns Versus Water Burns. What is the amount of heat input to your skin when it receives the heat released? (a) By 25.0 g of steam initially at 100.CC, when it is cooled to skin temperature...

The force on a charged particle moving in a magnetic field can be computed as the vector sum of the forces due to each separate component of the magnetic field. As an example, a particle with charge...

Figure gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by Es = 5.0 x...

In Figure a, we move an electron from an infinite distance to a point at distance R = 8.00 cm from a tiny charged ball. The move requires work W = 2.76 x 10-13 J by us. (a) What is the charge Q on...

On average, an eye blink lasts about 100ms. How far does a MiG-25 "Fox bat" fighter travel during a pilot's blink it the plane's average velocity is 3400 km/h?

Two blocks, of masses M = 2.0 kg and 2M, are connected to a spring of spring constant k = 200 N/m that has one end fixed, as shown in Figure. The horizontal surface and the pulley are frictionless,...

As the drawing illustrates, a pond has the shape of an inverted cone with the tip sliced off and has a depth of 5.00 m. The atmospheric pressure above the pond is 1.01 105 Pa. The circular top...

Given two 2.00-+C charges, as shown in Figure P25.16, and a positive test charge q = 1.28 x 10-18 C at the origin, (a) What is the net force exerted by the two 2.00-+C charges on the test charge q?...

In a purely inductive AC circuit, as shown in Figure 33.6, Vmax = 100 V. (a) The maximum current is 7.50 A at 50.0 Hz. Calculate the inductance L. (b) What If? At what angular frequency w is the...

(a) What is the equivalent resistance of the circuit shown in Fig. 19-70? (b) What is the current in the 18- resistor? (c) What is the current in the 12- resistor? (d) What is the power dissipation...

If the potassium isotope 40/19K gives 60 decays/s in a liter of milk, estimate how much 40/19K and regular 36/19K are in a liter of milk. Use Appendix B.

A 4.78-MeV alpha particle from a 226Ra decay makes a head-on collision with a uranium nucleus. A uranium nucleus has 92 protons. (a) What is the distance of closest approach of the alpha particle to...

A hollow conducting cylinder has inner radius a and outer radius b and carries current I along the positive z-direction. Find H everywhere.

Light of wavelength 0 in a vacuum has a wavelength of 438 nm in water and a wavelength of 390 nm in benzene. (a) What is the wavelength 0? (b) Using only the given wavelengths, determine the ratio of...

Water is flowing from the 150-mm-diameter fire hydrant with a velocity vB = 15 m/s. Determine the horizontal and vertical components of force and the moment developed at the base joint A, if the...

A sinusoidal voltage v (t) = (40.0 V) sin(100t) is applied to a series RLC circuit with L = 160 mH, C = 99.0 F, and R = 68.0 . (a) What is the impedance of the circuit? (b) What is the maximum...

Torque on a Dipole. An electric dipole with dipole moment p is in a uniform electric field E. (a) Find the orientations of the dipole for which the torque on the dipole is zero. (b) Which of the...

When UV light of wavelength 285nm falls on a metal surface, the maximum kinetic energy of emitted electrons is 1.40eV. What is the work function of the metal?

A uniform rod rotates in a horizontal plane about a vertical axis through one end. The rod is 6.00 m long, weighs 10.0 N and rotates at 240 rev/min. Calculate (a) Its rotational inertia about the...

A clock with a brass pendulum has a period of 1.000 s at 20.0C. If the temperature increases to 30.0C, (a) By how much does the period change, and (b) How much time does the clock gain or lose in one...

Using Kirchhoffs rules, (a) Find the current in each resistor in Figure P28.24. (b) Find the potential difference between points c and f. Which point is at the higher potential?

A uniform 2.00-m ladder of mass 9.00 kg is leaning against a vertical wall while making an angle of 53.0 with the floor. Worker posses the ladder up against the wall until it is vertical. How much...

A battery with an emf of 12.0V shows a terminal voltage of 11.8V when operating in a circuit with two lightbulb rated at 3.0 W (at 12.0V) which are connected in parallel. What is the batterys...

(a) In MeV/c, what is the magnitude of the momentum associated with a photon having an energy equal to the electron rest energy? What are the (b) Wavelength and (c) Frequency of the corresponding...

An air-filled hollow rectangular waveguide is 150 m long and is capped at the end with a metal plate. If a short pulse of frequency 7.2 GHz is introduced into the input end of the guide, how long...

Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression. 240 lb 20 in 16 in -15 in.-

What must be the pressure difference between the two ends of a 1.9-km section of pipe. 29cm in diameter, if it is to transport oil (p = 950kg/m3.n = 0.20Pa s) at a rate of 450 cm3/s?

A 15-g lead bullet traveling at 220m/s passes through a thin wall and emerges at a speed of 160 m/s. If the bulled absorbs 50% of the heat generated. (a) What will be the temperature rise of the...

Show that the Schwarzschild radius for a star with mass equal to that (a) Of our Sun is 2.95km, and (b) Of Earth is 8.9mm.

In a region of space, a magnetic field points in the + x-direction (toward the right). Its magnitude varies with position according to the formula Bx = B0 + bx, where Bo and b are positive constants,...

A square, conducting wire loop of side L, total mass m. and total resistance R initially lies in 1he horizontal xy-plane, with corners at (x, y, z) = (0,0,0), (0,L,0), (L, 0, 0), and (L.L.O). There...

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.10 m/s2, and the automobile...

A current I flows to the right through a rectangular bar of conducting material, in the presence of a uniform magnetic field B pointing out of the page (Fig. 5.56). (a) If the moving charges are...

A long solenoid has 100 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.30 cm perpendicular to the solenoid axis. The speed of the electron is 0.0460c (c...

In Figure a 120-turn coil of radius 1.8 cm and resistance 5.3?? is coaxial with a solenoid of 220 turns/cm and diameter 3.2 cm. The solenoid current drops from 1.5 A to zero in time interval t =...