Two transmission belts pass over a double-sheaved pulley that is attached to an axle supported by bearings at A and D. The radius of the inner sheave is 125 mm and the radius of the outer sheave is...

Stopping Distance (a) If the coefficient of kinetic friction between tires and dry pavement is 0.80, what is the shortest distance in which you can stop an automobile by locking the brakes when...

Suppose the 2.0-kg model car in Exercise 6.37 is initially at rest at x = 0 and F is the net force acting on it. Use the work-energy theorem to find the speed of the car at (a) x = 3.0 m; (b) x =...

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...

List several similarities and differences between electric and magnetic forces.

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...

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

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...

An astronaut in orbit can just resolve two point sources on the earth that are 75.0 m apart. Assume that the resolution is diffraction limited, and use Rayleigh's criterion. What is the astronaut's...

The thin plastic rod of length L = 10.0 cm in Figure has a non-uniform linear charge density = cx, where c = 49.9pC/m2. (a) With V = 0 at infinity find the electric potential at point P2 on the y...

The true weight of an object can be measured in a vacuum, where buoyant forces are absent. An object of volume V is weighed in air on a balance with the use of weights of density P. If the density of...

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...

The sun radiates energy at a rate of about 4 X 1026W. (a) At what rate is the suns mass decreasing? (b) How long does it take for the sun to lose a mass equal to that of earth? (c) Estimate how long...

Three charged particles form a triangle: particle 1 with charge Q1 = 80.0nC is at xy coordinates (0, 3.00 mm), particle 2 with charge Q2 is at (0, -3.00mm), and particle 3 with charge q = 18.0nC is...

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...

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 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)...

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...

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

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...

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...

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...

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

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)?

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.

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...

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...

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...

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...

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...

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...

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...

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...

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) 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...

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...

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...

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?

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,...

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...

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 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...

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...

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 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...

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...

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....

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...

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?

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

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...

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...

Find the output voltage vo(t) in the circuit of Fig. 8.94. t=0 10 512

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.)...

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...

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.-

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...

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).

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?

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...

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 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?

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...

The circuit in Figure P28.37 has been connected for a long time. (a) What is the voltage across the capacitor? (b) If the battery is disconnected, how long does it take the capacitor to discharge to...

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...

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...

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?

(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...

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...

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...

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...

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...

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...

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 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...

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...

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?

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

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?

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...

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...

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 cantilever beam of rectangular cross section is subjected to a concentrated load P = 17 k acting at the free end (see figure). The beam has width b = 3 in. and height h = 12 in. Point A is located...

A spring is suspended vertically from the ceiling of a room. When a mass is attached to the bottom of the spring, the amount of stretch is recorded. A plot of stretch versus mass is given in FIGURE...

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 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 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.

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) 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...