Question: A small sphere with mass m carries

> Experimenting with pendulums, you attach a light string to the ceiling and attach a small metal sphere to the lower end of the string. When you displace the sphere 2.00 m to the left, it nearly touches a vertical wall; with the string taut, you release t

> You hang various masses m from the end of a vertical, 0.250-kg spring that obeys Hooke’s law and is tapered, which means the diameter changes along the length of the spring. Since the mass of the spring is not negligible, you must replace m in the equati

> A mass m is attached to a spring of force constant 75 N/m and allowed to oscillate. Figure P14.89 shows a graph of its velocity component vx as a function of time t. Find (a) the period, (b) the frequency, and (c) the angular frequency of this motion. (d

> Two identical thin rods, each with mass m and length L, are joined at right angles to form an L-shaped object. This object is balanced on top of a sharp edge (Fig. P14.88). If the L-shaped object is deflected slightly, it oscillates. Find the frequency o

> A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force constant k is attached to the lower end of the rod, with the other end of the spring att

> A large, 34.0-kg bell is hung from a wooden beam so it can swing back and forth with negligible friction. The bell’s center of mass is 0.60 m below the pivot. The bell’s moment of inertia about an axis at the pivot is 18.0 kg.m2. The clapper is a small,

> In Fig. P14.85 the upper ball is released from rest, collides with the stationary lower ball, and sticks to it. The strings are both 50.0 cm long. The upper ball has mass 2.00 kg, and it is initially 10.0 cm higher than the lower ball, which has mass 3.0

> Two uniform solid spheres, each with mass M = 0.800 kg and radius R = 0.0800 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with force constant k = 160 N/m has one end att

> A rifle bullet with mass 8.00 g and initial horizontal velocity 280 m/s strikes and embeds itself in a block with mass 0.992 kg that rests on a frictionless surface and is attached to one end of an ideal spring. The other end of the spring is attached to

> An object is moving with SHM of amplitude A on the end of a spring. If the amplitude is doubled, what happens to the total distance the object travels in one period? What happens to the period? What happens to the maximum speed of the object? Discuss how

> An interesting, though highly impractical example of oscillation is the motion of an object dropped down a hole that extends from one side of the earth, through its center, to the other side. With the assumption (not realistic) that the earth is a sphere

> While on a visit to Minnesota (“Land of 10,000 Lakes”), you sign up to take an excursion around one of the larger lakes. When you go to the dock where the 1500-kg boat is tied, you find that the boat is bobbing up and down in the waves, executing simple

> A 40.0-N force stretches a vertical spring 0.250 m. (a) What mass must be suspended from the spring so that the system will oscillate with a period of 1.00 s? (b) If the amplitude of the motion is 0.050 m and the period is that specified in part (a), whe

> 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 from a height of 0.40 m. The steak makes a totally inelastic collision with the

> A 0.0200-kg bolt moves with SHM that has an amplitude of 0.240 m and a period of 1.500 s. The displacement of the bolt is +0.240 m when t = 0. Compute (a) the displacement of the bolt when t = 0.500 s; (b) the magnitude and direction of the force acting

> A 5.00-kg partridge is suspended from a pear tree by an ideal spring of negligible mass. When the partridge is pulled down 0.100 m below its equilibrium position and released, it vibrates with a period of 4.20 s. (a) What is its speed as it passes throug

> A uniform beam is suspended horizontally by two identical vertical springs that are attached between the ceiling and each end of the beam. The beam has mass 225 kg, and a 175-kg sack of gravel sits on the middle of it. The beam is oscillating in SHM with

> A 2.00-kg bucket containing 10.0 kg of water is hanging from a vertical ideal spring of force constant 450 N/m and oscillating up and down with an amplitude of 3.00 cm. Suddenly the bucket springs a leak in the bottom such that water drops out at a stead

> An object with mass 0.200 kg is acted on by an elastic restoring force with force constant 10.0 N/m. (a) Graph elastic potential energy U as a function of displacement x over a range of x from -0.300 m to +0.300 m. On your graph, let 1 cm = 0.05 J vertic

> A square object of mass m is constructed of four identical uniform thin sticks, each of length L, attached together. This object is hung on a hook at its upper corner (Fig. P14.73). If it is rotated slightly to the left and then released, at what frequen

> What would Kepler’s third law be for circular orbits if an amendment to Newton’s law of gravitation made the gravitational force inversely proportional to r3? Would this change affect Kepler’s other two laws? Explain.

> An object with height h, mass M, and a uniform cross-sectional area A floats upright in a liquid with density r. (a) Calculate the vertical distance from the surface of the liquid to the bottom of the floating object at equilibrium. (b) A downward force

> An apple weighs 1.00 N. When you hang it from the end of a long spring of force constant 1.50 N/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing from side to side through a small angle, the frequency

> A 10.0-kg mass is traveling to the right with a speed of 2.00 m/s on a smooth horizontal surface when it collides with and sticks to a second 10.0-kg mass that is initially at rest but is attached to a light spring with force constant 170.0 N/m. (a) Find

> A 1.50-kg, horizontal, uniform tray is attached to a vertical ideal spring of force constant 185 N>m and a 275-g metal ball is in the tray. The spring is below the tray, so it can oscillate up and down. The tray is then pushed down to point A, which is 1

> A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k. The other end of the spring is attached to a wall (Fig. P14.68). A second block with mass m rests on top of the first block. The coefficient

> At the end of a ride at a winter-theme amusement park, a sleigh with mass 250 kg (including two passengers) slides without friction along a horizontal, snow-covered surface. The sleigh hits one end of a light horizontal spring that obeys Hooke’s law and

> Four passengers with combined mass 250 kg compress the springs of a car with worn-out shock absorbers by 4.00 cm when they get in. Model the car and passengers as a single body on a single ideal spring. If the loaded car has a period of vibration of 1.92

> An object is undergoing SHM with period 1.200 s and amplitude 0.600 m. At t = 0 the object is at x = 0 and is moving in the negative x-direction. How far is the object from the equilibrium position when t = 0.480 s ?

> An object is undergoing SHM with period 0.300 s and amplitude 6.00 cm. At t = 0 the object is instantaneously at rest at x = 6.00 cm. Calculate the time it takes the object to go from x = 6.00 cm to x = -1.50 cm.

> For each of the eight planets Mercury to Neptune, the semi-major axis a of their orbit and their or bital period T are as follows: (a) Explain why these values, when plotted as T2 versus a3, fall close to a straight line. Which of Keplerâ€&#

> A musical interval of an octave corresponds to a factor of 2 in frequency. By what factor must the tension in a guitar or violin string be increased to raise its pitch one octave? To raise it two octaves? Explain your reasoning. Is there any danger in at

> For transverse waves on a string, is the wave speed the same as the speed of any part of the string? Explain the difference between these two speeds. Which one is constant?

> What is the best explanation for the observation that the electric charge on the stem became positive as the charged bee approached (before it landed)? (a). Because air is a good conductor, the positive charge on the bee’s surface flowed through the air

> Consider a bee with the mean electric charge found in the experiment. This charge represents roughly how many missing electrons? (a). 1.9 × 108; (b). 3.0 × 108; (c). 1.9 × 1018; (d). 3.0 × 1018.

> Two thin rods of length L lie along the x-axis, one between x = 1 2 a and x = 1 2 a + L and the other between x = - 1 2 a and x = - 1 2 a - L. Each rod has positive charge Q distributed uniformly along its length. (a). Calculate the electric field p

> Two charges are placed as shown in Fig. P21.96. The magnitude of q1 is 3.00 µC, but its sign and the value of the charge q2 are not known. The direction of the net electric field

> Three charges are placed as shown in Fig. P21.95. The magnitude of q1 is 2.00 µC, but its sign and the value of the charge q2 are not known. Charge q3 is +4.00 µC, and the net force

> Positive charge Q is distributed uniformly around a very thin conducting ring of radius a, as in Fig. 21.23. You measure the electric field E at points on the ring axis, at a distance x from the center of the ring, over a wide range of values of x. Fig

> Two small spheres, each carrying a net positive charge, are separated by 0.400 m. You have been asked to perform measurements that will allow you to determine the charge on each sphere. You set up a coordinate system with one sphere (charge q1) at the or

> Inkjet printers can be described as either continuous or drop-on-demand. In a continuous inkjet printer, letters are built up by squirting drops of ink at the paper from a rapidly moving nozzle. You are part of an engineering group working on the design

> A thin disk with a circular hole at its center, called an annulus, has inner radius R1 and outer radius R2 (Fig. P21.91). The disk has a uniform positive surface charge density s on its surface. (a). Determine the total electric charge on the annulus.

> Two very large horizontal sheets are 4.25 cm apart and carry equal but opposite uniform surface charge densities of magnitude

> Suppose that the charge shown in Fig. 21.28a is fixed in position. A small, positively charged particle is then placed at some location and released. Will the trajectory of the particle follow an electric field line? Why or why not? Suppose instead that

> Repeat Problem 21.88 for the case where sheet B is positive. Problem 21.88: Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of -8.80 µC/m2, and sheet B, which is to the right of A, carries a uniform ch

> Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of -8.80 µC/m2, and sheet B, which is to the right of A, carries a uniform charge density of -11.6 µC/m2. Assume that the sheets are large enough to be tre

> Two 1.20-m nonconducting rods meet at a right angle. One rod carries +2.50 µC of charge distributed uniformly along its length, and the other carries -2.50 µC distributed uniformly along it (Fig. P21.87). Fig. P21.87: (a). F

> A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge -Q is distributed uniformly around the righ

> Negative charge -Q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin. Find the x- and y-components of the net electric field at the origin.

> A uniformly charged disk like the disk in Fig. 21.25 has radius 2.50 cm and carries a total charge of 7.0 × 10-12 C. Fig. 21.25: (a). Find the electric field (magnitude and direction) on the x-axis at x = 20.0 cm. (b). Show that for x &

> Positive charge Q is distributed uniformly along the positive y-axis between y = 0 and y = a. A negative point charge -q lies on the positive x-axis, a distance x from the origin (Fig. P21.82). Fig. P21.82: (a). Calculate the x- and y-components of t

> A negative point charge q1 = -4.00 nC is on the x-axis at x = 0.60 m. A second point charge q2 is on the x-axis at x = -1.20 m. What must the sign and magnitude of q2 be for the net electric field at the origin to be (a). 50.0 N/C in the +x-direction an

> In a region where there is a uniform electric field that is upward and has magnitude 3.60 × 104 N/C, a small object is projected upward with an initial speed of 1.92 m/s. The object travels upward a distance of 6.98 cm in 0.200 s. What is the object’s ch

> If the electric field of a point charge were proportional to 1/r3 instead of 1/r2, would Gauss’s law still be valid? Explain your reasoning. (Hint: Consider a spherical Gaussian surface centered on a single point charge.)

> Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. A positive point charge q is located on the positive x-axis at x = a + r, a distance r to the right of the end of Q (Fig. P21.79). Fig. P21.79: (a). Calculate the x- and

> A small object with mass m, charge q, and initial speed v0 = 5.00 × 103 m/s is projected into a uniform electric field between two parallel metal plates of length 26.0 cm (Fig. P21.78). The electric field between the plates is directed downw

> A proton is projected into a uniform electric field that points vertically upward and has magnitude E. The initial velocity of the proton has a magnitude v0 and is directed at an angle

> The earth has a downward-directed electric field near its surface of about 150 N/C. If a raindrop with a diameter of 0.020 mm is suspended, motionless, in this field, how many excess electrons must it have on its surface?

> Consider a model of a hydrogen atom in which an electron is in a circular orbit of radius r = 5.29 × 10-11 m around a stationary proton. What is the speed of the electron in its orbit?

> Two tiny spheres of mass 6.80 mg carry charges of equal magnitude, 72.0 nC, but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m. When a horizontal uniform electric field E that is directed to the left is turned on

> 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 attraction and the electric repulsion that each bag exerts on the other. (c). Are

> Two point charges q1 and q2 are held in place 4.50 cm apart. Another point charge Q = -1.75 µC, of mass 5.00 g, is initially located 3.00 cm from both of these charges (Fig. P21.72) and released from rest. You observe that the initial accele

> Three identical point charges q are placed at each of three corners of a square of side L. Find the magnitude and direction of the net force on a point charge -3q placed (a). at the center of the square and (b). at the vacant corner of the square. In e

> A charge of -3.00 nC is placed at the origin of an xy-coordinate system, and a charge of 2.00 nC is placed on the y-axis at y = 4.00 cm. (a). If a third charge, of 5.00 nC, is now placed at the point x = 3.00 cm, y = 4.00 cm, find the x- and y-component

> Figure Q21.7 shows some of the electric field lines due to three point charges arranged along the vertical axis. All three charges have the same magnitude. Figure Q21.7: (a). What are the signs of the three charges? Explain your reasoning. (b). At wh

> A charge +Q is located at the origin, and a charge +4Q is at distance d away on the x-axis. Where should a third charge, q, be placed, and what should be its sign and magnitude, so that all three charges will be in equilibrium?

> In a region of space there is an electric field

> If the proposed plant is built and produces 10 MW but the rate at which waste heat is exhausted to the cold water is 165 MW, what is the plant’s actual efficiency? (a). 5.7%; (b). 6.1%; (c). 6.5%; (d). 16.5%.

> Which statement is true about

> What is the direction of

> What is the magnitude of

> Suppose that to repel electrons in the radiation from a solar flare, each sphere must produce an electric field

> A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density

> Compare the entropy change of the warmer water to that of the colder water during one cycle of the heat engine, assuming an ideal Carnot cycle. (a). The entropy does not change during one cycle in either case. (b). The entropy of both increases, but th

> What is the change in entropy of the ammonia vaporized per second in the 10-MW power plant, assuming an ideal Carnot efficiency of 6.5%? (a) +6 × 106 J/K per second; (b). +5 × 105 J/K per second; (c). +1 × 105 J/K per second; (d) 0.

> Estimate how many electrons there are in your body. Make any assumptions you feel are necessary, but clearly state what they are. (Hint: Most of the atoms in your body have equal numbers of electrons, protons, and neutrons.) What is the combined charge o

> Four identical charges Q are placed at the corners of a square of side L. (a). In a free-body diagram, show all of the forces that act on one of the charges. (b). Find the magnitude and direction of the total force exerted on one charge by the other th

> A very long, solid insulating cylinder has radius R; bored along its entire length is a cylindrical hole with radius a. The axis of the hole is a distance b from the axis of the cylinder, where a < b < R (Fig. P22.58). The solid material of the cylinder

> You are conducting experiments to study prototype heat engines. In one test, 4.00 mol of argon gas are taken around the cycle shown in Fig. P20.57. The pressure is low enough for the gas to be treated as ideal. You measure the gas temperature in states a

> For a refrigerator or air conditioner, the coefficient of performance K (often denoted as COP) is, as in Eq. (20.9), the ratio of cooling output |QC| to the required electrical energy input 0W0 , both in joules. The coefficient of performance is also exp

> In your summer job with a venture capital firm, you are given funding requests from four inventors of heat engines. The inventors claim the following data for their operating prototypes: (a). Based on the TC and TH values for each prototype, find the m

> To heat 1 cup of water (250 cm3) to make coffee, you place an electric heating element in the cup. As the water temperature increases from 200C to 780C, the temperature of the heating element remains at a constant 1200C. Calculate the change in entropy o

> An object of mass m1, specific heat c1, and temperature T1 is placed in contact with a second object of mass m2, specific heat c2, and temperature T2 &gt; T1. As a result, the temperature of the first object increases to T and the temperature of the seco

> A person with skin of surface area 1.85 m2 and temperature 30.0°C is resting in an insulated room where the ambient air temperature is 20.0°C. In this state, a person gets rid of excess heat by radiation. By how much does the person change the entropy of

> The pV-diagram in Fig. P20.51 shows the cycle for a refrigerator operating on 0.850 mol of H2. Assume that the gas can be treated as ideal. Process ab is isothermal. Find the coefficient of performance of this refrigerator. Fig. P20.51: p (atm) a 0

> An air conditioner operates on 800 W of power and has a performance coefficient of 2.80 with a room temperature of 21.00C and an outside temperature of 35.00C. (a). Calculate the rate of heat removal for this unit. (b). Calculate the rate at which heat

> An uncharged metal sphere hangs from a nylon thread. When a positively charged glass rod is brought close to the metal sphere, the sphere is drawn toward the rod. But if the sphere touches the rod, it suddenly flies away from the rod. Explain why the sph

> 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 distance that the piston moves during the compression in Fig. 20.5, called the stroke

> A typical coal-fired power plant generates 1000 MW of usable power at an overall thermal efficiency of 40%. (a). What is the rate of heat input to the plant? (b). The plant burns anthracite coal, which has a heat of combustion of 2.65 × 107 J/kg. How m

> Negative charge -Q is distributed uniformly over the surface of a thin spherical insulating shell with radius R. Calculate the force (magnitude and direction) that the shell exerts on a positive point charge q located a distance (a). r > R from the cent

> A monatomic ideal gas is taken around the cycle shown in Fig. P20.46 in the direction shown in the figure. The path for process c→ a is a straight line in the pV-diagram. (a). Calculate Q, W, and 

> A cylinder contains oxygen at a pressure of 2.00 atm. The volume is 4.00 L, and the temperature is 300 K. Assume that the oxygen may be treated as an ideal gas. The oxygen is carried through the following processes: (i). Heated at constant pressure from

> You decide to use your body as a Carnot heat engine. The operating gas is in a tube with one end in your mouth (where the temperature is 37.0°C) and the other end at the surface of your skin, at 30.0°C. (a). What is the maximum efficiency of such a heat

> An experimental power plant at the Natural Energy Laboratory of Hawaii generates electricity from the temperature gradient of the ocean. The surface and deep-water temperatures are 270C and 60C, respectively. (a). What is the maximum theoretical efficie

> The pV-diagram in Fig. E20.5 shows a cycle of a heat engine that uses 0.250 mol of an ideal gas with &Icirc;&sup3; = 1.40. Process ab is adiabatic. Fig. E20.5: (a). Find the pressure of the gas at point a. (b). How much heat enters this gas per cycle

> A gasoline engine has a power output of 180 kW (about 241 hp). Its thermal efficiency is 28.0%. (a). How much heat must be supplied to the engine per second? (b). How much heat is discarded by the engine per second?

> A Gasoline Engine. A gasoline engine takes in 1.61 × 104 J of heat and delivers 3700 J of work per cycle. The heat is obtained by burning gasoline with a heat of combustion of 4.60 × 104 J/g. (a). What is the thermal efficiency? (b). How much heat is d

> Your clothing tends to cling together after going through the dryer. Why? Would you expect more or less clinging if all your clothing were made of the same material (say, cotton) than if you dried different kinds of clothing together? Again, why? (You ma

> An aircraft engine takes in 9000 J of heat and discards 6400 J each cycle. (a). What is the mechanical work output of the engine during one cycle? (b). What is the thermal efficiency of the engine?

> If you carry out the integral of the electric field