Question: A light rod of length ℓ = 1.00

> (a) Find the work done by an ideal gas as it expands from point A to point B along the path shown in Figure P12.8. (b) How much work is done by the gas if it compressed from B to A along the same path? Figure P12.8:

> A sample of helium behaves as an ideal gas as it is heated at constant pressure from 273 K to 373 K. If 20.0 J of work is done by the gas during this process, what is the mass of helium present?

> A gas follows the PV diagram in Figure P12.6. Find the work done on the gas along the paths (a) AB, (b) BC, (c) CD, (d) DA, and (e) ABCDA. Figure P12.6:

> A gas expands from I to F along the three paths indicated in Figure P12.5. Calculate the work done on the gas along paths (a) IAF, (b) IF, and (c) IBF. Figure P12.5:

> Find the numeric value of the work done on the gas in (a) Figure P12.4a and (b) Figure P12.4b. Figure P12.4:

> There is an old admonition given to experimenters to “keep one hand in the pocket” when working around high voltages. Why is this warning a good idea?

> Gas in a container is at a pressure of 1.5 atm and a volume of 4.0 m3. What is the work done on the gas (a) If it expands at constant pressure to twice its initial volume, and (b) If it is compressed at constant pressure to one-quarter its initial volum

> Sketch a PV diagram and find the work done by the gas during the following stages. (a) A gas is expanded from a volume of 1.0 L to 3.0 L at a constant pressure of 3.0 atm. (b) The gas is then cooled at constant volume until the pressure falls to 2.0 atm.

> A balloon holding 5.00 moles of helium gas absorbs 925 J of thermal energy while doing 102 J of work expanding to a larger volume. (a) Find the change in the balloon’s internal energy. (b) Calculate the change in temperature of the gas.

> (a) Determine the work done on a fluid that expands from i to f as indicated in Figure P12.10. (b) How much work is done on the fluid if it is compressed from f to i along the same path? Figure P12.10:

> An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of 8.00 x 103 g and an area of 5.00 cm2 and is free to slide up and down, keeping the pressure of the gas constant. (a) How much work is done on the gas as t

> Lake Erie contains roughly 4.00 x 1011 m3 of water. (a) How much energy is required to raise the temperature of that volume of water from 11.0°C to 12.0°C? (b) How many years would it take to supply this amount of energy by using the 1.00 x 104-MW exhaus

> An aluminum rod is 20.0 cm long at 20.0°C and has a mass of 0.350 kg. If 1.00 x 104 J of energy is added to the rod by heat, what is the change in length of the rod?

> The highest recorded waterfall in the world is found at Angel Falls in Venezuela. Its longest single waterfall has a height of 807 m. If water at the top of the falls is at 15.0°C, what is the maximum temperature of the water at the bottom of the falls?

> A wood stove is used to heat a single room. The stove is cylindrical in shape, with a diameter of 40.0 cm and a length of 50.0 cm, and operates at a temperature of 400.°F. (a) If the temperature of the room is 70.0°F, determine the amount of radiant ener

> Earth’s surface absorbs an average of about 960. W/m2 from the Sun’s irradiance. The power absorbed is Pabs = (960. W/m2) (Adisc), where Adisc = πR2E is Earth’s projected area. An equal amount of power is radiated so that Earth remains in thermal equilib

> Two light-bulbs are each connected to a voltage of 120 V. One has a power of 25 W, the other 100 W. (a) Which light-bulb has the higher resistance? (b) Which light-bulb carries more current?

> If you were asked to design a capacitor in which small size and large capacitance were required, what would be the two most important factors in your design?

> Two astronauts (Fig. P8.80), each having a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particle

> A uniform ladder of length L and weight w is leaning against a vertical wall. The coefficient of static friction between the ladder and the floor is the same as that between the ladder and the wall. If this coefficient of static friction is μs = 0.500, d

> An object of mass M = 12.0 kg is attached to a cord that is wrapped around a wheel of radius r = 10.0 cm (Fig. P8.78). The acceleration of the object down the frictionless incline is measured to be a = 2.00 m/s2 and the incline makes an angle Î&ced

> A 40.0-kg child stands at one end of a 70.0-kg boat that is 4.00 m long (Fig. P8.77). The boat is initially 3.00 m from the pier. The child notices a turtle on a rock beyond the far end of the boat and proceeds to walk to that end to catch the turtle. (a

> Figure P8.76 shows a clawhammer as it is being used to pull a nail out of a horizontal board. If a force of magnitude 150 N is exerted horizontally as shown, find (a) The force exerted by the hammer claws on the nail and (b) The force exerted by the surf

> A 0.50-kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane, with the cord making a 30° angle with the vertical. (See Fig. P7.75.) (a) Determine the ball’s speed. (b) If, instead, the ball i

> A massless spring of constant k = 78.4 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance d, as in Figure P7.74. The block (initially at rest) is then released and travel

> In a popular amusement park ride, a rotating cylinder of radius 3.00 m is set in rotation at an angular speed of 5.00 rad/s, as in Figure P7.73. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum

> The maximum lift force on a bat is proportional to the square of its flying speed v. For the hoary bat (Lasiurus cinereus), the magnitude of the lift force is given by The bat can fly in a horizontal circle by “bankingâ€&#15

> (a) A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 20.0° with the horizontal. A 30.0-kg piece of luggage i

> Blood pressure is normally measured with the cuff of the sphygmomanometer around the arm. Suppose the blood pressure is measured with the cuff around the calf of the leg of a standing person. Would the reading of the blood pressure be (a) The same here a

> A 0.275-kg object is swung in a vertical circular path on a string 0.850 m long as in Figure P7.70. (a) What are the forces acting on the ball at any point along this path? (b) Draw free-body diagrams for the ball when it is at the bottom of the circle a

> A 4.00-kg object is attached to a vertical rod by two strings as shown in Figure P7.69. The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension in (a) The upper string and (b) The lower string. Figure P7.69:

> A coin rests 15.0 cm from the center of a turntable. The coefficient of static friction between the coin and turntable surface is 0.350. The turntable starts from rest at t = 0 and rotates with a constant angular acceleration of 0.730 rad/s2. (a) Once th

> A minimum-energy orbit to an outer planet consists of putting a spacecraft on an elliptical trajectory with the departure planet corresponding to the perihelion of the ellipse, or closest point to the Sun, and the arrival planet corresponding to the aphe

> The pilot of an airplane executes a constant-speed loopthe- loop maneuver in a vertical circle as in Figure 7.13b. The speed of the airplane is 2.00 x 102 m/s, and the radius of the circle is 3.20 x 103 m. (a) What is the pilot’s appare

> Suppose a 1800-kg car passes over a bump in a roadway that follows the arc of a circle of radius 20.4 m, as in Figure P7.65. (a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 8.94 m/s? (b)

> A stuntman whose mass is 70 kg swings from the end of a 4.0-m-long rope along the arc of a vertical circle. Assuming he starts from rest when the rope is horizontal, find the tensions in the rope that are required to make him follow his circular path (a)

> A skier starts at rest at the top of a large hemispherical hill (Fig. P7.63). Neglecting friction, show that the skier will leave the hill and become airborne at a distance h = R/3 below the top of the hill. Figure P7.63:

> Casting of molten metal is important in many industrial processes. Centrifugal casting is used for manufacturing pipes, bearings, and many other structures. A cylindrical enclosure is rotated rapidly and steadily about a horizontal axis, as in Figure P7.

> In a home laundry dryer, a cylindrical tub containing wet clothes is rotated steadily about a horizontal axis, as shown in Figure P7.61. So that the clothes will dry uniformly, they are made to tumble. The rate of rotation of the smooth-walled tub is cho

> Several common barometers are built using a variety of fluids. For which fluid will the column of fluid in the barometer be the highest? (Refer to Table 9.1.) Table 9.1: (a) Mercury (b) Water (c) Ethyl alcohol (d) Benzene

> Each of the following objects has a radius of 0.180 m and a mass of 2.40 kg, and each rotates about an axis through its center (as in Table 8.1) with an angular speed of 35.0 rad/s. Find the magnitude of the angular momentum of each object. (a) A hoop (b

> A 2.00-kg solid, uniform ball of radius 0.100 m is released from rest at point A in Figure P8.59, its center of gravity a distance of 1.50 m above the ground. The ball rolls without slipping to the bottom of an incline and back up to point B where it is

> Use conservation of energy to determine the angular speed of the spool shown in Figure P8.58 after the 3.00-kg bucket has fallen 4.00 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwin

> A 10.0- kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.0 m/s, determine (a) The translational kinetic energy of its center of gravity, (b) The rotational kinetic energy about its center o

> A constant torque of 25.0 N · m is applied to a grindstone whose moment of inertia is 0.130 kg · m2. Using energy principles and neglecting friction, find the angular speed after the grindstone has made 15.0 revolutions. Hint: The angular equivalent of W

> The top in Figure P8.55 has a moment of inertia of 4.00 = 10-4 kg · m2 and is initially at rest. It is free to rotate about a stationary axis AA´. A string wrapped around a peg along the axis of the top is pulled in such a mann

> A car is designed to get its energy from a rotating solid- disk flywheel with a radius of 2.00 m and a mass of 5.00 = 102 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel’s rotational speed up to 5.00 = 103 rev/

> A solid, uniform disk of radius 0.250 m and mass 55.0 kg rolls down a ramp of length 4.50 m that makes an angle of 15.0° with the horizontal. The disk starts from rest from the top of the ramp. Find (a) The speed of the disk’s center of mass when it reac

> A 240-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 37° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest?

> The pressure at the bottom of a glass filled with water (p = 1000 kg/m3) is P. The water is poured out and the glass is filled with ethyl alcohol (p = 806 kg/m3). The pressure at the bottom of the glass is now (a) Smaller than P (b) Equal to P (c) Larger

> Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell—each have a mass of 4.80 kg and a radius of 0.230 m. (a) Find the moment of inertia for each object as it rotates about the axes shown

> A horizontal 800.-N merry-go-round of radius 1.50 m is started from rest by a constant horizontal force of 50.0 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 3.00 s. (Assume it is a solid cylinder.)

> A 2.50-kg solid, uniform disk rolls without slipping across a level surface, translating at 3.75 m/s. If the disk’s radius is 0.100 m, find its (a) Translational kinetic energy and (b) Rotational kinetic energy.

> The uniform thin rod in Figure P8.47 has mass M = 3.50 kg and length L = 1.00 m and is free to rotate on a frictionless pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of (a) The rod’s an

> An Atwood’s machine consists of blocks of masses m1 = 10.0 kg and m2 = 20.0 kg attached by a cord running over a pulley as in Figure P8.46. The pulley is a solid cylinder with mass M = 8.00 kg and radius r = 0.200 m. The block of mass m

> A 150.- kg merry - go - round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force must be exerted on the rope to bring the merry - g

> A bicycle wheel has a diameter of 64.0 cm and a mass of 1.80 kg. Assume that the wheel is a hoop with all the mass concentrated on the outside radius. The bicycle is placed on a stationary stand, and a resistive force of 120 N is applied tangent to the r

> A model airplane with mass 0.750 kg is tethered by a wire so that it flies in a circle 30.0 m in radius. The airplane engine provides a net thrust of 0.800 N perpendicular to the tethering wire. (a) Find the torque the net thrust produces about the cente

> A potter’s wheel having a radius of 0.50 m and a moment of inertia of 12 kg · m2 is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 s by pressing a wet rag against the rim and exerting a radially inward force of 70 N. Find the effecti

> An approximate model for a ceiling fan consists of a cylindrical disk with four thin rods extending from the disk’s center, as in Figure P8.41. The disk has mass 2.50 kg and radius 0.200 m. Each rod has mass 0.850 kg and is 0.750 m long

> Suppose you have one cubic meter of gold, two cubic meters of silver, and six cubic meters of aluminum. Rank them by mass, from smallest to largest. (a) Gold, aluminum, silver (b) Gold, silver, aluminum (c) Aluminum, gold, silver (d) Silver, aluminum, go

> An oversized yo-yo is made from two identical solid disks each of mass M = 2.00 kg and radius R = 10.0 cm. The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in Figure P8.40. Take the center of the cylinder as the

> A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 250. N applied to its edge causes the wheel to have an angular acceleration of 0.940 rad/s2. (a)

> If the system shown in Figure P8.37 is set in rotation about each of the axes mentioned in Problem 37, find the torque that will produce an angular acceleration of 1.50 rad/s2 in each case. Axes From Problem 37: (a) The x-axis, (b) The y-axis, and (c) A

> Four objects are held in position at the corners of a rectangle by light rods as shown in Figure P8.37. Find the moment of inertia of the system about (a) The x-axis, (b) The y-axis, and (c) An axis through O and perpendicular to the page. Figure P8.37:

> One end of a uniform 4.0-m-long rod of weight w is supported by a cable at an angle of θ = 37° with the rod. The other end rests against a wall, where it is held by friction. (See Fig. P8.36.) The coefficient of static friction be

> The large quadriceps muscle in the upper leg terminates at its lower end in a tendon attached to the upper end of the tibia (Fig. P8.35a). The forces on the lower leg when the leg is extended are modeled as in Figure P8.35b, where T( is the force of tens

> A 1200-N uniform boom at (( = 65° to the horizontal is supported by a cable at an angle θ = 25.0° to the horizontal as shown in Figure P8.34. The boom is pivoted at the bottom, and an object of weight w = 2000 N hangs f

> The chewing muscle, the masseter, is one of the strongest in the human body. It is attached to the mandible (lower jawbone) as shown in Figure P8.33a. The jawbone is pivoted about a socket just in front of the auditory canal. The forces acting on the jaw

> Write the necessary equations of equilibrium of the object shown in Figure P8.32. Take the origin of the torque equation about an axis perpendicular to the page through the point O. Figure P8.32:

> A refrigerator of width w and height h rests on a rough incline as in Figure P8.31. Find an expression for the maximum value θ can have before the refrigerator tips over. Note, the contact point between the refrigerator and incline shifts as

> You observe two helium balloons floating next to each other at the ends of strings secured to a table. The facing surfaces of the balloons are separated by 1–2 cm. You blow through the opening between the balloons. What happens to the balloons? (a) They

> A strut of length L = 3.00 m and mass m = 16.0 kg is held by a cable at an angle of θ = 30.0° with respect to the horizontal as shown in Figure P8.30. (a) Sketch a force diagram, indicating all the forces and their placement on th

> Figure P8.29 shows a uniform beam of mass m pivoted at its lower end, with a horizontal spring attached between its top end and a vertical wall. The beam makes an angle u with the horizontal. Find expressions for (a) The distance d the spring is stretche

> A hungry bear weighing 700. N walks out on a beam in an attempt to retrieve a basket of goodies hanging at the end of the beam (Fig. P8.28). The beam is uniform, weighs 200. N, and is 6.00 m long, and it is supported by a wire at an angle of Î&cedi

> A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes, as indicated by the blue vectors in Figure P8.27. Find the tension in each rope when a 700.-N person is d = 0.500 m from the left end. Figure P8.27:

> A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 200 N and is 3.00 m long. What is the tension in each rope when the 700-N worker stands 1.00 m from one end?

> A 500.-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 100.-N rod as indicated in Figure P8.25. The left end of the rod is supported by a hinge, and the right end is supported by a thin cable m

> When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure P8.24a. The total gravitational force on the body, F(g, is supported by the force n( exerted by the floor on the toes of one foot. A mechanical model of

> A person bending forward to lift a load “with his back” (Fig. P8.23a) rather than “with his knees” can be injured by large forces exerted on the muscles and vertebrae. The spine pivo

> A beam resting on two pivots has a length of L = 6.00 m and mass M = 90.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot placed a distance â„“ = 4.00 m from the left end exerts a normal force n

> In exercise physiology studies, it is sometimes important to determine the location of a person’s center of gravity. This can be done with the arrangement shown in Figure P8.21. A light plank rests on two scales that read Fg1 = 380. N a

> If global warming continues, it’s likely that some ice from the polar ice caps of the Earth will melt and the water will be distributed closer to the equator. If this occurs, would the length of the day (one rotation) (a) Increase, (b) Decrease, or (c) R

> A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 50.0-gram mass is attached at the 10.0-cm mark, the fulcrum must be moved to the 39.2-cm mark for balance. What is the mass of the meter stick?

> A cook holds a 2.00-kg carton of milk at arm’s length (Fig. P8.19). What force F(B must be exerted by the biceps muscle? (Ignore the weight of the forearm.) Figure P8.19:

> A uniform 35.0-kg beam of length (â„“ = 5.00 m is supported by a vertical rope located d = 1.20 m from its left end as in Figure P8.18. The right end of the beam is supported by a vertical column. Find (a) The tension in the rope and (b)

> The arm in Figure P8.17 weighs 41.5 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force F(t in the deltoid muscle and the force F(s exerted by the shoulder on the humerus (upper-arm bone) to hold

> Spectators watch a bicycle stunt rider travel off the end of a 60.0° ramp, rise to the top of his trajectory and, at that instant, suddenly push his bike away from him so that he falls vertically straight down, reaching the ground 0.550 s later. How far

> A hiker inspects a tree frog sitting on a small stick in his hand. Suddenly startled, the hiker drops the stick from rest at a height of 1.85 m above the ground and, at the same instant, the frog leaps vertically upward, pushing the stick down so that it

> The Xanthar mothership locks onto an enemy cruiser with its tractor beam (Fig. P8.14); each ship is at rest in deep space with no propulsion following a devastating battle. The mothership is at x = 0 when its tractor beams are first engaged, a distance d

> A block of mass m = 1.50 kg is at rest on a ramp of mass M = 4.50 kg which, in turn, is at rest on a frictionless horizontal surface (Fig. P8.13a). The block and the ramp are aligned so that each has its center of mass located at x = 0. When released, th

> Find the x- and y -coordinates of the center of gravity for the boomerang in Figure P8.12a, modeling the boomerang as in Figure P8.12b, where each uniform leg of the model has a length of 0.300 m and a mass of 0.250 kg. (Note: Treat the legs like thin ro

> Find the x- and y-coordinates of the center of gravity of a 4.00-ft by 8.00-ft uniform sheet of plywood with the upper right quadrant removed as shown in Figure P8.11. Hint: The mass of any segment of the plywood sheet is proportional to the area of that

> A horizontal disk with moment of inertia I1 rotates with angular speed v1 about a vertical frictionless axle. A second horizontal disk having moment of inertia I2 drops onto the first, initially not rotating but sharing the same axis as the first disk. B

> Three solid, uniform boxes are aligned as in Figure P8.10. Find the x- and y-coordinates of the center of mass of the three boxes, measured from the bottom left corner of box A. Figure P8.10:

> Two bowling balls are at rest on top of a uniform wooden plank with their centers of mass located as in Figure P8.9. The plank has a mass of 5.00 kg and is 1.00 m long. Find the horizontal distance from the left end of the plank to the center of mass of

> Consider the following mass distribution, where x- and y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.0 kg at (0.0, 4.0) m, and 4.0 kg at (3.0, 0.0) m. Where should a fourth object of 8.0 kg be placed so that the center of mass of the four-

> A simple pendulum consists of a small object of mass 3.0 kg hanging at the end of a 2.0-m-long light string that is connected to a pivot point. (a) Calculate the magnitude of the torque (due to the force of gravity) about this pivot point when the string

> A dental bracket exerts a horizontal force of 80.0 N on a tooth at point B in Figure P8.6. What is the torque on the root of the tooth about point A? Figure P8.6:

> The density of air is 1.3 kg/m3 at sea level. From your knowledge of air pressure at ground level, estimate the height of the atmosphere. As a simplifying assumption, take the atmosphere to be of uniform density up to some height, after which the density