Question: Car tires are sometimes “balanced” on a

> In hot-air ballooning, a large balloon is filled with air heated by a gas burner at the bottom. Why must the air be heated? How does the balloonist control ascent and descent?

> Identical-size lead and aluminum cubes are suspended at different depths by two wires in a large vat of water (Fig. Q12.30). (a) Which cube experiences a greater buoyant force? (b) For which cube is the tension in the wire greater? (c) Which cube experie

> A helium-filled balloon is tied to a light string inside a car at rest. The other end of the string is attached to the floor of the car, so the balloon pulls the string vertical. The car now accelerates forward. Does the balloon move? If so, does it move

> An ice cube floats in a glass of water. When the ice melts, will the water level in the glass rise, fall, or remain unchanged? Explain.

> Two identical buckets are filled to the brim with water, but one of them has a piece of wood floating in it. Which bucket of water weighs more? Explain.

> You are floating in a canoe in the middle of a swimming pool. Your friend is at the edge of the pool, carefully noting the level of the water on the side of the pool. You have a bowling ball with you in the canoe. If you carefully drop the bowling ball o

> A rubber hose is attached to a funnel, and the free end is bent around to point upward. When water is poured into the funnel, it rises in the hose to the same level as in the funnel, even though the funnel has a lot more water in it than the hose does. W

> A rigid, lighter-than-air dirigible filled with helium cannot continue to rise indefinitely. Why? What determines the maximum height it can attain?

> In describing the size of a large ship, one uses such expressions as “it displaces 20,000 tons.” What does this mean? Can the weight of the ship be obtained from this information?

> You have probably noticed that the lower the tire pressure, the larger the contact area between the tire and the road. Why?

> Equation (12.7) shows that an area ratio of 100 to 1 can give 100 times more output force than input force. Doesn’t this violate conservation of energy? Explain.

> Comparing Example 12.1 (Section 12.1) and Example 12.2 (Section 12.2), it seems that 700 N of air is exerting a downward force of 2.0 × 106 N on the floor. How is this possible?

> When a smooth-flowing stream of water comes out of a faucet, it narrows as it falls. Explain.

> Airports at high elevations have longer runways for takeoffs and landings than do airports at sea level. One reason is that aircraft engines develop less power in the thin air well above sea level. What is another reason

> A tornado consists of a rapidly whirling air vortex. Why is the pressure always much lower in the center than at the outside? How does this condition account for the destructive power of a tornado?

> In a store-window vacuum cleaner display, a table-tennis ball is suspended in midair in a jet of air blown from the outlet hose of a tank-type vacuum cleaner. The ball bounces around a little but always moves back toward the center of the jet, even if th

> A piece of iron is glued to the top of a block of wood. When the block is placed in a bucket of water with the iron on top, the block floats. The block is now turned over so that the iron is submerged beneath the wood. Does the block float or sink? Does

> If the velocity at each point in space in steady-state fluid flow is constant, how can a fluid particle accelerate?

> You are floating in a canoe in the middle of a swimming pool. A large bird flies up and lights on your shoulder. Does the water level in the pool rise or fall?

> There is a small but appreciable amount of elastic hysteresis in the large tendon at the back of a horse’s leg. Explain how this can cause damage to the tendon if a horse runs too hard for too long a time.

> The material in human bones and elephant bones is essentially the same, but an elephant has much thicker legs. Explain why, in terms of breaking stress.

> A gyroscope is precessing as in Fig. 10.32. What happens if you gently add some weight to the end of the flywheel axis farthest from the pivot? Fig. 10.32: Circular motion of flywheel axis (precession) Flywheel Flywheel аxis Pivot Path followed w R

> A gyroscope takes 3.8 s to precess 1.0 revolution about a vertical axis. Two minutes later, it takes only 1.9 s to precess 1.0 revolution. No one has touched the gyroscope. Explain.

> Compare the mechanical properties of a steel cable, made by twisting many thin wires together, with the properties of a solid steel rod of the same diameter. What advantages does each have?

> In a common design for a gyroscope, the flywheel and flywheel axis are enclosed in a light, spherical frame with the flywheel at the center of the frame. The gyroscope is then balanced on top of a pivot so that the flywheel is directly above the pivot. D

> When rubber mounting blocks are used to absorb machine vibrations through elastic hysteresis, as mentioned in Section 11.5, what becomes of the energy associated with the vibrations?

> Suppose the door of a room makes an airtight but frictionless fit in its frame. Do you think you could open the door if the air pressure on one side were standard atmospheric pressure and the air pressure on the other side differed from standard by 1%? E

> As discussed in Section 10.6, the angular momentum of a circus acrobat is conserved as she tumbles through the air. Is her linear momentum conserved? Why or why not?

> In Example 10.10 (Section 10.6) the rotational kinetic energy of the professor and dumbbells increases. But since there are no external torques, no work is being done to change the rotational kinetic energy. Then, by Eq. (10.22), the kinetic energy must

> If a metal wire has its length doubled and its diameter tripled, by what factor does its Young’s modulus change?

> A point particle travels in a straight line at constant speed, and the closest distance it comes to the origin of coordinates is a distance l. With respect to this origin, does the particle have nonzero angular momentum? As the particle moves along its s

> A piece of iron is glued to the top of a block of wood. When the block is placed in a bucket of water with the iron on top, the block floats. The block is now turned over so that the iron is submerged beneath the wood. Does the block float or sink? Does

> During the Great Mississippi Flood of 1993, the levees in St. Louis tended to rupture first at the bottom. Why?

> At a certain depth in an incompressible liquid, the absolute pressure is p. At twice this depth, will the absolute pressure be equal to 2p, greater than 2p, or less than 2p? Justify your answer.

> During pregnancy, women often develop back pains from leaning backward while walking. Why do they have to walk this way?

> Certain features of a person, such as height and mass, are fixed (at least over relatively long periods of time). Are the following features also fixed? (a) location of the center of gravity of the body; (b) moment of inertia of the body about an axis th

> Why is it easier to hold a 10-kg dumbbell in your hand at your side than it is to hold it with your arm extended horizontally?

> An old question is “Which weighs more, a pound of feathers or a pound of lead?” If the weight in pounds is the gravitational force, will a pound of feathers balance a pound of lead on opposite pans of an equal-arm balance? Explain, taking into account bu

> The mighty Zimbo claims to have leg muscles so strong that he can stand flat on his feet and lean forward to pick up an apple on the floor with his teeth. Should you pay to see him perform, or do you have any suspicions about his claim? Why?

> In pioneer days, when a Conestoga wagon was stuck in the mud, people would grasp the wheel spokes and try to turn the wheels, rather than simply pushing the wagon. Why?

> The force of gravity acts on the baton in Fig. 10.11, and forces produce torques that cause a body’s angular velocity to change. Why, then, is the angular velocity of the baton in the figure constant? Fig. 10.11: The motion of thi

> Suppose that the object in Question 11.9 is released from rest with the bar tilted at 60° above the horizontal with the ball at the upper end. As it is falling, will it (a) rotate about its center of gravity until it is horizontal; (b) rotate about its c

> An object consists of a ball of weight W glued to the end of a uniform bar also of weight W. If you release it from rest, with the bar horizontal, what will its behavior be as it falls if air resistance is negligible? Will it (a) remain horizontal; (b) r

> A valued client brings a treasured ball to your engineering firm, wanting to know whether the ball is solid or hollow. He has tried tapping on it, but that has given insufficient information. Design a simple, inexpensive experiment that you could perform

> You can probably stand flatfooted on the floor and then rise up and balance on your tiptoes. Why are you unable do it if your toes are touching the wall of your room? (Try it!)

> When you turn on an electric motor, it takes longer to come up to final speed if a grinding wheel is attached to the shaft. Why?

> When an acrobat walks on a tightrope, she extends her arms straight out from her sides. She does this to make it easier for her to catch herself if she should tip to one side or the other. Explain how this works.

> Does the center of gravity of a solid body always lie within the material of the body? If not, give a counter example.

> You push a piece of wood under the surface of a swimming pool. After it is completely submerged, you keep pushing it deeper and deeper. As you do this, what will happen to the buoyant force on it? Will the force keep increasing, stay the same, or decreas

> Can a single force applied to a body change both its translational and rotational motions? Explain.

> If the elephant were to snorkel in salt water, which is more dense than freshwater, would the maximum depth at which it could snorkel be different from that in freshwater? (a) Yes—that depth would increase, because the pressure would be lower at a given

> His body is leaning back at 30.0° to the vertical, but the coefficient of static friction between his feet and the ground is suddenly reduced to 0.50. What will happen? (a) His entire body will accelerate forward; (b) his feet will slip forward; (c) his

> His body is again leaning back at 30.0° to the vertical, but now the height at which the rope is held above—but still parallel to—the ground is varied. The tension in the rope in front of the competitor (T1) is measured as a function of the shortest dist

> If the body’s center of mass were not placed on the rotational axis of the turntable, how would the person’s measured moment of inertia compare to the moment of inertia for rotation about the center of mass? (a) The measured moment of inertia would be t

> A doubling of the torque produces a greater angular acceleration. Which of the following would do this, assuming that the tension in the rope doesn’t change? (a) Increasing the pulley diameter by a factor of √2; (b) increasing the pulley diameter by a fa

> While the turntable is being accelerated, the person suddenly extends her legs. What happens to the turntable? (a) It suddenly speeds up; (b) it rotates with constant speed; (c) its acceleration decreases; (d) it suddenly stops rotating.

> The moment of inertia of the empty turntable is 1.5 kg m2. With a constant torque of 2.5 N.m, the turntable–person system takes 3.0 s to spin from rest to an angular speed of 1.0 rad/s. What is the person’s moment of inertia about an axis through her cen

> If he leans slightly farther back (increasing the angle between his body and the vertical) but remains stationary in this new position, which of the following statements is true? Assume that the rope remains horizontal. (a) The difference between T1 and

> A cargo ship travels from the Atlantic Ocean (salt water) to Lake Ontario (freshwater) via the St. Lawrence River. The ship rides several centimeters lower in the water in Lake Ontario than it did in the ocean. Explain.

> What is tension T2 in the rope behind him? (a) 590 N; (b) 650 N; (c) 860 N; (d) 1100 N.

> How does the force the diaphragm experiences due to the difference in pressure between the lungs and abdomen depend on the abdomen’s distance below the water surface? The force (a) increases linearly with distance; (b) increases as distance squared; (c)

> The maximum force the muscles of the diaphragm can exert is 24,000 N. What maximum pressure difference can the diaphragm withstand? (a) 160 mm Hg; (b) 760 mm Hg; (c) 920 mm Hg; (d) 5000 mm Hg.

> For the situation shown, the tissues in the elephant’s abdomen are at a gauge pressure of 150 mm Hg. This pressure corresponds to what distance below the surface of a lake? (a) 1.5 m; (b) 2.0 m; (c) 3.0 m; (d) 15 m.

> The Environmental Protection Agency is investigating an abandoned chemical plant. A large, closed cylindrical tank contains an unknown liquid. You must determine the liquid’s density and the height of the liquid in the tank (the vertica

> You have a bucket containing an unknown liquid. You also have a cube-shaped wooden block that you measure to be 8.0 cm on a side, but you don’t know the mass or density of the block. To find the density of the liquid, you perform an exp

> The density values in Table 12.1 are listed in increasing order. A chemistry student notices that the first four chemical elements that are included are also listed in order of increasing atomic mass. (a) See whether there is a simple relationship betwee

> A liquid flowing from a vertical pipe has a definite shape as it flows from the pipe. To get the equation for this shape, assume that the liquid is in free fall once it leaves the pipe. Just as it leaves the pipe, the liquid has speed v0 and the radius o

> Two very large open tanks A and F (Fig. P12.83) contain the same liquid. A horizontal pipe BCD, having a constriction at C and open to the air at D, leads out of the bottom of tank A, and a vertical pipe E opens into the constriction at C and dips into t

> In 1993 the radius of Hurricane Emily was about 350 km. The wind speed near the center (“eye”) of the hurricane, whose radius was about 30 km, reached about 200 km>h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum r

> The purity of gold can be tested by weighing it in air and in water. How? Do you think you could get away with making a fake gold brick by gold-plating some cheaper material?

> Water flows steadily from an open tank as in Fig. P12.81. The elevation of point 1 is 10.0 m, and the elevation of points 2 and 3 is 2.00 m. The cross-sectional area at point 2 is 0.0480 m2; at point 3 it is 0.0160 m2. The area of the tank is very large

> A cylindrical bucket, open at the top, is 25.0 cm high and 10.0 cm in diameter. A circular hole with a cross-sectional area 1.50 cm2 is cut in the center of the bottom of the bucket. Water flows into the bucket from a tube above it at the rate of 2.40 ×

> You hold a hose at waist height and spray water horizontally with it. The hose nozzle has a diameter of 1.80 cm, and the water splashes on the ground a distance of 0.950 m horizontally from the nozzle. If you constrict the nozzle to a diameter of 0.750 c

> Your uncle is in the below-deck galley of his boat while you are spear fishing in the water nearby. An errant spear makes a small hole in the boat’s hull, and water starts to leak into the galley. (a) If the hole is 0.900 m below the water surface and ha

> Water stands at a depth H in a large, open tank whose side walls are vertical (Fig. P12.77). A hole is made in one of the walls at a depth h below the water surface. (a) At what distance R from the foot of the wall does the emerging stream strike the flo

> A barge is in a rectangular lock on a freshwater river. The lock is 60.0 m long and 20.0 m wide, and the steel doors on each end are closed. With the barge floating in the lock, a 2.50 × 106 N load of scrap metal is put onto the barge. The metal has dens

> A cubical block of density

> Assume that crude oil from a supertanker has density 750 kg/m3. The tanker runs aground on a sandbar. To refloat the tanker, its oil cargo is pumped out into steel barrels, each of which has a mass of 15.0 kg when empty and holds 0.120 m3 of oil. You can

> A plastic ball has radius 12.0 cm and floats in water with 24.0% of its volume submerged. (a) What force must you apply to the ball to hold it at rest totally below the surface of the water? (b) If you let go of the ball, what is its acceleration the ins

> Block A in Fig. P12.72 hangs by a cord from spring balance D and is submerged in a liquid C contained in beaker B. The mass of the beaker is 1.00 kg; the mass of the liquid is 1.80 kg. Balance D reads 3.50 kg, and balance E reads 7.50 kg. The volume of b

> A bullet spins on its axis as it emerges from a rifle. Explain how this prevents the bullet from tumbling and keeps the streamlined end pointed forward.

> Serious bicyclists say that if you reduce the weight of a bike, it is more effective if you do so in the wheels rather than in the frame. Why would reducing weight in the wheels make it easier on the bicyclist than reducing the same amount in the frame?

> A closed and elevated vertical cylindrical tank with diameter 2.00 m contains water to a depth of 0.800 m. A worker accidently pokes a circular hole with diameter 0.0200 m in the bottom of the tank. As the water drains from the tank, compressed air above

> In seawater, a life preserver with a volume of 0.0400 m3 will support a 75.0-kg person (average density 980 kg / m3), with 20% of the person’s volume above the water surface when the life preserver is fully submerged. What is the density of the material

> A firehose must be able to shoot water to the top of a building 28.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m3/s and shoots out of a round nozzle. (a) What is the maximum diameter this nozzle can have (b) If the o

> When an open-faced boat has a mass of 5750 kg, including its cargo and passengers, it floats with the water just up to the top of its gunwales (sides) on a freshwater lake. (a) What is the volume of this boat? (b) The captain decides that it is too dange

> The densities of air, helium, and hydrogen (at p = 1.0 atm and T = 20°C) are 1.20 kg/m3, 0.166 kg/m3, and 0.0899 kg/m3, respectively. (a) What is the volume in cubic meters displaced by a hydrogen-filled airship that has a total “lift” of 90.0 kN? (The “

> A piece of wood is 0.600 m long, 0.250 m wide, and 0.080 m thick. Its density is 700 kg/m3. What volume of lead must be fastened underneath it to sink the wood in calm water so that its top is just even with the water level? What is the mass of this volu

> Advertisements for a certain small car claim that it floats in water. (a) If the car’s mass is 900 kg and its interior volume is 3.0 m3, what fraction of the car is immersed when it floats? Ignore the volume of steel and other materials. (b) Water gradua

> A single ice cube with mass 16.4 g floats in a glass completely full of 420 cm3 of water. Ignore the water’s surface tension and its variation in density with temperature (as long as it remains a liquid). (a) What volume of water does the ice cube displa

> An open barge has the dimensions shown in Fig. P12.63. If the barge is made out of 4.0-cm-thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in freshwater without sinking? Is there enough room in the barge t

> A hot-air balloon has a volume of 2200 m3. The balloon fabric (the envelope) weighs 900 N. The basket with gear and full propane tanks weighs 1700 N. If the balloon can barely lift an additional 3200 N of passengers, breakfast, and champagne when the out

> Which has a greater buoyant force on it: a 25-cm3 piece of wood floating with part of its volume above water or a 25-cm3 piece of submerged iron? Or, must you know their masses before you can answer? Explain.

> A large, 40.0-kg cubical block of wood with uniform density is floating in a freshwater lake with 20.0% of its volume above the surface of the water. You want to load bricks onto the floating block and then push it horizontally through the water to an is

> On the afternoon of January 15, 1919, an unusually warm day in Boston, a 17.7-mhigh, 27.4-m-diameter cylindrical metal tank used for storing molasses ruptured. Molasses flooded into the streets in a 5-mdeep stream, killing pedestrians and horses and knoc

> A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height of the water column is 15.0 cm (Fig. P12.59). (a) What is the gauge pressure at t

> A narrow, U-shaped glass tube with open ends is filled with 25.0 cm of oil (of specific gravity 0.80) and 25.0 cm of water on opposite sides, with a barrier separating the liquids (Fig. P12.58). (a) Assume that the two liquids do not mix, and find the fi

> A 0.180-kg cube of ice (frozen water) is floating in glycerine. The gylcerine is in a tall cylinder that has inside radius 3.50 cm. The level of the glycerine is well below the top of the cylinder. If the ice completely melts, by what distance does the h

> It has been proposed that we could explore Mars using inflated balloons to hover just above the surface. The buoyancy of the atmosphere would keep the balloon aloft. The density of the Martian atmosphere is 0.0154 kg/m3 (although this varies with tempera

> The upper edge of a gate in a dam runs along the water surface. The gate is 2.00 m high and 4.00 m wide and is hinged along a horizontal line through its center (Fig. P12.55). Calculate the torque about the hinge arising from the force due to the water.