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physics
college physics 2nd
College Physics A Strategic Approach 4th Edition Randall D. Knight, Brian Jones - Solutions
In the Pirate Boat ride at the amusement park, riders swing back and forth in a pendulumlike “boat.” The distance from the boat to the pivot point is 13 m, and the maximum angle the boat reaches is 40°.a. What is the maximum speed the boat attains?b. What is the apparent weight of a 55 kg
If you let go of a helium balloon, it quickly rises. As it rises, the balloon gets larger and larger until it pops. Why does the balloon expand as it rises?
Scuba divers are warned that if they must make a rapid ascent, they should exhale on the way up. If a diver rapidly ascends to the surface with lungs full of air, his lungs could be damaged. Explain why this is so.
Freshwater fish tend to have larger swim bladders than saltwater fish. Explain why you would expect this to be true.
Elephant seals do deep dives to forage for food. The energy used by the seals in diving depends on their body composition; for example, fatter seals use less energy to swim to the surface at the end of a dive, allowing them to take longer, more productive dives. Explain why you’d expect this to
A higher level of hemoglobin in the blood increases the blood’s density. This is the basis for a simple test that can be used to see if a prospective blood donor has a high enough hemoglobin level to donate safely. A drop of blood is placed in a copper sulfate solution, and the time for the drop
Early airships—craft that relied on large volumes of low density gas to rise from the ground—were filled with hydrogen, but safety concerns necessitated a switch to helium. When an airship made the switch, how did this affect its cargo capacity? Explain.
The air in a hot-air balloon can be heated only so much; the temperature of the gas inside the balloon can only be so high before damaging the nylon envelope. This means that hot-air balloons can lift a larger load on a cool morning than on a warm afternoon. Explain.
You are looking for a deep spot to take a swim in a local river. The width of the river is about the same all along its length, but there are places where the water flows quickly and places where it flows slowly. Which is a better choice for a swim?
A 55 g soapstone cube—a whisky stone—is used to chill a glass of whisky. Soapstone has a density of 3000 kg/m3 , whisky a density of 940 kg/m3 . What is the approximate normal force of the bottom of the glass on a single stone?A. 0.1 NB. 0.2 NC. 0.3 ND. 0.4 N
At the surface of a freshwater spring, a manatee with a small amount of air in its lungs is neutrally buoyant. The manatee now dives to a depth of 10 m. At this greater depth, the buoyant force isA. Less than the weight force.B. The same as the weight force.C. Greater than the weight force.
A 68 kg college student’s body has a typical density of 1050 kg/m2 . What is his volume?
A 5.0 kg freshwater fish at the surface of a lake is neutrally buoyant. If the density of its body with its swim bladder deflated is 1060 kg/m3 , what volume of gas must be in the swim bladder for the fish to be neutrally buoyant?
Fat cells in humans are composed almost entirely of pure triglycerides with an average density of about 900 kg/m3 . If 20% of the mass of a 70 kg student’s body is fat (a typical value), what is the total volume of the fat in his body?
James Cameron piloted a submersible craft to the bottom of the Challenger Deep, the deepest point on the ocean’s floor, 11,000 m below the surface. What was the total inward force on the 1.1-m-diameter pilot sphere in which Cameron sat?
Snorkelers breathe through tubes that extend above the surface of the water. In principle, a snorkeler could go deeper with a longer tube, but the extra pressure at the greater depth would make breathing too difficult. If a snorkeler can develop a pressure in her lungs that is 10 kPa below the
A city uses a water tower to store water for times of high demand. When demand is light, water is pumped into the tower. When demand is heavy, water can flow from the tower without overwhelming the pumps. To provide water at a typical 350 kPa gauge pressure, how tall must the tower be?
Hippos spend much of their lives in water, but amazingly, they don’t swim. They have, like manatees, very little body fat. The density of a hippo’s body is approximately 1030 kg/m3 , so it sinks to the bottom of the freshwater lakes and rivers it frequents—and then it simply walks on the
The classic Goodyear blimp is essentially a helium balloon— a big one, containing 5700 m3 of helium. If the envelope and gondola have a total mass of 4300 kg, what is the maximum cargo load when the blimp flies at a sea-level location? Assume an air temperature of 20°C.
Sharks are generally negatively buoyant; the upward buoyant force is less than the weight force. This is one reason sharks tend to swim continuously; water moving past their fins causes a lift force that keeps sharks from sinking. A 92 kg bull shark has a density of 1040 kg/m3 .a. What lift force
A milkshake has a viscosity of 0.50 Pa • s. To drink this shake through a straw of diameter 0.56 cm and length 22 cm, you need to reduce the pressure at the top of the straw to less than atmospheric pressure. If you want to drain a 480 mL shake in 2.0 minutes, what pressure difference is needed?
How easy is it to breathe through a straw? When you breathe deeply, you pull in 4.0 L of air in about 3.0 s. This requires a pressure difference of about 4.0 kPa between the air in your lungs and the outside air. What additional pressure difference is required to pull 20°C air through a straw that
When you hold your hands at your sides, you may have noticed that the veins sometimes bulge—the height difference between your heart and your hands produces increased pressure in the veins. The same thing happens in the arteries. Estimate the distance that your hands are below your heart. If
To keep blood from pooling in their lower legs on plane trips, some people wear compression socks. These socks are sold by the pressure they apply; a typical rating is 20 mm Hg. Over what vertical distance can this pressure move the blood?
Using the data in Figure 13.37 for the venules, and assuming a typical blood flow rate of 5.0 L per minute,a. What is the flow speed in the venules?b. What is the pressure difference across a 1.0 cm length of venule? 2.0 m/s 200 kPa Oil 3.0 m/s 10 m FIGURE P13.37
A mass hanging from a spring undergoes vertical simple harmonic motion.a. Where in the motion is the magnitude of the net force equal to zero?b. Where in the motion is the velocity equal to zero?c. Where in the motion does the acceleration have its greatest magnitude?d. Where in the motion is
If a mass on a spring moving horizontally were taken to the moon, how would its frequency change? What about a mass on a spring moving vertically? A pendulum?
A young girl and her mother are swinging on a swing set. Who, if either, has the longer period of oscillation? Explain.
In 1831, soldiers marched across the Broughton Bridge in England in “lock step”—that is, marching in time together. As they marched, the bridge began to bounce in time with their footsteps; the amplitude of this bouncing became larger and larger until the bridge suddenly collapsed. Explain
A diver leaps from a high platform, speeds up as she falls, and then slows to a stop in the water. How do you define the system so that the energy changes are all transformations internal to an isolated system?
When your hands are cold, you can rub them together to warm them. Explain the energy transformations that make this possible.
Ferns that eject spores generally do so in pairs, with two spores flying off in opposite directions. The structure from which the spores are launched is quite lightweight. If it takes a certain amount of energy to eject each spore, explain how launching the spores in pairs provides for the greatest
Figure Q10.24 shows a potential-energy diagram for a particle. The particle is at rest at point A and is then given a slight nudge to the right. Describe the subsequent motion. FIGURE Q10.24 Energy +x A B C D E CDE
A dog can provide sufficient power to pull a sled with a 60 N force at a steady 2.0 m/s. Suppose the dog is hitched to a different sled that requires 120 N to move at a constant speed. How fast can the dog pull this second sled?A. 0.50 m/s B. 1.0 m/s C. 1.5 m/s D. 2.0 m/s
Most of the energy you expend in cycling is dissipated by the drag force. If you double your speed, you increase the drag force by a factor of 4. This increases the power to cycle at this greater speed by what factor?A. 2 B. 4 C. 8 D. 16
When the Glen Canyon hydroelectric power plant in Arizona is running at capacity, 690 m3 of water flows through the dam each second. The water is released 220 m below the top of the reservoir. If the generators that the dam employs are 90% efficient, what is the maximum possible electric power
A pronghorn, the fastest North American animal, is capable of running at 18 m/s (40 mph) for 10 minutes, after which it must slow down. The time limit isn’t because the pronghorn runs out of energy; it’s because the pronghorn’s temperature rises, and it must stop to cool down. Why does the
When the hoof of a galloping horse hits the ground, the digital flexor tendon in its lower leg may stretch by 5% in length, a significant stretch for this 45 cm tendon. The tendon is elastic; most—but not all—of the energy stored in the stretch is returned, which allows for efficient
A typical wind turbine extracts 40% of the kinetic energy of the wind that blows through the area swept by the blades. For a large turbine, 110,000 kg of air moves past the blades at 15 m/s every second. If the wind turbine extracts 40% of this kinetic energy, and if 80% of this energy is converted
If you want to jump as high as possible, it’s best to move downward quickly to a deep crouch, stretching tendons and muscles, before pushing off and leaving the ground rather than simply pushing off from a stationary crouch. Explain how this provides additional energy for the jump.
We noted that, under ideal conditions, metabolizing one molecule of glucose can form 38 molecules of ATP. A more realistic value is 30 molecules of ATP. For this lower number, what is the efficiency of the process of converting the chemical energy of glucose to that of ATP?
When you grind wheat to make flour, the flour comes out very warm—you can actually scorch the flour if you grind too quickly. Explain how this temperature rise comes about.
Jessie and Jaime complete a 5.0 km race. Each has a mass of 68 kg. Jessie runs the race at 15 km/h; Jaime walks it at 5 km/h. How much metabolic energy does each use to complete the course?
If you ask for an iced coffee, the barista will add ice cubes to hot coffee to cool it down. To cool 350 mL of coffee at 90°C to 0°C, what is the minimum mass of 0°C ice required?
You are pulling a child in a wagon. The rope handle is inclined upward at a 60° angle. The tension in the handle is 20 N. How much work do you do if you pull the wagon 100 m at a constant speed?
A typical muscle fiber is 2.0 cm long and has a cross-section area of 3.1 × 10-9 m2 . When the muscle fiber is stimulated, it pulls with a force of 1.2 mN. What is the work done by the muscle fiber as it contracts to a length of 1.6 cm?
A wind turbine works by slowing the air that passes its blades and converting much of the extracted kinetic energy to electric energy. A large wind turbine has 45-m-radius blades. In typical conditions, 92,000 kg of air moves past the blades every second. If the air is moving at 12 m/s before it
A 60 kg runner in a sprint moves at 11 m/s. A 60 kg cheetah in a sprint moves at 33 m/s. By what factor does the kinetic energy of the cheetah exceed that of the human runner?
The opposite of a wind turbine is an electric fan: The electric energy that powers the fan is converted to the kinetic energy of moving air. A fan is putting 1.0 J of kinetic energy into the air every second. Then the fan speed is increased by a factor of 2. Air moves through the fan faster, so the
A fielder tosses a 0.15 kg baseball at 32 m/s at a 30° angle to the horizontal. What is the ball’s kinetic energy at the start of its motion? What is the kinetic energy at the highest point of its arc?
A school has installed a modestly-sized wind turbine. The three blades are 4.6 m long; each blade has a mass of 45 kg. You can assume that the blades are uniform along their lengths. When the blades spin at 240 rpm, what is the kinetic energy of the blade assembly?
A typical meteor that hits the earth’s upper atmosphere has a mass of only 2.5 g, about the same as a penny, but it is moving at an impressive 40 km/s. As the meteor slows, the resulting thermal energy makes a glowing streak across the sky, a shooting star. The small mass packs a surprising
The spring in a retractable ballpoint pen is 1.8 cm long, with a 300 N/m spring constant. When the pen is retracted, the spring is compressed by 1.0 mm. When you click the button to extend the pen, you compress the spring by an additional 6.0 mm. How much energy is required to extend the pen?
Scallops use muscles to close their shells. Opening the shell is another story—muscles can only pull, they can’t push. Instead of muscles, the shell is opened by a spring, a pad of a very elastic biological material called abductin. When the shell closes, the pad compresses; a restoring force
When you skid to a stop on your bike, you can significantly heat the small patch of tire that rubs against the road surface. Suppose a person skids to a stop by hitting the brake on his back tire, which supports half the 80 kg combined mass of the bike and rider, leaving a skid mark that is 40 cm
If you slide down a rope, it’s possible to create enough thermal energy to burn your hands or your legs where they grip the rope. Suppose a 40 kg child slides down a rope at a playground, descending 2.0 m at a constant speed. How much thermal energy is created as she slides down the rope?
Some runners train with parachutes that trail behind them to provide a large drag force. These parachutes are designed to have a large drag coefficient. One model expands to a square 1.8 m on a side, with a drag coefficient of 1.4. A runner completes a 200 m run at 5.0 m/s with this chute trailing
The famous cliff divers of Acapulco leap from a perch 35 m above the ocean. How fast are they moving when they reach the water surface? What happens to their kinetic energy as they slow to a stop in the water?
You can, in an emergency, start a manual transmission car by putting it in neutral, letting the car roll down a hill to pick up speed, then putting it in gear and quickly letting out the clutch. If the car needs to be moving at 3.5 m/s for this to work, how high a hill do you need? (You can ignore
A 480 g peregrine falcon reaches a speed of 75 m/s in a vertical dive called a stoop. If we assume that the falcon speeds up under the influence of gravity only, what is the minimum height of the dive needed to achieve this speed?
Monica pulls her daughter Jessie in a bike trailer. The trailer and Jessie together have a mass of 25 kg. Monica starts up a 100-m-long slope that’s 4.0 m high. On the slope, Monica’s bike pulls on the trailer with a constant force of 8.0 N. They start out at the bottom of the slope with a
Mosses don’t spread by dispersing seeds; they disperse tiny spores. The spores are so small that they will stay aloft and move with the wind, but getting them to be windborne requires the moss to shoot the spores upward. Some species do this by using a spore-containing capsule that dries out and
When you stand on a trampoline, the surface depresses below equilibrium, and the surface pushes up on you, as the data for a real trampoline in Figure P10.48 show. The linear variation of the force as a function of distance means that we can model the restoring force as that of a spring. A 72 kg
The Special Olympics raises money through “plane pull” events in which teams of 25 people compete to see who can pull a 74,000 kg airplane 3.7 m across the tarmac. The inertia of the plane is an issue—but so is the 14,000 N rolling friction force that works against the teams. If a team pulls
A shooting star is actually the track of a meteor, typically a small chunk of debris from a comet that has entered the earth’s atmosphere. As the drag force slows the meteor down, its kinetic energy is converted to thermal energy, leaving a glowing trail across the sky. A typical meteor has a
A 500 kg horse can provide a steady output power of 750 W (that is, 1 horsepower) when pulling a load. How about a 38 kg sled dog? Data show that a 38 kg dog can pull a sled that requires a pulling force of 60 N at a steady 2.2 m/s. What are the specific power values for the dog and the horse? What
A world-class sprinter running a 100 m dash was clocked at 5.4 m/s 1.0 s after starting running and at 9.8 m/s 1.5 s later. In which of these time intervals, 0 to 1.0 s or 1.0 s to 2.5 s, was his output power greater?
A 95 kg quarterback accelerates a 0.42 kg ball from rest to 24 m/s in 0.083 s. What is the specific power for this toss?
Humans can produce an output power as great as 20 W/kg during extreme exercise. Sloths are not so energetic. At its maximum speed, a 4.0 kg sloth can climb a height of 6.0 m in 2.0 min. What’s the specific power for this climb?
The energy yield of a nuclear weapon is often defined in terms of the equivalent mass of a conventional explosive. 1 ton of a conventional explosive releases 4.2 GJ. A typical nuclear warhead releases 250,000 times more, so the yield is expressed as 250 kilotons. That is a staggering explosion, but
Swordfish are capable of stunning output power for short bursts. A 650 kg swordfish has a cross-section area of 0.92 m2 and a drag coefficient of 0.0091—exceptionally low due to a number of adaptations. Such a fish can sustain a speed of 30 m/s for a few seconds. Assume seawater has a density of
Diesel engines give more miles per gallon than gasoline engines, but some of this is due to the higher energy content of diesel fuel. At highway speeds, it takes 0.20 MJ to move an aerodynamic car 1.0 km. At highway speeds, with a gasoline engine, a car gets 16 km per liter of fuel; with a diesel
Walking up a set of stairs and running up the stairs require approximately the same metabolic energy. Explain why you’d expect this to be the case.
Tessa and Jody, each of mass 68 kg, go out for some exercise together. Tessa runs at 15 km/h; Jody cycles alongside at the same speed. After 20 minutes, how much metabolic energy has each used?
Each time he does one pushup, Jose, who has a mass of 75 kg, raises his center of mass by 25 cm. He completes an impressive 150 pushups in 5 minutes, exercising at a steady rate.a. If we assume that lowering his body has no energetic cost, what is his metabolic power during this workout?b. In
The basis of muscle action is the power stroke of the myosin protein pulling on an actin filament. It takes the energy of one molecule of ATP, 5.1 × 10-20 J, to produce a displacement of 10 nm against a force of 1.0 pN. What is the efficiency?
If you leave a fan running, it actually warms up the air in the room, a fact that surprises many people. Explain why a fan would be expected to warm the air that passes through it.
In an extreme marathon, participants run a total of 100 km; world-class athletes maintain a pace of 15 km/h. How many 230 Calorie energy bars would be required to fuel such a run for a 68 kg athlete?
A 10 kg migratory swan cruises at 20 m/s. A calculation that takes into account the necessary forces shows that this motion requires 200 W of mechanical power. If we assume an efficiency similar to humans, a reasonable assumption, then the metabolic power of the swan is significantly higher than
Your car’s engine is a heat engine; it converts the thermal energy from burning fuel into energy to move your car and power its systems. On a cold winter day, you needn’t feel guilty about cranking up the heat in your car; running the heater doesn’t cost any additional energy beyond the small
The geothermal power plant at Brady Hot Springs in Nevada uses the outside air as the cold reservoir. The plant has a higher electricity output in the morning than it does in the evening. Why would you expect this to be the case?
You can save money on electricity if you put your refrigerator in the basement, which is usually cooler than the rest of your house. Explain.
Living creatures generally have a higher temperature than their environment. Explain why this makes sense.
A reaction happens in a perfectly sealed and insulated container. Does the total energy of the system decrease? The free energy?
On clear day, sunlight delivers approximately 1000 J each second to a 1 m2 surface; smaller areas receive proportionally less—half the area receives half the energy. A 12% efficient solar cell, a square 15 cm on a side, is in bright sunlight. How much electric power does it produce?A. 0.9
Your roommate leaves a 120 W fan running in your apartment. Over the course of an hour, how much thermal energy does the fan add to the air?
For locations that have no electric service, companies are designing bicycle-powered generators that are nearly 100% efficient that can be used to charge cell phones or power lights. If you are the person chosen to pedal and your friends need a total of 150 W of electric power, how much metabolic
Compressing air to fill a scuba tank warms it up. A dive shop compensates by putting the tank in a tub of water, keeping the tank and the gas inside it at a constant temperature as it is filled. If the system is the tank, what are the signs of W and Q for this process? What can you say about the
A California geothermal power plant generates 4.3 MW by extracting 24 MW of heat from an underground source at 108°C and then discharging waste heat into the 17°C air.a. What is the actual efficiency of the plant?b. What is the theoretical efficiency?
A NATO base in northern Norway is warmed with a heat pump that uses 7.0°C ocean water as the cold reservoir. Heat extracted from the ocean water warms fluid to 80°C; this warmed fluid is used to heat the building. When the system is working at full capacity, 2000 kW of heat are delivered to the
The inside of your refrigerator is approximately 0°C. Heat from the inside of your refrigerator is deposited into the air in your kitchen, which has a temperature of approximately 20°C. At these operating temperatures, what is the maximum possible coefficient of performance of your refrigerator?
Entropy can be used as a measure of the overall health of an ecosystem—higher entropy correlates with better health. A thermal image of a landscape, where color indicates temperature, can be used for a quick assessment. What would be the thermal signature of a healthy ecosystem?
What is the typical speed of a helium atom in a child’s balloon at a room temperature of 20°C?
For a normal car riding on tires with relatively flexible sidewalls, the weight of the car is held up, in large measure, by the pressure of the air in the tires. If you look at one of your car’s tires, you’ll note that the tire is flattened slightly to make a rectangle where it touches the
The interior of the earth is at a higher temperature than it would be if it were cooling steadily; there must be internal sources of heat. Current models of the earth’s interior suggest that one source of heat is the crystallization of liquid iron. Explain how this process provides heat to the
We’ve discussed elevators that are raised with cables, but many elevators use pistons. A pump provides fluid at very high pressure to the piston; the resulting force on the piston raises the elevator and passengers. For a typical piston elevator, the mass of the elevator and passengers is 2000 kg
If you are exposed to water vapor at 100°C, you are likely to experience a worse burn than if you are exposed to liquid water at 100°C. Why is water vapor more damaging than liquid water at the same temperature?
When night falls, the temperature of the earth’s surface starts to drop. On a cool night, dew starts to form on the grass as water vapor condenses. Once dew starts to form, the rate of temperature decrease slows. Explain why this change occurs.
The pressure inside a champagne bottle can be quite high and can launch a cork explosively. Suppose you open a bottle at sea level. The absolute pressure inside a champagne bottle is 6 times atmospheric pressure; the cork has a mass of 7.5 g and a diameter of 18 mm. Assume that once the cork starts
Some jellyfish can eject stingers with remarkable force and speed. One species does this by building up a 15 MPa gauge pressure that pushes against the base of a 2.0-μm-diameter stylet, forcing it outward.a. What force does the excess pressure exert on the stylet?b. The mass set into motion is a
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