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college physics reasoning
College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions
Conceptualizing units. A small burrito, like those bought at your local fast-food restaurant, has a mass of approximately 100 g and contains about 300 C. (The capital “C” indicates that this unit is a “food Calorie.”) From what height would you need to drop the burrito to give it a kinetic
Counting calories. The chemical potential energy in foods is measured in units called Calories (notice the capital C). This “food Calorie” is equal to 1000 calories. For example, a typical apple contains approximately 75 Calories, which is actually 75 kilo calories. If all the energy in an
Repeat Problem 85, but replace the apple with a typical fast-food hamburger (approximately 400 C).Data From Problem 85Counting calories. The chemical potential energy in foods is measured in units called Calories (notice the capital C). This “food Calorie” is equal to 1000 calories. For
A doughnut contains roughly 350 C (1.5 × 106 J) of potential energy locked in chemical bonds. Find the ratio of the potential energy in the doughnut to that in an equivalent volume of TNT (trinitrotoluene), which has a density of 1.65 g/cm3 and releases 4.7 × 106 J per kg of explosive. Aren’t
One gallon of gasoline contains 3.1 × 107 calories of potential energy that are released during combustion. If 1 gal of gasoline can provide the force that moves a car through a displacement of 25 mi, what is the average force produced by the gasoline?
Tarzan (m = 74 kg) commutes to work swinging from vine to vine. He leaves the platform of his tree house and swings on the end of a vine of length L = 8.0 m. (a) If the platform is 1.9 m above the lowest point in the swing, what is the tension in the vine at the lowest point in the
A toy gun shoots spherical plastic projectiles by means of a spring. A typical projectile has mass m = 25 g. The spring used has spring constant k = 15 N/m, and when put under load, it is displaced an amount ??x = 6.0 cm as shown in Figure P6.90. The barrel of the gun exerts a slight frictional
A bomb that is initially at rest breaks into several pieces of approximately equal mass, two of which are shown with their velocity vectors in Figure Q7.1. Use conservation of momentum to determine if there might be other pieces of the bomb not shown in the figure. Assume there is only one missing
A pole vaulter of mass 70 kg can run horizontally with a top speed of 10.0 m/s. The current record height for the pole vault is about 6.2 m. (a) For the vaulter to clear this height, approximately how much energy must be stored in the pole just before he leaves the ground? Assume the
A spring is mounted at angle u = 35° on a friction less incline as illustrated in Figure P6.92. The spring is compressed by 15 cm where it is allowed to propel a mass of 5.5 kg up the incline.? (a) If the spring constant is 550 N/m, how fast is the mass moving when it leaves the spring?? (b) To
Consider the system in Problem 92 and assume the coefficient of kinetic friction between the mass and the incline is 0.17. (a) At what position, measured from the starting point, does the maximum velocity occur? (b) What is the maximum velocity attained by the mass at this point? (c)
Spring shoes. Tae-Hyuk Yoon of South Korea is the inventor of a novel method of human locomotion: the Poweriser spring boot shown in Figure P6.94. Promotional materials claim that an 80-kg man can jump up to 2 m high while wearing these devices. Estimate the spring constant of the leaf springs on
A chairlift rises in elevation 600 m (about 2000 ft) up a ski slope and has a total of 200 chairs evenly spaced every 12 m (about 40 ft) apart. On a busy weekend, the ski lift is at full capacity (two people per seat), and skiers come off the lift every 10 s. Assuming a skier has a mass of 80 kg
A 70-kg skydiver reaches a terminal velocity of 50 m/s. At what rate is the drag force dissipating his kinetic energy? How does this rate compare with his rate of change in potential energy?
The world record for the highest-altitude skydive was made by Joseph Kittinger in 1960. Kittinger jumped from a high- altitude balloon (Fig. P6.97) at a height of 102,800 ft (31,330 m) above sea level and, according to reports, attained speeds up to 624 mi/h (279 m/s) allowed by the thin air of the
The NEAR spacecraft flew by the asteroid Eros in 1997 (Fig. P6.98). The fly by allowed the craft to measure the asteroid???s density at 2.7 g/cm3. Assume most asteroids have similar composition and you personally can jump 1.0 m high on the Earth.? (a) What is the radius of the largest spherical
Aerobic workout. After a 5-min workout on a Climb Max stair machine, the readout panel (Fig. P6.99) reports that the 75-kg user burned 19.7 Calories (see Problem 85) and climbed a total of 180 steps.? (a) If each step is 15 cm in height, how much would the potential energy of the user have changed
The expression for the force due to air drag described in Chapter 3 (Eq. 3.20) ignores the aerodynamic shape of an object. Some objects, such as a race car, are shaped so as to minimize the drag force. This can be accounted for by adding a factor called the drag coefficient CD. The drag force then
For a car moving with speed v, the force of air drag is proportional to v2. If the power output of the car’s engine is doubled, by what factor does the speed of the car increase?
The Roche limit. Some ???bodies??? in the solar system are a collection of rocks held together solely or mainly by their gravitational attraction. When such an object comes close to a planet, so-called tidal forces will break the object apart. Consider an asteroid composed of two pieces, each of
Collisions of commercial aircraft with birds are a serious safety hazard, especially when a plane is taking off or landing. Consider a typical goose that collides with an airplane taking off at 70 m/s (about 150 mi/h) and compare the impact with that of a 500-kg mass (about half the size of a small
On your vacation, you fly from Atlanta to San Francisco (a total distance of 3400 km) in 4.0 h. (a) Draw a qualitative sketch of how the speed of your airplane varies with time. (b) What is the average speed during your trip? (c) Estimate the top speed during your trip. You reach
Figure P2.27 shows the velocity???time curve of a falling brick. Make a careful estimate of the slope to find the acceleration of the brick at t 5 3.0 s. Figure P2.27 ? 0+i-2–3–4–5–6- t (s) - 10- -20 -30 -40 - 50 -60 v (m/s)
In Insight 5.2, we discussed how, because of the force of gravity from the Moon, the Earth moves in an orbit around a point that lies between it and the Moon. (a) Find the radius of the Earth’s orbit. (b) Does the center of the Earth’s orbit lie inside or outside the Earth itself?
Proponents of astrology claim that the positions of the planets at the time of a baby’s birth will affect the life of that person in important ways. Some assert that this effect is due to gravity. Use Newton’s law of gravity to examine this claim. Calculate the ratio of the maximum force
Will your apparent weight at the top of Mount Everest (altitude 8850 m = 29,035 ft) be more or less than at sea level at the same latitude (27.98° N)? What is the ratio of your apparent weight on Mount Everest to that at sea level? For simplicity, consider only the effect of altitude and ignore
For the bicycle wheel in Problem 1, what is the centripetal acceleration of a point that is 0.10 m from the outer edge of the wheel? Explain why this value is different from the answer to part (a) of Problem 1.Data From Problem 1A bicycle wheel of radius 0.30 m is spinning at a rate of 60
It is sometimes claimed by astrologers (but not by astronomers!) that because the Moon dramatically affects the seas of the world, as evidenced by the tides, the Moon must also affect individual people because more than 60% of an average adult’s mass is water. Does that claim make sense? Use
Consider the motion of a rock tied to a string of length 0.50 m. The string is spun so that the rock travels in a vertical circle as shown in Figure P5.16. The mass of the rock is 1.5 kg, and it is twirling at constant speed with a period of 0.33 s. (a) Draw free-body diagrams for the rock when it
Consider a Ferris wheel in which the chairs hang down from the main wheel via a cable. The cable is L = 2.0 m long, and the radius of the wheel is 12 m (Fig. P5.30). When a chair is in the orientation shown in the figure (the ???3 o???clock??? position), the cable attached to the chair makes an
A rock of mass m = 1.5 kg is tied to a string of length L = 2.0 m and is twirled in a vertical circle as shown in Figure 5.10. The speed v of the rock is constant; that is, it is the same at the top and the bottom of the circle. If the tension in the string is zero when the rock is at its highest
Find the gravitational force of the Sun on the Earth.
Calculate the acceleration due to gravity on the surface of Mars.
Suppose the density of the Earth was somehow reduced from its actual value to 1000 kg/m3 (the density of water). Find the value of g, the acceleration due to gravity, on this new planet. Assume the radius does not change.
You are an astronaut (m = 95 kg) and travel to a planet that is the same radius and mass as the Earth, but it has a rotational period of only 2 h. What is your apparent weight at the equator of this planet?
In Section 5.4, we showed that the radius of a geosynchronous orbit about the Earth is 4.2 × 107 m, compared with the radius of the Earth, which is 6.4 × 106 m. By what factor is the force of gravity smaller when you are in geosynchronous orbit than when you are on the Earth’s surface?
Saturn makes one complete orbit of the Sun every 29.4 years. Calculate the radius of the orbit of Saturn.
The region of the solar system between Mars and Jupiter contains many asteroids that orbit the Sun. Consider an asteroid in a circular orbit of radius 5.0 × 1011 m. Find the period of the orbit.
A newly discovered asteroid is found to have a circular orbit, with a radius equal to 27 times the radius of the Earth’s orbit. How long does this asteroid take to complete one orbit around the Sun?
In recent years, a number of nearby stars have been found to possess planets. Suppose the orbital radius of such a planet is found to be 4.0 × 1011 m, with a period of 1100 days. Find the mass of the star.
In Figure 5.31, we saw that tides on the Earth are due to the variation of the Moon???s gravitational force with distance. Find the approximate ratio of the Moon???s gravitational force on two portions of the ocean, one nearest the Moon and one on the opposite side of the Earth. Figure 5.31
Mars has two moons, Phobos and Deimos. It is known that the larger moon, Phobos, has an orbital radius of 9.4 × 106 m and a mass of 1.1 × 1016 kg. Find its orbital period.
In our derivation of Kepler???s laws, we assumed the only force on a planet is due to the Sun. In a real solar system, however, the gravitational forces from the other planets can sometimes be important. Calculate the gravitational force of Jupiter on the Earth and compare it to the magnitude of
What is the speed of a satellite in a geosynchronous orbit about the Earth? Compare it with the speed of the Earth as it orbits the Sun.
Syzygy. We have seen that normal tides are due to the gravitational force exerted by the Moon on the Earth???s oceans. When the Moon, Sun, and Earth are aligned as shown in Figure P5.56, the magnitude of the tide increases due to the gravitational force exerted by the Sun on the oceans (at the
Your weight is due to the gravitational attraction of the Earth. The Moon, though, also exerts a gravitational force on you, and when it is overhead, your weight decreases by a small amount. Calculate the effect of the Moon on your weight. Express your result as a percentage change for the cases of
During an eclipse, the Sun, Earth, and Moon are arranged in a line as shown in Figure P5.59. There are two types of eclipse: (a) a lunar eclipse, when the Earth is between the Sun and the Moon, and (b) a solar eclipse, when the Moon is between the Sun and the Earth. Calculate the percentage change
In the film Mission to Mars (released in 2000), the spacecraft (Fig. P5.60) features a rotating section to provide artificial gravity for the long voyage. A physicist viewing a scene from the interior of the spacecraft notices that the diameter of the rotating portion of the ship is about five
A man stands 6.0 ft tall at sea level on the North Pole as shown in Figure P5.62.? (a) What is the difference in the value of g (the gravitational acceleration) between his head and his feet?? (b) The man is now put in a space suit and transported to a location one Earth radius away from a black
An ancient and deadly weapon, a sling consists of two braided cords, each about half an arm???s length long, attached to a leather pocket. The pocket is loaded with a projectile made of lead, carved rock, or clay and made to swing in a vertical circle as shown in Figure P5.64. The projectile is
A popular circus act features daredevil motorcycle riders encased in the ???Globe of Death??? (Fig. P5.65), a spherical metal cage of diameter 16 ft.? (a) A rider of mass 65 kg on a 125-cc (95-kg) motorcycle keeps his bike horizontal as he rides around the ???equator??? of the globe. What
Asteroid satellite. While on its way to Jupiter in 1993, the Galileo spacecraft made a fly by of asteroid Ida. Images captured of Ida (Fig. P5.66) showed that the asteroid has a tiny moon of its own, since given the name Dactyl. Measurements found Ida to be about 56 ?? 24 ?? 21 km (35 ?? 15 ?? 13
The death spiral. An Olympic pair figure- skating routine features an element called the death spiral shown in Figure P5.67. In this routine, the male skater swings his female partner in a circle. If the rotation rate is three-fourths a rotation per second, estimate the tension in the arms that the
Consider a hypothetical extra solar world, planet Tungsten, that has twice the radius of the Earth and twice its density. (a) What is the acceleration due to gravity on the surface of planet Tungsten? (b) An interstellar astronaut lands on the equator of this planet and finds that his
The movie 2001: A Space Odyssey (released in 1968) features a massive rotating space station of radius 100 m, similar to the one in Figure 5.13B.? (a) What period of rotation is needed to provide an artificial gravity of g at the rim?? (b) At what speed is the rim moving?? (c) What is your apparent
An astronaut stands on the surface of Vesta, which, with an average radius of 270 m, makes it the third largest object in the asteroid belt. The astronaut picks up a rock and drops it from a height of 1.5 m. He times the fall and finds that the rock strikes the ground after 3.2 s. (a)
The International Space Station orbits at an average height of 350 km above sea level. (a) Determine the acceleration due to gravity at that height and find the orbital velocity and the period of the space station. (b) The Hubble Space Telescope orbits at 600 km. What is the telescope’s
Oil exploration. When searching for gold, measurements of g can be used to find regions within the Earth where the density is larger than that of normal soil. Such measurements can also be used to find regions in which the density of the Earth is smaller than normal soil; these regions might
A rock of mass m is tied to a string of length L and swung in a horizontal circle of radius r. The string can withstand a maximum tension Tmax before it breaks. (a) What is the maximum speed vmax the rock can have without the string breaking? (b) The speed of the rock is now increased to
Lake Baikal in Siberia is the deepest lake on the Earth, with a maximum depth of 1600 m. Consider the weight of twin brothers with the same mass. One twin is in a rowboat in the middle of Lake Baikal, while his brother is standing on solid ground a few kilometers from the lake. What is the ratio of
Experiments have shown that riders in a car begin to feel uncomfortable while traveling around a turn if their acceleration is greater than about 0.40 × g. Use this fact to calculate the minimum radius of curvature for turns at (a) 10 m/s (appropriate for driving in town) (b) 30 m/s
Consider the coffee centrifuge in Question 20 (Fig. Q5.20). If this cup is moving in a circle with constant speed, what is the approximate minimum speed that will keep the coffee in the cup? Figure Q5.20
Gravitational tractor. In some science fiction stories, a “tractor beam” is used to pull an object from one point in space to another. That may not be just science fiction. It has been proposed that a “gravitational tractor” could be used to “tow” an asteroid. In theory, this tractor
Some communications and television towers are much taller than any buildings. These towers have been used to study how the Earth’s gravitational force varies with distance from the center of the Earth. Calculate the ratio of the acceleration due to the Earth’s gravity at the top of a tower that
Find the ratio of your weight on the Earth to your weight on the surface of the Sun. WEarth W Sun
When a spacecraft travels from the Earth to the Moon, both the Earth and the Moon exert a gravitational force on the spacecraft. Eventually, the spacecraft reaches a point where the Moon’s gravitational attraction overcomes the Earth’s gravity. How far from the Earth must the spacecraft be for
Suppose the bowling balls in Problem 41 are increased in size (radius) by a factor of two, but their density does not change. By what factor does the gravitational force change? Data From Problem 41Estimate the gravitational force between two bowling balls that are nearly touching.
Estimate the gravitational force between two bowling balls that are nearly touching.
Travel and lose pounds! Your apparent weight is the force you feel on the bottoms of your feet when you are standing. Due to the Earth’s rotation, your apparent weight is slightly more when you are at the South Pole than when you are at the equator. What is the ratio of your apparent weights at
Three lead balls of mass m1= 15 kg, m2= 25 kg, and m3= 9.0 kg are arranged as shown in Figure P5.37. Find the total gravitational force exerted by balls 1 and 2 on ball 3. Be sure to give the magnitude and the direction of this force. Figure P5.37 ? y (m) 3 2 -x-(m) loLL1l2131415. 4)
If the masses of the objects in Problem 35 are both increased by a factor of √5, by what factor does the gravitational force change? Do not use a calculator to solve this problem!Data From Problem 35Two small objects of mass 20 kg and 30 kg are a distance 1.5 m apart. What is the gravitational
Two small objects of mass 20 kg and 30 kg are a distance 1.5 m apart. What is the gravitational force of one of these objects on the other?
NASA has built centrifuges to enable astronauts to train in conditions in which the acceleration is very large. The device in Figure P5.34 shows one of these ???human centrifuges.??? If the device has a radius of 8.0 m and attains accelerations as large as 5.0 ?? g, what is the rotation
A centrifuge can be used to separate DNA molecules from solution. Estimate how long it will take the centrifuge in Example 5.6 to separate a DNA molecule from water. Assume the centrifuge tube is 2.0 cm long. For this case, the drag coefficient in Stokes’s law (Eq. 5.14) is C = 0.020 N · s/m2.
We saw in Example 5.6 how a centrifuge can be used to separate cells from a liquid. To increase the rate at which objects can be separated from solution, it is useful to make the centrifuge’s speed as large as possible. If you want to design a centrifuge of diameter 1.5 m to have a force of
A car of mass 1700 kg is traveling without slipping on a flat, curved road with a radius of curvature of 35 m. If the car’s speed is 12 m/s, what is the frictional force between the road and the tires?
A child of mass m - 50 kg sits at the end of a rope of length L = 3.2 m. The other end of the rope is fastened to a ceiling in a gymnasium, and the child travels so that he moves in a horizontal circle of radius r - 2.50 m as sketched in Figure P5.28.? (a) Draw a picture showing the motion of the
Consider the circular space station in Figure 5.13. Suppose the station has a radius of 15 m and is designed to have an acceleration due to “artificial gravity†of g/2. Find the speed of the rim of the space station.Figure 5.13 ác 12
Spin out! An interesting amusement park activity involves a cylindrical room that spins about a vertical axis (Fig. P5.26). Participants in the ???ride??? are in contact with the wall of the room, and the circular motion of the room results in a normal force from the wall on the riders. When the
A coin is sitting on a record as sketched in Figure P5.25. It is found that the coin slips off the record when the rotation rate is 0.30 rev/s. What is the coefficient of static friction between the coin and the record?Figure P5.25 115 cm
A rock is tied to a string and spun in a circle of radius 1.5 m as shown in Figure P5.24. The speed of the rock is 10 m/s.(a) Draw a picture giving both a top view and a side view of the motion of the rock.(b) What are all the forces acting on the rock? Add them to your pictures in part (a). Then
Consider a roller coaster as it travels near the bottom of its track as sketched in Figure P5.23. At this point, the normal force on the roller coaster is three times its weight. If the speed of the roller coaster is 20 m/s, what is the radius of curvature of the track? Figure P5.23 ? た
On a popular amusement park ride, the rider sits in a chair suspended by a cable as shown in Figure P5.22. The top end of the cable is tied to a rotating frame that spins, hence moving the chair in a horizontal circle with r = 10 m. The ride makes one complete revolution every 10 s.? (a) Draw
A car of mass 1000 kg is traveling over the top of a hill as shown in Figure P5.21.? (a) If the hill has a radius of curvature of 40 m and the car is traveling at 15 m/s, what is the normal force between the hill and the car at the top of the hill?? (b) If the driver increases her speed
A coffee centrifuge? In one popular demonstration, a full cup of hot coffee is placed on a platform suspended by strings to the lecturer???s hand as seen in Figure Q5.20. With some practice, the platform, coffee and all, can be made to rotate in a vertical circle. How does the coffee stay in the
A roller-coaster track is designed so that the car travels upside down on a certain portion of the track as shown in Figure P5.20. What is the minimum speed the roller coaster can have without falling from the track? Assume the track has a radius of curvature of 30 m. Figure P5.20 ?
Pluto’s mass. In 1978, it was discovered that Pluto had a moon of its own. The moon was given the name Charon (now known to be one of three; see Fig. Q5.19). After the discovery of this moon,Figure Q5.19the hitherto unknown mass of Pluto was calculated to a precision of less than 1%. How did
The track near the top of your favorite roller coaster has a circular shape with a diameter of 20 m. When you are at the top, as in Figure 5.11, you feel as if your weight is only one-third your true weight. What is the speed of the roller coaster? Figure 5.11 ? y N. mg Circular path
An astronaut on the peak of a mountain on the Moon fires a rifle along the horizontal direction. Is it possible, given a sufficient initial speed for the bullet, that the bullet might hit her in the back? Explain how it could happen.
A stone of mass 0.30 kg is tied to a string of length 0.75 m and is swung in a horizontal circle with speed v. The string has a breaking-point force of 50 N. What is the largest value v can have without the string breaking? Ignore any effects due to gravity.
The difference in the gravitational force is only about 10% less on an object that is in a low Earth orbit than it is for the same object on the ground. Why is it that an astronaut in orbit experiences weightlessness?
Consider the motion of the rock in Figure P5.16. What is the minimum speed the rock can have without the string becoming ???slack???? Figure P5.16 ? т %3D 1.5 kg m r = 0.50 m
The Sun exerts an overall force on the Earth many times greater than that of the Moon. How can it then be that the ocean tides are primarily due to the influence of the Moon and, to a much lesser extent, the Sun?
How does your weight on a ship in the middle of the ocean compare with your weight when you are standing on solid ground? Explain why they are not the same.
Consider again the problem of a car traveling along a banked turn. Sometimes roads have a “reversed” banking angle. That is, the road is tilted “away” from the center of curvature of the road. If the coefficient of static friction between the tires and the road is mS = 0.50, the radius of
You are a prospector looking for gold by taking high-precision measurements of the acceleration due to gravity, g, at different points on the Earth’s surface. In one region, you find that g is slightly higher than its average value. Are you standing over what might be a deposit of gold or over an
The Daytona 500 stock car race is held on a track that is approximately 2.5 mi long, and the turns are banked at an angle of 31°. It is currently possible for cars to travel through the turns at a speed of about 180 mi/h. Assuming these cars are on the verge of slipping into the outer wall of the
NASA uses a specially equipped airplane (called the “Vomit Comet”) to provide a simulated zero-gravity environment for training and experiments. This airplane flies in a long, parabolic path. Explain how a passenger can feel “weightless” near the top of the parabola.
At a practice for a recent automobile race, officials found that the drivers were nearly “blacking out,” which led to cancellation of the race. The cars were traveling at about 240 mi/h, and the track was approximately 1.5 mi long. Find the centripetal acceleration during a turn and compare it
When a planet orbits around a star, the star also moves in an “orbit.” Since it is much more massive than the planet, the star’s orbital radius rstar is much smaller than that of the planet rplanet. Work out how the ratio rstar /rplanet depends on the ratio of the masses. Discuss how this
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