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physics
mechanics
Questions and Answers of
Mechanics
Find the acceleration due to gravity on the surface of(a) Mercury(b) Venus.
At what altitude above the Earth's surface is the acceleration due to gravity equal to g/4?
Two 6.4-kg bowling balls, each with a radius of 0.11 m, are in contact with one another. What is the gravitational attraction between the bowling balls?
What is the acceleration due to Earth's gravity at a distance from the center of the Earth equal to the orbital radius of the Moon?
Kepler-62e is an exoplanet that orbits within the habitable zone around its parent star. The planet has a mass that is 3.57 times larger than Earth's and a radius that is 1.61 times larger than
At a certain distance from the center of the Earth, a 5.0-kg object has a weight of 3.6 N.(a) Find this distance.(b) If the object is released at this location and allowed to fall toward the Earth,
The acceleration due to gravity on the Moon's surface is known to be about one-sixth the acceleration due to gravity on the Earth. Given that the radius of the Moon is roughly one-quarter that of the
A 6.3-kg bowling ball and a 7.1-kg bowling ball rest on a rack 0.85 m apart. (a) What is the force of gravity exerted on each of the balls by the other ball? (b) At what separation is the force of
At some point along the direct path from the center of the Earth to the center of the Moon, the gravitational force of attraction on a spacecraft from the Moon becomes greater than the force from the
Several volcanoes have been observed erupting on the surface of Jupiter's closest Galilean moon, Io. Suppose that material ejected from one of these volcanoes reaches a height of 5.00 km after being
Consider an asteroid with a radius of 19 km and a mass of 3.35 × 1015 kg. Assume the asteroid is roughly spherical.(a) What is the acceleration due to gravity on the surface of the asteroid?(b)
A satellite orbits the Earth in a circular orbit of radius r. At some point its rocket engine is fired so that its speed increases rapidly by a small amount. As a result, do the(a) Apogee distance
Laser reflectors left on the surface of the Moon by the Apollo astronauts show that the average distance from the Earth to the Moon is increasing at the rate of 3.8 cm per year.(a) As a result, will
On Apollo missions to the Moon, the command module orbited at an altitude of 110 km above the lunar surface. How much time did it take for the command module to complete one orbit?
Find the orbital speed of a satellite in a geosynchronous circular orbit 3.58 × 107 m above the surface of the Earth.
In July of 1999 a planet was reported to be orbiting the Sun-like star Iota Horologii with a period of 320 days. Find the radius of the planet's orbit, assuming that Iota Horologii has the same mass
Phobos, one of the moons of Mars, orbits at a distance of 9378 km from the center of the red planet. What is the orbital period of Phobos?
The asteroid 243 Ida has its own small moon, Dactyl. (See the photo on p. 394.) Another such system, asteroid 624 Hektor, has a mass of 7.9 × 1018 kg, with its moon orbiting at a radius of 623.5 km
A communications satellite with a mass of 520 kg is in a circular orbit about the Earth. The radius of the orbit is 35,000 km as measured from the center of the Earth. Calculate(a) The weight of the
GPS (Global Positioning System) satellites orbit at an altitude of 2.0 × 107 m. Find(a) The orbital period,(b) The orbital speed of such a satellite.
Two satellites orbit the Earth, with satellite 1 at a higher altitude than satellite 2.(a) Which satellite has the greater orbital speed? Explain.(b) Calculate the orbital speed of a satellite that
Satellite A has a mass of 1000 kg and satellite B has a mass of 2000 kg.(a) When each satellite orbits at one Earth radius above the surface of the Earth, will the period of satellite B be longer,
The Martian moon Deimos has an orbital period that is greater than the other Martian moon, Phobos. Both moons have approximately circular orbits.(a) Is Deimos closer to or farther from Mars than
(a) Calculate the orbital period of a satellite that orbits at two Earth radii above the surface of the Earth.(b) If the Earth suddenly became more massive while the satellite remains in circular
Alpha Centauri A and Alpha Centauri B are binary stars with a separation of 3.45 × 1012 m and an orbital period of 2.52 × 109 s. Assuming the two stars are equally massive (which is approximately
The first artificial satellite to orbit the Earth was Sputnik I, launched October 4, 1957. The mass of Sputnik I was 83.5 kg, and its distances from the center of the Earth at apogee and perigee were
How much gravitational potential energy is required to lift a 9380-kg Progress spacecraft to the altitude of the International Space Station, 422 km above the surface of the Earth?
(a) Is the amount of energy required to get a spacecraft from the Earth to the Moon greater than, less than, or equal to the energy required to get the same spacecraft from the Moon to the Earth?(b)
Consider the four masses shown in Figure 12-35.(a) Find the total gravitational potential energy of this system.(b) How does your answer to part (a) change if all the masses in the system are
Ceres, the largest asteroid known, has a mass of roughly 8.7 × 1020 kg. If Ceres passes within 14,000 km of the spaceship in which you are traveling, what force does it exert on you? (Use an
Calculate the gravitational potential energy of a 9.50-kg mass(a) On the surface of the Earth(b) At an altitude of 325 km.(c) Take the difference between the results for parts (b) and (a), and
Three bowling balls form an equilateral triangle, as shown in FIGURE 12-36. Each ball has a radius of 10.8 cm and a mass of 7.26 kg. What is the total gravitational potential energy of this system?
Two 0.59-kg basketballs, each with a radius of 12 cm, are just touching. How much energy is required to change the separation between the centers of the basketballs to(a) 1.0 m(b) 10.0 m?
Find the minimum kinetic energy needed for a 32,000-kg rocket to escape(a) The Moon(b) The Earth.
Suppose the Earth were to suddenly shrink to half its current diameter, with its mass remaining constant. (a) Would the escape speed of the Earth increase, decrease, or stay the same? (b) Choose the
Is the energy required to launch a rocket vertically to a height h greater than, less than, or equal to the energy required to put the same rocket into orbit at the height h? Explain.
Suppose one of the Global Positioning System satellites has a speed of 4.46 km/s at perigee and a speed of 3.64 km/s at apogee. If the distance from the center of the Earth to the satellite at
Several meteorites found in Antarctica are believed to have come from Mars, including the famous ALH84001 meteorite that was once thought to contain fossils of ancient life on Mars. Meteorites from
What is the launch speed of a projectile that rises vertically above the Earth to an altitude equal to one Earth radius before coming to rest momentarily?
A projectile launched vertically from the surface of the Moon rises to an altitude of 425 km. What was the projectile's initial speed?
In one hand you hold a 0.13-kg apple, in the other hand a 0.22-kg orange. The apple and orange are separated by 0.75 m. What is the magnitude of the force of gravity that(a) The orange exerts on the
(a) How much gravitational potential energy must a 3130-kg satellite acquire in order to attain a geosynchronous orbit?(b) How much kinetic energy must it gain? Note that because of the rotation of
Halley's Comet, which passes around the Sun every 76 years, has an elliptical orbit. When closest to the Sun (perihelion) it is at a distance of 8.823 × 1010 m and moves with a speed of 54.6 km/s.
On Apollo Moon missions, the lunar module would blast off from the Moon's surface and dock with the command module in lunar orbit. After docking, the lunar module would be jettisoned and allowed to
If a projectile is launched vertically from the Earth with a speed equal to the escape speed, how high above the Earth's surface is it when its speed is one-third the escape speed?
Suppose a planet is discovered orbiting a distant star. If the mass of the planet is 10 times the mass of the Earth, and its radius is one tenth the Earth's radius, how does the escape speed of this
A projectile is launched vertically from the surface of the Moon with an initial speed of 1010 m/s. At what altitude is the projectile's speed one-half its initial value?
To what radius would the Sun have to be contracted for its escape speed to equal the speed of light?
Two baseballs, each with a mass of 0.148 kg, are separated by a distance of 395 m in outer space, far from any other objects.(a) If the balls are released from rest, what speed do they have when
On Earth, a person can jump vertically and rise to a height h. What is the radius of the largest spherical asteroid from which this person could escape by jumping straight upward? Assume that each
The magnitude of the tidal force exerted on a linear object of mass m and length L is approximately 2GmML/r3. In this expression, M is the mass of the body causing the tidal force and r is the
A spaceship of mass m travels from the Earth to the Moon along a line that passes through the center of the Earth and the center of the Moon.(a) At what distance from the center of the Earth is the
The magnitude of the tidal force between the International Space Station (ISS) and a nearby astronaut on a spacewalk is approximately 2GmMa/r3. In this expression, M is the mass of the Earth, r =
A dumbbell has a mass m on either end of a rod of length 2a. The center of the dumbbell is a distance r from the center of the Earth, and the dumbbell is aligned radially. If >> a, show that
Referring to the previous problem, suppose the rod connecting the two masses m is removed. In this case, the only force between the two masses is their mutual gravitational attraction. In addition,
You weigh yourself on a scale inside an airplane flying due east above the equator. If the airplane now turns around and heads due west with the same speed, will the reading on the scale increase,
Rank objects A, B, and C in FIGURE 12-37 in order of increasing net gravitational force experienced by the object. Indicate ties where appropriate.
Referring to Figure 12-37, rank objects A, B, and C in order of increasing initial acceleration each would experience if it alone were allowed to move. Indicate ties where appropriate.
Skylab, the largest spacecraft ever to fall back to the Earth, met its fiery end on July 11, 1979, after flying directly over Everett, WA, on its last orbit. On the CBS Evening News the night before
Consider a system consisting of three masses on the x axis. Mass m1 = 1.00 kg is at x = 1.00 m; mass m2 = 2.00 kg is at x = 2.00 m; and mass m3 = 3.00 kg is at x = 3.00 m. What is the total
An astronaut exploring a distant solar system lands on an unnamed planet with a radius of 3520 km. When the astronaut jumps upward with an initial speed of 2.91 m/s, she rises to a height of 0.525 m.
When the Moon is in its third-quarter phase, the Earth, Moon, and Sun form a right triangle, as shown in Figure 12-34. Calculate the magnitude of the force exerted on the Moon by(a) The Earth(b) The
At new moon, the Earth, Moon, and Sun are in a line, as indicated in FIGURE 12-33. Find the direction and magnitude of the net gravitational force exerted on(a) The Earth,(b) The Moon, and(c) The
An equilateral triangle 10.0 m on a side has a 1.00-kg mass at one corner, a 2.00-kg mass at another corner, and a 3.00-kg mass at the third corner (FIGURE 12-38). Find the magnitude and direction of
Suppose that each of the three masses in Figure 12-38 is replaced by a mass of 5.95 kg and radius 0.0714 m. If the masses are released from rest, what speed will they have when they collide at the
In the early morning hours of June 14, 2002, the Earth had a remarkably close encounter with an asteroid the size of a small city. The previously unknown asteroid, now designated 2002 MN, remained
Suppose a planet is discovered that has the same total mass as the Earth, but half its radius.(a) Is the acceleration due to gravity on this planet more than, less than, or the same as the
Show that the speed of a satellite in a circular orbit a height h above the surface of the Earth is
A spherical asteroid of average density would have a mass of 8.7 × 1013 kg if its radius were 2.0 km.(a) If you and your spacesuit had a mass of 125 kg, how much would you weigh when standing on the
In a binary star system, two stars orbit about their common center of mass, as shown in FIGURE 12-39. If r2 = 2r1, what is the ratio of the masses m2/m1 of the two stars?
Find the orbital period of the binary star system described in the previous problem.
In the not-too-distant future astronauts will travel to Mars to carry out scientific explorations. As part of their mission, it is likely that a "geosynchronous" satellite will be placed above a
In 2004, a NASA spacecraft named Stardust flew within 147 miles of Comet Wild 2 (pronounced "Vilt 2"), zooming by it at 6200 m/s, about six times the speed of a rifle bullet. Photos taken by Stardust
When the Earth, Moon, and Sun form a right triangle, with the Moon located at the right angle, as shown in FIGURE 12-34, the Moon is in its third-quarter phase. (The Earth is viewed here from above
(a) If you want to launch a probe that orbits the Sun with a period of 2.00 years, what should be its orbital radius? Give your answer in astronomical units. The astronomical unit AU is defined as
A satellite is placed in Earth orbit at an altitude of 23,300 mi, which is 1100 miles higher than the altitude of a geosynchronous satellite.(a) Is the period of this satellite greater than or less
Show that the force of gravity between the Moon and the Sun is always greater than the force of gravity between the Moon and the Earth.
The astronomical unit AU is defined as the mean distance from the Sun to the Earth (1 AU = 1.50 × 1011 m). Apply Kepler's third law (Equation 12-7) to the solar system, and show that it can be
(a) Find the kinetic energy of a 1940-kg satellite in a circular orbit about the Earth, given that the radius of the orbit is 12,600 miles.(b) How much energy is required to move this satellite to a
The International Space Station (m = 4.5 × 105 kg) orbits at an altitude of 415 km above the Earth's surface.(a) Does the orbital speed of the station depend on its mass? Explain.(b) Find the speed
A Russian Soyuz module, with three astronauts and a full load of cargo, has a mass of 7500 kg. The International Space Station (ISS) has a mass of 420,000 kg. When Soyuz docks at the ISS, the two
Consider an object of mass m orbiting the Earth at a radius r.(a) Find the speed of the object.(b) Show that the total mechanical energy of this object is equal to (-1) times its kinetic energy.(c)
The Earth's orbit around the Sun is slightly elliptical (see Conceptual Example 12-7). At Earth's closest approach to the Sun (perihelion) the orbital radius is 1.471 × 1011 m, and at its farthest
Three identical stars, at the vertices of an equilateral triangle, orbit about their common center of mass (FIGURE 12-41). Find the period of this orbital motion in terms of the orbital radius, R,
Repeat the previous problem, this time finding the magnitude and direction of the net force acting on the Sun. Give the direction relative to the line connecting the Sun and the Moon.When the Earth,
Find an expression for the kinetic energy of a satellite of mass m in an orbit of radius r about a planet of mass M.
What is the minimum kinetic energy an impact must give to a 3.0-m-diameter rock for the rock to be able to escape from the Earth?A. 5.3 × 103 JB. 1.3 × 106 JC. 2.7 × 1012 JD. 2.1 ×
What is the speed a rock needs to be given at the surface of the Earth in order for it to have a residual speed of 2.5 km/s?A. 8.7 km/sB. 10.9 km/sC. 11.5 km/sD. 13.7 km/s
Would increasing the ejection speed from 12 km/s to 13 km/s change the residual speed by more than, less than, or the same amount as increasing the ejection speed from 15 km/s to 16 km/s?
Consider a similar plot for rocks ejected from Mars. Where would this plot intercept the x axis?A. The plot for Mars would intercept the x axis at 5.0 km/s.B. The plot for Mars would intercept the x
Find the orbital radius that corresponds to a "year" of 150 days.
Suppose the mass of the Sun is suddenly doubled, but the Earth's orbital radius remains the same.(a) Would the length of an Earth year increase, decrease, or stay the same?(b) Find the length of a
(a) If the mass of the Earth were doubled, would the escape speed of a rocket increase, decrease, or stay the same?(b) Calculate the escape speed of a rocket for the case of an Earth with twice its
Suppose the Earth is suddenly shrunk to half its present radius without losing any of its mass.(a) Would the escape speed of a rocket increase, decrease, or stay the same?(b) Find the escape speed
A person rides on a Ferris wheel that rotates with constant angular speed. If the Sun is directly overhead, does the person's shadow on the ground undergo periodic motion? Does it undergo simple
If a mass m and a mass 2m oscillate on identical springs with identical amplitudes, they both have the same maximum kinetic energy. How can this be? Shouldn't the larger mass have more kinetic
The position of an object undergoing simple harmonic motion is given by x = A cos(Bt). Explain the physical significance of the constants A and B. What is the frequency of this object's motion?
A person in a rocking chair completes 12 cycles in 21 s. What are the period and frequency of the rocking?
The position of a mass oscillating on a spring is given by x = (3.9 cm) cos[2πt/(0.38 s)].(a) What is the period of this motion?(b) What is the first time the mass is at the position x = 0?
The position of a mass oscillating on a spring is given by x = (7.8 cm) cos[2πt/(0.68 s)].(a) What is the frequency of this motion?(b) When is the mass first at the position x = -7.8 cm?
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