University Physics Volume 1 18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: William Moebs, Samuel J. Ling, Jeff Sanny
1 Units And Measurement 2 Vectors 3 Motion Along A Straight Line 4 Motion In Two And Three Dimensions 5 Newton's Law Of Motion 6 Applications Of Newton's Laws 7 Work And Kinetic Energy 8 Potential Energy And Conservation Of Energy 9 Linear Momentum And Collisions 10 Fixed-axis Rotation 11 Angular Momentum 12 Static Equilibrium And Elasticity 13 Gravitation 14 Fluid Mechanics 15 Oscillations 16 Waves 17 Sound Chapter13: Gravitation
Chapter Questions Section: Chapter Questions
Problem 13.1CYU: Check Your Understanding What happens to force and accleration as the vehicles fall together? What... Problem 13.2CYU: Check Your Understanding How does your weight at the top of a tall building compare with that on the... Problem 13.3CYU: Check Your Understanding Why not use the simpler expression U=mg(y2y1) ? How significant would the... Problem 13.4CYU: Check Your Understanding If we send a probe out of the solar system starting form Earth’s surface,... Problem 13.5CYU: Check Your Understanding Assume you are in a spacecraft in orbit about the Sun at Earth’s orbit, but... Problem 13.6CYU: Check Your Understanding By what factor must the radius change to reduce the orbital velocity of a... Problem 13.7CYU: Check Your Understanding There is another consideration to this last calculation of ME. We derived... Problem 13.8CYU: Check Your Understanding Galaxies are not single objects. How does the gravitiational force of one... Problem 13.9CYU: Check Your Understanding The nearly circular orbit of Saturn has an average radius of about 9.5 AU... Problem 13.10CYU: Check Your Understanding Earth exerts a tidal force on the Moon. Is it greater than, the same as, or... Problem 13.11CYU: Check Your Understanding Consider the density required to make Earth a black hole compared to that... Problem 1CQ: Action at a distance, such as is the case for gravity, was once thought to be illogical and... Problem 2CQ: In the law of universal gravitation, Newton assumed that the force was proportional to the product... Problem 3CQ: Must engineers take Earth’s rotation into account when constructing very tall buildings at any... Problem 4CQ: It was stated that a satellite with negative total energy is in a bound orbit, whereas one with zero... Problem 5CQ: It was shown that the energy required to lift a satellite into a low Earth orbit (the change in... Problem 6CQ: One student argues that a satellite in orbit is in free fall because the satellite keeps falling... Problem 7CQ: Many satellites are placed in geosynchronous orbits. What is special about these orbits? For a... Problem 8CQ: Are Kepler’s laws purely descriptive, or do they contain causal information? Problem 9CQ: In the diagram below for a satellite in an elliptical orbit about a much larger mass, indicate where... Problem 10CQ: As an object falls into a black hole, tidal forces increase. Will these tidal forces always tear the... Problem 11CQ: The principle of equivalence states that all experiments done in a lab in a uniform gravitational... Problem 12CQ: As a person approaches the Schwarzschild radius fo a black hole, outside observers see all the... Problem 13P: Evaluate the magnitude of gravitational force between two 5-kg spherical steel balls separated by a... Problem 14P: Estimate the gravitational force between two sumo wrestlers, with masses 220 kg and 240 kg, when... Problem 15P: Astrology makes much of the position of the planets at the moment of one’s birth. The only known... Problem 16P: A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00 of his weight.... Problem 17P: The International Space Station has a mass of approximately 370,000 kg. (a) What is the force on a... Problem 18P: Asteroid Toutatis passed near Earth in 2006 at four times the distance to our Moon. This was the... Problem 19P: (a) What was the acceleration of Earth caused by asteroid Toutatis (see previous problem) at its... Problem 20P: (a) Calculate Earth’s mass given the acceleratioln due to gravity at the North Pole is measured to... Problem 21P: (a) What is the acceleration due to gravity on the surface of the Moon? (b) On the surface of Mars?... Problem 22P: (a) Calculate the acceleration due to gravity on the surface of the Sun. (b) By what factor would... Problem 23P: The mass of a particle is 15 kg. (a) What is its weight on Earth? (b) What is its weight on the... Problem 24P: On a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass... Problem 25P: The mean diameter of the planet Saturn is 1.2108m , and its mean mass density is 0.69g/cm3 . Find... Problem 26P: The mean diameter of the planet Mercury is 4.88106m , and the acceleration due to gravity at its... Problem 27P: The acceleration due to gravity on the surface of a planet is three times as large as it is on the... Problem 28P: A body on the surface of a planet with the same radius as Earth’s weighs 10 times more than it does... Problem 29P: Find the escape speed of a projectile from the surface of Mars. Problem 30P: Find the escape speed of a projectile from the surface of Jupiter. Problem 31P: What is the escape speed of a satellite located at the Moon’s orbit about Earth? Assume the Moon is... Problem 32P: (a) Evaluate the gravitational potential energy between two 5.00-kg spherical steel balls separated... Problem 33P: An average-sized asteroid located 5.0107km from Earth with mass 2.01013kg is detected headed... Problem 34P: (a) What will be the kinetic energy of the asteroid in the previous problem just before it hits... Problem 35P: (a) What is the change in energy of a 1000-kg payload taken from rest at the surface of Earth and... Problem 36P: If a planet with 1.5 times the mass of Earth was traveling in Earth’s orbit, what would its period... Problem 37P: Two planets in circular orbits around a star have speed of v and 2v . (a) What is the ratio of the... Problem 38P: Using the average distance of Earth from the Sun, and the orbital peirod of Earth, (a) find the... Problem 39P: What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable... Problem 40P: Calculate the mass of the Sun based on data for Earth’s orbit and compare the value obtained with... Problem 41P: Find the mass of Jupiter based on the fact that I0 , its innermost moon, has an average orbital... Problem 42P: Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011... Problem 43P: (a) In order to keep a small satellite from drifting into a nearby asteroid, it is placed in orbit... Problem 44P: The Moon and Earth rotate about their common center of mass, which is located about 4700 km from the... Problem 45P: The Sun orbits the Milky Way galaxy once each 2.60108 years, with a roughly circular orbit averaging... Problem 46P: A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits... Problem 47P: Calculate the mass of the Sun based on data for average Earth’s orbit and compare the value obtained... Problem 48P: I0 orbits Jupiter with an average radius of 421,700 km and a period of 1.769 days. Based upon these... Problem 49P: The “mean” orbital radius listed for astronomical objects orbiting the Sun is typically not an... Problem 50P: The perihelion of Halley’s comet is 0.586 AU and the aphelion is 17.8 AU. Given that its speed at... Problem 51P: The perihelion of the comet Legerkvist is 2.61 AU and it has a period of 7.36 years. Show that the... Problem 52P: What is the ratio of the speed at perihelion to that at aphelion for the comet Lagerkvist in the... Problem 53P: Eros has an elliptical orbit about the Sun, with a perihelion distance of 1.13 AU and aphelion... Problem 54P: What is the difference between the force on a 1.0-kg mass on the near side of I0 has mean radius of... Problem 55P: If the Sun were to collapse into a black hole, the point of no return for an investigator would be... Problem 56P: Consider Figure 13.23 in Tidal Forces. This diagram represents the tidal forces for spring tides.... Problem 57P: What is the Schwarzschild radius for the black hole at the center of our galaxy if it has the mass... Problem 58P: What would be the Schwarzschild radius, in light years, if our Milky Way galaxy of 100 billion stars... Problem 59AP: A neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass... Problem 60AP: (a) How far from the center of Earth would the net gravitational force of Earth and the Moon on an... Problem 61AP: How far from the center of the Sun would the net gravitational force of Earth and the Sun on a... Problem 62AP: Calculate the values of g at Earth’s surface for the following changes in Earth’s properties: (a)... Problem 63AP: Suppose you can communicate with the inhabitants of a planet in another solar system. They tell you... Problem 64AP: (a) Suppose that your measured weight at the equator is one-half your measured weight at the pole on... Problem 65AP: A body of mass 100 kg is weighed at the North Pole and at the equator with a spring scale. What is... Problem 66AP: Find the speed needed to escape from the solar system starting from the surface of Earth. Assume... Problem 67AP: Consider the previous problem and include the fact that Earth has an orbital speed about the Sun of... Problem 68AP: A comet is observed 1.50 AU from the Sun with a speed of 24.3km/s . Is this comet in a bound or... Problem 69AP: An asteroid has speed 15.5km/s when it is located 2.00 AU from the sun. At its closest approach, it... Problem 70AP: Space debris left from old satellites and their launchers is becoming a hazard to other satellites.... Problem 71AP: A satellite of mass 1000 kg is in circular orbit about Earth. The radius of the orbit of the... Problem 72AP: After Cares was promoted to a dwarf planet, we now recognize the largest known asteroid to be Vesta,... Problem 73AP: (a) Using the data in the previous problem for the asteroid Vesta which has a diameter of 520 km and... Problem 74AP: What is the orbital velocity of our solar system about the center of the Milky Way? Assume that the... Problem 75AP: (a) Using the information in the previous problem, what velocity do you need to escape the Milky Way... Problem 76AP: Circular orbits in Equation 13.10 for conic sections must have eccentricity zero. From this, and... Problem 77AP: Show that for eccentricity equal to one in Equation 13.10 for conic sections, the path is a... Problem 78AP: Using the technique shown in Satellite Orbits and Energy, show that two masses m1 and m2 in circular... Problem 79AP: Given the perihelion distance, p , and aphelion distance, q , for an elliptical orbit, show that the... Problem 80AP: Comet P/1999 R1 has a perihelion of 0.0570 AU and aphelion of 4.99 AU. Using the results of the... Problem 81CP: A tunnel is dug through the center of a perfectly spherical and airless planet fo radius R. Using... Problem 82CP: Following the technique used in Gravitation Near Earth’s Surface, find the value of g as a function... Problem 83CP: Show that the areal velocity for a circular orbit of radius r about a mass M is At=12GMr . Does your... Problem 84CP: Show that the period of orbit for two masses, m1 and m2 , in circular orbits of radii r1 and r2 ,... Problem 85CP: Show that for small changes in height h, such that hRE , Equation 13.4 reduces to the expression... Problem 86CP: Using Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at... Problem 87CP: (a) Show that tidal force on a small object of mass m, defined as the difference in the... Problem 88CP: Find the Hohmann transfer velocities, vEllipseEarth and vEllipseMars ,needed for a trip to Mars. Use... Problem 76AP: Circular orbits in Equation 13.10 for conic sections must have eccentricity zero. From this, and...
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Concept explainers
A 3 kg rock tied to the end of a 1m long string is swung in a circle with θ0 = 0o , ω0 = +π rad/s, α = 1 rad/s2 (ignore gravity); after it’s swung around for 3 seconds derive the following:
a) Angular location:
b) Angular velocity :
c) Tangential velocity:
d) Centripetal Force :
Definition Definition Force on a body along the radial direction. Centripetal force is responsible for the circular motion of a body. The magnitude of centripetal force is given by F C = m v 2 r m = mass of the body in the circular motion v = tangential velocity of the body r = radius of the circular path
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