Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 6, Problem 2Q
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Consider the following pairs of objects with varying masses and separation distances. Which of these pairs has the largest gravitational potential energy?
(a) 1 (b) 2 (c) 3 (d) 4
(a) Evaluate the gravitational potential energy between two 5.00-kg spherical steel balls separated by a center-to-center distance of 15.0 cm. (b) Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast will they be traveling upon impact. Each sphere has a radius of 5.10 cm.
An object of mass m is launched from a planet of mass M and radius R.
a)Derive and enter an expression for the minimum launch speed needed for the object to escape gravity, i.e. to be able to just reach r = ∞.
b)Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M = 6 × 1023 kg and R = 76 × 104 km.
Chapter 6 Solutions
Physics Fundamentals
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- A system consists of five particles. How many terms appear in the expression for the total gravitational potential energy of the system? (a) 4 (b) 5 (c) 10 (d) 20 (e) 25arrow_forwardA planet has two moons with identical mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. The magnitude of the gravitational force exerted by the planet on Moon 2 is (a) four times as large (b) twice as large (c) the same (d) half as large (e) one-fourth as large as the gravitational force exerted by the planet on Moon 1.arrow_forwardSuppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forward
- A planet has two moons with identical mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. The magnitude of the gravitational force exerted by the planet on Moon 2 is (a) four times as large (b) twice as large (c) the same (d) half as large (e) one-fourth as large as the gravitational force exerted by the planet on Moon 1.arrow_forwardTwo objects, with masses m 1 and m 2 , are originally a distance r apart. The gravitational force between them has a magnitude F. The second object has its mass changed to 2m, and the distance is changed to r / 4 . what is the new speed?arrow_forwardTwo masses m, = 100 kg and m, = 8100 kg are held 1 m apart. (a) At what point on the line joining them is the gravitational field equal to zero? Find the gravi- tational potential at that point. (b) Find the gravitational potential energy of the system. Given G = 6.67 × 10-" Nm? kg.arrow_forward
- (a) Evaluate the gravitational potential energy (in J) between two 6.00 kg spherical steel balls separated by a center-to-center distance of 19.0 cm. (b) Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast (in m/s) will they each be traveling upon impact. Each sphere has a radius of 5.20 cm. m/sarrow_forwardQuestion 4 of 7 GMm where If the gravitational force between two objects of mass M and m, separated by a distancer, has magnitude G = 6.67 × 10-1" m°kg¬'s¯², then the work required to increase the separation from a distance r¡ to a distance r2 is GMm(r,' – r,'). Compute the work required to move a 1500-kg satellite from an orbit 1000 km above the surface of Earth to an orbit 1500 km above the surface of Earth. Assume that Earth is a sphere of radius R = 6.37 × 10° m and mass M. = 5.98 × 1024 kg. Treat the satellite as a point mass. (Write your answer in scientific notation with two decimal places.) 1.47 x107 J W = Incorrect Question Source: Rogawski 4e Calculus Early Transcendentals| Publisher: W.H. Fm 014 étv hulu MacBook PrOarrow_forwardGravitational attraction force between two objects with masses m1 and m2, separated bydistance x, is F= G((m1m2)/x2))where G = 6.67 × 10−11 is constant.Suppose a 1.5 × 1013 [kg] comet is passing the orbit of Mars (x= 2.28 × 1011[m] )heading straight for the Sun (m= 2 × 1030[kg]) at a speed v = 3.5 × 104[m/s]. Whatwill its speed be when it crosses the orbit of Mercury (x = 5.79 × 109[m] ) ?[Hint: How much work is done by gravity when the separation changes from x1 to x2 ?]arrow_forward
- A particle of mass 3m is located 1.00 m from a particle of mass m. Where should you put a third mass M so that the net gravitational force on M due to the two masses is exactly zero?arrow_forwardTwo 0.56-kg basketballs, each with a radius of 15 cm , are just touching. How much energy is required to change the separation between the centers of the basketballs to 1.4 m ? (Ignore any other gravitational interactions.) How much energy is required to change the separation between the centers of the basketballs to 14 m ? (Ignore any other gravitational interactions.)arrow_forwardThe escape velocity from a massive object is the speed needed to reach an infinite distance from it and have just slowed to a stop, that is, to have just enough kinetic energy to climb out of the gravitational potential well and have none left. You can find the escape velocity by equating the total kinetic and gravitational potential energy to zero E = = muesc - GmM/r=0 Vesc = √2GM/r where G is Newton's constant of gravitation, M is the mass of the object from which the escape is happening, and r is its radius. This is physics you have seen in the first part of the course, and you should be able to use it to find an escape velocity from any planet or satellite. For the Earth, for example the escape velocity is about 11.2 km/s, and for the Moon it is 2.38 km/s. A very important point about escape velocity: it does not depend on what is escaping. A spaceship or a molecule must have this velocity or more away from the center of the planet to be free of its gravity, 1. In the atmosphere of…arrow_forward
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