Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Let G denote the universal gravitational constant and let M and m denote masses a distance r apart. (a) According to Newton’s Law of Universal Gravitation, M and m attract each other with a force of magnitude _____ . (b) If r is the radius vector from M to m, then the force of attraction that mass M exerts on mass m is ______ .
A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ? = 2.67 × 106 g/m3 and volume V =1.71 × 1012 m3. Recall that the universal gravitational constant is G = 6.67 × 10-11 (Nm2)/(kg2).
One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M= 4.1 * 1024 kg and R = 6.0 *106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?
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- a square of edge length 20.0 cm is formed by four spheres of masses m1 = 5.00 g, m2 = 3.00 g, m3 = 1.00 g, and m4 = 5.00 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.50 g?arrow_forwardA uniform solid sphere of radius R produces a gravitational acceleration of ag on its surface. At what distance from the sphere’s center are there points (a) inside and (b) outside the sphere where the gravitational acceleration is ag/3?arrow_forwardCalculate the gravitational potential V for a hemisphere of radius R with uniform mass distribution.arrow_forward
- The inverse square law of gravitational attraction between two masses m1 and m2 is given by F = −Gm m r / || r ||3 , where r = x i + y j + z k . Show that F is conservative. Find a potential function for F.arrow_forwardConsider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?arrow_forwardFour uniform spheres, with masses mA= 40 kg,mB = 35 kg, mC = 200 kg, and mD= 50 kg, have (x, y) coordinates of (0, 50 cm),(0, 0), (-80 cm, 0), and (40 cm, 0), respectively. In unit-vector notation,what is the net gravitational force on sphere B due to theother spheres?arrow_forward
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