Modern Physics
Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 9, Problem 2P
To determine

To prove that the area swept by a orbiting particle is dAdt=|L|2m.

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The inertial mass of a particle is, by definition, the mass that appears in Newton's second law. Consider free fall of a particle with gravitational mass mº and inertial mass m' near the surface of a homogeneous planet having gravitational mass MC and radius R. Express the gravitational acceleration a of the particle in terms of these quantities. (Neglect any frictional forces.)
Consider a thought experiment performed in free space. In the experiment, a small cube C of mass m is placed at the centre of a large and highly massive disc D and a ball B of mass M revolves in circular path of radius R around the centre of the disc. The plane of the circle is perpendicular to the plane of the dise as shown in the figure. Intensity of the gravitational field of the disc near its centre is g. What should be range of coefficient of friction between the cube and the disc so that the cube remains motionless?
(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 5.78 × 10* m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) 38107.8 m/s (b) What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 × 10“ m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 x 104 m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar system (in m/s)? (Assume that the Earth and the point on Jupiter's orbit lie along the…
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