**6. Newton’s Law of Gravitation**Newton’s Law of Gravitation states that the magnitude \( F \) of the force exerted by a body of mass \( m \) on a body of mass \( M \) is \[F = \frac{{GmM}}{{r^2}}\]where \( G \) is the gravitational constant and \( r \) is the distance between the bodies.**(a)** Find \( \frac{{dF}}{{dr}} \) and explain its meaning. What does the minus sign indicate?**(b)** Suppose it is known that the Earth attracts an object with a force that decreases at a rate of 1 N/km when \( r = 15,000 \) km. How fast does this force change when \( r = 5,000 \) km?

Newton's Law of Gravitation states that the magnitude of the force exerted by a body of mass on a…

6. Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a GmM body of mass M is F = - where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/ dr and explain its mean. What does the minus sign indicate? (b) Suppose it is known that the earth attracts an object with a force that decreases at a rate of 1N/km when r =15,000 km. How fast does this force change when r= 5,000 km?

6. Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a GmM body of mass M is F = - where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/ dr and explain its mean. What does the minus sign indicate? (b) Suppose it is known that the earth attracts an object with a force that decreases at a rate of 1N/km when r =15,000 km. How fast does this force change when r= 5,000 km?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**6. Newton’s Law of Gravitation**

Newton’s Law of Gravitation states that the magnitude \( F \) of the force exerted by a body of mass \( m \) on a body of mass \( M \) is

\[
F = \frac{{GmM}}{{r^2}}
\]

where \( G \) is the gravitational constant and \( r \) is the distance between the bodies.

**(a)** Find \( \frac{{dF}}{{dr}} \) and explain its meaning. What does the minus sign indicate?

**(b)** Suppose it is known that the Earth attracts an object with a force that decreases at a rate of 1 N/km when \( r = 15,000 \) km. How fast does this force change when \( r = 5,000 \) km?

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