Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is GmM 2 where G is the gravitational constant and r is the distance between the bodies. dF dr (a) Find dF dr = F= What is the meaning of df in the context of this problem? dr represents the rate of change of the distance between the bodies with respect to the force. O ο ο ο ο dr dF dr dr dF dr dF dr represents the amount of force per distance. represents the rate of change of the mass with respect to the distance between the bodies. represents the rate of change of the force with respect to the distance between the bodies. represents the rate of change of the mass with respect to the force. What does the minus sign in the expression indicate? O The minus sign indicates that the bodies are being forced in the negative direction. O The minus sign indicates that the force between the bodies is decreasing. O The minus sign indicates that as the distance between the bodies increases, the magnitude of the force increases. O The minus sign indicates that as the distance between the bodies decreases, the magnitude of the force remains constant. O The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases. (b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 2 N/km when r = 20,000 km. How fast does this force change when r= 10,000 km? N/km
Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is GmM 2 where G is the gravitational constant and r is the distance between the bodies. dF dr (a) Find dF dr = F= What is the meaning of df in the context of this problem? dr represents the rate of change of the distance between the bodies with respect to the force. O ο ο ο ο dr dF dr dr dF dr dF dr represents the amount of force per distance. represents the rate of change of the mass with respect to the distance between the bodies. represents the rate of change of the force with respect to the distance between the bodies. represents the rate of change of the mass with respect to the force. What does the minus sign in the expression indicate? O The minus sign indicates that the bodies are being forced in the negative direction. O The minus sign indicates that the force between the bodies is decreasing. O The minus sign indicates that as the distance between the bodies increases, the magnitude of the force increases. O The minus sign indicates that as the distance between the bodies decreases, the magnitude of the force remains constant. O The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases. (b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 2 N/km when r = 20,000 km. How fast does this force change when r= 10,000 km? N/km
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is
(a) Find
dF
dr
F =
where G is the gravitational constant and r is the distance between the bodies.
dF
dr
=
55 55 55 55 55
dF
What is the meaning of in the context of this problem?
dr
dF
dr
dF
dr
dr
GmM
²
dF
I
dr
dF
dr
represents the rate of change of the distance between the bodies with respect to the force.
represents the amount of force per distance.
represents the rate of change of the mass with respect to the distance between the bodies.
represents the rate of change of the force with respect to the distance between the bodies.
represents the rate of change of the mass with respect to the force.
What does the minus sign in the expression indicate?
The minus sign indicates that the bodies are being forced in the negative direction.
The minus sign indicates that the force between the bodies is decreasing.
The minus sign indicates that as the distance between the bodies increases, the magnitude of the force increases.
The minus sign indicates that as the distance between the bodies decreases, the magnitude of the force remains constant.
The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases.
(b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 2 N/km when r = 20,000 km. How fast does this force change when r = 10,000 km?
N/km
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