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 F = where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr. dF dr = X What is the meaning of dF/dr? O dF/dr represents the rate of change of the distance between the bodies with respect to the force. O dF/dr represents the rate of change of the force with respect to the distance between the bodies. O dF/dr represents the rate of change of the mass with respect to the force. O dF/dr represents the rate of change of the mass with respect to the distance between the bodies. O dF/dr represents the amount of force per distance. What does the minus sign indicate? O The minus sign indicates that the bodies are being forced in the negative direction. 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 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 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 4 N/km when r = 20,000 km. How fast does this force change when r = 10,000 km? X 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 F = where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr. dF dr = X What is the meaning of dF/dr? O dF/dr represents the rate of change of the distance between the bodies with respect to the force. O dF/dr represents the rate of change of the force with respect to the distance between the bodies. O dF/dr represents the rate of change of the mass with respect to the force. O dF/dr represents the rate of change of the mass with respect to the distance between the bodies. O dF/dr represents the amount of force per distance. What does the minus sign indicate? O The minus sign indicates that the bodies are being forced in the negative direction. 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 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 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 4 N/km when r = 20,000 km. How fast does this force change when r = 10,000 km? X N/km
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 73E
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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
GmM
F =
where G is the gravitational constant and r is the distance between the bodies.
(a) Find dF/dr.
dF
dr
=
X
What is the meaning of dF/dr?
O dF/dr represents the rate of change of the distance between the bodies with respect to the force.
O dF/dr represents the rate of change of the force with respect to the distance between the bodies.
O dF/dr represents the rate of change of the mass with respect to the force.
O dF/dr represents the rate of change of the mass with respect to the distance between the bodies.
O dF/dr represents the amount of force per distance.
What does the minus sign indicate?
O The minus sign indicates that the bodies are being forced in the negative direction.
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 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 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 4 N/km when r = 20,000 km. How fast does this force change when r = 10,000 km?
X N/km
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