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 R F= where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr. dF dr = What is the meaning of dF/dr? O dF/dr represents the amount of force per distance. O dF/dr represents the rate of change of the mass with respect to the distance between the bodies. 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 mass with respect to the force. O dF/dr represents the rate of change of the force with respect to the distance between the bodies. What does the minus sign indicate? 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 decreases. 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 the bodies are being forced in the negative direction. (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 = 30,000 km. How fast does this force change when r= 15,000 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 R F= where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr. dF dr = What is the meaning of dF/dr? O dF/dr represents the amount of force per distance. O dF/dr represents the rate of change of the mass with respect to the distance between the bodies. 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 mass with respect to the force. O dF/dr represents the rate of change of the force with respect to the distance between the bodies. What does the minus sign indicate? 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 decreases. 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 the bodies are being forced in the negative direction. (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 = 30,000 km. How fast does this force change when r= 15,000 km N/km
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Chapter1: Units, Trigonometry. And Vectors
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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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Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
Question
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
=
What is the meaning of dF/dr?
O dF/dr represents the amount of force per distance.
O dF/dr represents the rate of change of the mass with respect to the distance between the bodies.
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 mass with respect to the force.
O dF/dr represents the rate of change of the force with respect to the distance between the bodies.
What does the minus sign indicate?
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 decreases.
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 the bodies are being forced in the negative direction.
(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 = 30,000 km. How fast does this force change when r = 15,000 km?
N/km
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