Newtons law of gravity states that the gravitational attraction F between two bodies is proportional
to 1 over the square of the distance d between their centers.
(a) Using k as the constant of proportionality, express F as a function of d.
(b) What happens to F near the pole at d = 0?
(c) Explain in practical terms the meaning of the pole at d = 0.
F = k/d^2
b) undefined because zero denominator (gets very big as d gets small)
c) If an object has mass, it also has size. It is impossible to get d = 0 because the objects bump before their centers of gravity collide. So, although the force can become large, it does not really approach infinity in practice (although bringing two neutrons together might be pretty interesting :)
Thank you so much
:)
You are welcome.
(a) Newton's law of gravity states that the gravitational attraction F between two bodies is proportional to 1 over the square of the distance d between their centers. Mathematically, this can be expressed as:
F = k / d^2
Where F is the gravitational attraction between the bodies, k is the constant of proportionality, and d is the distance between their centers.
(b) When the distance d approaches zero, meaning the bodies are very close or at the same location, the gravitational attraction F becomes infinitely large. This indicates an extremely strong attraction between the bodies. However, in reality, it is not possible for the distance between two objects to be exactly zero, as they would occupy the same space. This scenario is used to demonstrate that the gravitational force becomes exceptionally strong as the distance between the bodies decreases.
(c) In practical terms, the pole at d = 0 represents a situation where two objects are located at the exact same position, or they are in direct contact with each other. In the context of gravity, this is an extreme scenario where the gravitational force between the objects becomes infinitely strong. However, in reality, such a situation is not possible as objects cannot occupy the same space. The pole at d = 0 is a theoretical concept used to illustrate the behavior of gravity when the distance between two objects approaches zero.