R m A uniformly-dense, non-rotating planet has a radius R = 1 x 106 meters and a mass such that GM = 4.0 x 1012 m2/s. A tunnel is drilled through the planet along a diameter. An object of mass 3 x 106 kg is released from rest at one end of the tunnel. (a) While the object is within the tunnel, the force due to gravity can be expressed as F= -Cr. What is value of C? 12 N/m (b) Sketch a graph of the force on the object as a function of distance from the center of the planet. Let a force directed away from the center be positive. (c) How much work does gravity do on the object as it falls from the surface of the planet to the center? (d) What is the speed of the object when it reaches the center? m/s (e) Write a differential equation that relates the position of the mass r to its time of travel t. Do NOT solve the equation.
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.
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