Q.42 - Excercises And ProblemsExpert-verified
An object of mass is dropped from height above a planet of mass and radius Find an expression for the object’s speed as it hits the ground.
the expression for object's speed is
mass of an object is
height of an object to be dropped is
mass of the planet
radius of the planet
The initial mechanical energy of the object, when it is located at height h above the the planet, is just gravitational potential energy:
is the gravitational constant
is the mass of the planet
is the mass of the object
is the radius of the planet
is the altitude of the object
When the object hits the ground, its mechanical energy will sum of potential energy and kinetic energy:
is the speed of the object at the ground
Since the mechanical energy is conserved, we can write
and solving for , we find
A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth.
a. What is the ratio F1/F2 of the gravitational force on the first satellite to that on the second satellite? b. What is the ratio a1/a2 of the acceleration of the first satellite to that of the second satellite?
Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times. As a satellite spirals inward, does it speed up, slow down, or maintain the same speed? Explain.
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