The gravitational pull of the earth on an object is inversely proportional to th
ID: 2055614 • Letter: T
Question
The gravitational pull of the earth on an object is inversely proportional to the square of the distance of the object from the center of the earth. At the earth's surface this force is equal to the object's normal weight mg where g = 9.8 m/s^2 , and at large distances, the force is zero.
A) If a 20,000-kg asteroid falls to earth from a very great distance away, what will be its minimum speed as it strikes the earth's surface? You can ignore the effects of the earth's atmosphere.
B) How much kinetic energy will it impart to our planet
Explanation / Answer
a)
Potential energy of asteroid at great distance = 0
Potential energy at the earths surface = -GMm/R
= - 6.67 * 10-11 * 5.97 * 1024 * 2 * 104 / (6.37 * 106)
= -12.5 * 1012 J
As whole energy is converted to Kinetic Energy :
1/2 * m * v2 = 0 - (-12.5 * 1012)
v = 3.53 * 104 m/s = minimum speed.
b)
Kinetic Energy Imparted = 12.5 * 1012 J
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