Using Gravitational constant to get the final velocity

by hyperkkt
Tags: force, gravitational, integral, position, speed
 P: 2 1. The problem statement, all variables and given/known data Evil Alien has put an Asteroid with mass of 1,000,000kg to destroy mankind. Distance from center of the Earth to Asteroid (assume negligible center) is 10^8m and lets the gravitational force do the work. Earth radius is 6.4 x 10^6m and its mass is 5.98 x 10^24kg. If the atmosphere extends out to 500km beyond the surface and exrts an average friction force of 10^8N, calculate the speed of the asteroid just before it hits the ground. (Assume the asteroid rtains all of its mass as it travels through the atmosphere) 2. Relevant equation Fgrav = Gm1m2/r^2 3. The attempt at a solution I tried to use F=ma first by doing it so I get F=Gm1m2/r^2=m1a a=Gm2/r^2 However, could not do anything more since there is no dt. So, I tried taking an integral of it, finding the work and set it equal to kinetic energy (not sure whether indefinite/definite integral matters) integral of Gm1m2/r^2 = -Gm1m2/r -Gm2/r^2=v^2 but got this and it cannot happen because v^2 cannot be - number... v=i(imginary) I am stuck at this point have no further suggestion on what I should do. I've been working on it for about an hour and would appreciate any help. Thanks in advance
 Sci Advisor HW Helper Thanks P: 24,975 The potential energy PE(r)=-G*m1*m2/r. You find the change in potential energy by subtracting PE(r=10^8m)-PE(r=radius of the earth). The difference is positive, not negative.
 P: 2 Oh I see, but how do you get v after finding the change in PE? And from there how do I apply it to the interval which frictino decreases the speed? I may be understanding something wrong. Thanks again for the reply