An asteroid with mass m = 1.80 109 kg comes from deep space, effectively from in

Question

An asteroid with mass m = 1.80 109 kg comes from deep space, effectively from infinity, and falls toward Earth. (a) Find the change in potential energy when it reaches a point 4.10 108 m from the center of the Earth (just beyond the orbital radius of the Moon), assuming it falls from rest at infinity. In addition, find the work done by the force of gravity. PE = J Wgrav = J (b) Calculate the asteroid's speed at that point, assuming it was initially at rest when it was arbitrarily far away. m/s (c) How much work would have to be done on the asteroid by some other agent so the asteroid would be traveling at only half the speed found in (b) at the same point? J Please detail your work so I can better understand. Thank you in advance.

Explanation / Answer

Part A : change in PE = GMm/r

G is universa gravitational cnstant = 6.67 e -11

M is mass of earth

m is mass of aasteriod

r is its location
so here

dPE = 6.67 e -11 * 5.98 e 24 * 1.80 e9/(4.1 e 10)

dPE = 1.75 e 13 Joules

Work done W = - chagne in PE

W = - 1.75 e 13 J

part B : W = 0.5 mv^2 = 17.5 e 12

v^2 = 2* 17.5 e 12/(1.8 e9)

V = 139. 44 m/s

------------------------------

C. Work W = dKE + d PE

W = 0.5 mv^2 - 17.5 e 12

W = 0.5 * 1.8 e 9 * 139.44 * 139.44 - 17.5 e 12

W = 1.74 e 13 - 17.3 e 12

W = 8.37 e 8 JOuels

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