Two small spherical asteroids, each of mass 850 kg, are traveling through deep s

Question

Two small spherical asteroids, each of mass 850 kg, are traveling through deep space along the same line and in the same direction. Initially they arc 23 m apart and both have a speed of 4500 m/s. Assume there are no external forces acting on the system, so the velocity of the system's center of mass does not change. However, the individual speeds of the asteroids will change due to the gravitational force between them. Later the asteroids are 2.1 m apart. What was their change in speed, in meters per second? Give the absolute value, as their speeds change by equal but opposite amounts. Delta v =

Explanation / Answer

since no external forces are acting on the sytem then ,its energy should be conserved

using law of conservation of energy

K1 + U1 = K2+ U2

(0.5*m*v1^2*2) - (G*m1*m2/r1) = (0.5*m*v2^2) -(G*m1*m2/r2)

(0.5*850*4500^2*2)-(6.67*10^-11*850*850/23) = (0.5*850*v2^2*2)-(6.67*10^-11*850*850/2.1)

v2 = 4500 m/sec

so there is no change in speed

delta V = 0 m/sec

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