Take a deep breath and keep yourself centered.
Three spheres labeled A, B, and C, each with radius 0.1 m and mass 3 kg, are initially at rest at the following coordinates (all coordinates are in meters):
A: (-2, 7)
B: (19, 3)
C: (7, -5)
The only forces the spheres exert on each other are the normal force when they hit each other, and the gravitational force each sphere exerts on the others due to their masses. There are no other forces.
Let , , and be the x-coordinates of the three masses after seconds has elapsed.
Find in meters.
The answer is 24.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Since there are no external forces, the three spheres can be treated as a closed system. As such, the momentum of this closed system, which starts out at zero in the reference frame described in the problem, must be conserved.
That means the total momentum of the system remains zero for all time, from which we can infer that the center of mass of this system remains stationary in its initial position.
The position of the center of mass of the system can be found with a weighted average of the coordinates. Since all the masses are the same, a simple average will do; averaging the x-coordinates, we find that
x C M = 3 x A + x B + x C = 8 m
Thus, at the end of any amount of time, the sum of those three x-coordinates must be
x A + x B + x C = 2 4 m