A system consists of three balls at different locations on the x-axis. Ball 1 ha

Question

A system consists of three balls at different locations on the x-axis. Ball 1 has a mass of 8.00 kg and is located at x = +3 m; ball 2 has a mass of 2.00 kg and is located at x = -1 m; ball 3 has an unknown mass and is located at x = -4 m.

(a) If the center of mass of this system is located at x = -2 m, what is the mass of ball 3?
kg

(b) Let’s say that you can make ball 3 as light or as heavy as you like. By adjusting the mass of ball 3, what range of positions on the x-axis can the center of mass of this system occupy?
The most negative position possible is x = m.
The most positive position possible is x = m.

Explanation / Answer

Let the mass of ball3 = m

Now, center of mass is given by COMx = [8*3 + 2*(-1) + m*(-4)]/8+2+m

-2 = [24-2-4m]/[10+m]

-20 - 2m = 22 - 4m

2m = 42

m = 21 kg

The general expression which we got for COMx =  [24-2-4m]/[10+m]

Putting m = 0 , we get , COM = 2.2

Putting m tending to infinity, we have, COMx = -1

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