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 5.00 kg and is located at x = +3 m; ball 2 has a mass of 4.00 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?

(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

centre of mass, Cx=(5*3+4*(-1)+m*(-4))/(5+4+m) =-2
so, m=14.5 kg <---------answer (a)

from the equation above we get,

Cx=(11-4m)/(9+m)

we can see,

for the center of mass to be most negative, m should tend to infinity

so, for this Cx= -4

for the center of mass to be most +ve, m should be 0

so, for this, Cx=11/9=1.22

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