Six-point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.

Home » Six-point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.

Six-point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.

$AE = AG + EG$

$AG + AG = 2AG$

$= 2l cos 30^{o}$

$AE = AC = \sqrt3l$

$AD = 2l$

As a result,

$\frac{Gm^{2}}{l^{2}}$ is the force on A due to B along B to A

$\frac{Gm^{2}}{3l^{2}}$ is the force on A due to C along D to A

$\frac{Gm^{2}}{4l^{2}}$ is the force on A due to D along D to A

$\frac{Gm^{2}}{3l^{2}}$ is the force on A due to E along E to A

As a result, total force will be,

$F = \frac{Gm^{2}}{l^{2}}(1+\frac{1}{\sqrt3}+\frac{1}{3})$ along DA

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