# 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.

Given

Side of hexagon = l

The force on the masses will be the resultant of the forces of all the other masses. Let the masses be m each. Now the distance AC is given by the parallelogram law i.e.

Due to symmetry we have AC = AE =

Now the force on mass at A due to b is

Also

The force on mass A due to C is

Also due to symmetry, we have

The force on mass at A due to mass at D is

Now, the forces Fae and Fac make equal angles with the direction AD viz. 30°, and therefore by parallelogram law of vector addition their resultant is along AD and therefore the magnitude of the resultant,

Similarly, Fab and Faf also make equal angles with AD viz. 60° and therefore they are also along AD and

Therefore, the net force on mass at A will be

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