Question

Example 9.2 Three equal masses of m kg
each are fixed at the vertices of an equilateral triangle ABC.
(a)what is the force acting on a mass 2m placed at the centroid O of the triangle?
(B)what is the force if the mass at the vertex A is doubled?
Take AO=BO=CO=1m​

Answer 1

Answer:

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Answer 2

Answer:

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Explanation:

ANSWER

From Figure, the gravitational force on mass 2m at G due to mass at A is

F1=G12m×2m=2Gm2 along GA

Gravitational force on mass 2m at G due to mass at B is

F2=G12m×2m=2Gm2 along BG

Gravitational force on mass 2m at G due to mass at C is F3=G12m×2m=2Gm2 along GC

Draw DE parallel to BC passing through point G. Then ∠EGC=30o=∠DGB.

Resolving F2 and F3 into two rectangular components, we have

F2cos30o along GD and F2sin30o along GH

F3cos30o along GE and F2sin30o along GH

Here, F2cos30o and F3sin30o are equal in magnitude and acting in opposite directions, and cancel out each other. The resultant force on mass 2m at G is

F1−(F2