Physics

Physics

Problem

Three point masses, each of 5 kg5\,\text{kg}, are fixed at the vertices of an equilateral triangle of side 0.5 m0.5\,\text{m}. Using G=6.67×10−11 N m2kg−2G = 6.67\times10^{-11}\,\text{N\,m}^2\text{kg}^{-2}, calculate the magnitude and direction of the net gravitational force acting on the mass at one vertex due to the other two masses.
Intuitive explanation

The key is recognizing that gravitational forces are vectors—you must find the force each distant mass exerts on your target mass, then add them as vectors using geometry. Since the triangle is equilateral, the two forces have equal magnitude but point along different directions; the symmetry of the setup means they meet at a 60°60° angle, so you'll use vector addition (or the law of cosines) to find the resultant. The direction will point toward the center of the triangle by symmetry.

Intuitive explanation

The key is recognizing that gravitational forces are vectors—you must find the force each distant mass exerts on your target mass, then add them as vectors using geometry. Since the triangle is equilateral, the two forces have equal magnitude but point along different directions; the symmetry of the setup means they meet at a 60°60° angle, so you'll use vector addition (or the law of cosines) to find the resultant. The direction will point toward the center of the triangle by symmetry.

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