find the potential energy of a system of four particles of mass 'm'each place at the vertices of square of site T ?
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Let the square be ABCD. Let us denote the mass m at each point by the vertex. Let the side be equal to a. Diagonal is equal to a √2.
Potential energy exists for each pair of the masses.
U = - G m1 * m2 / d
Number of pairs: 4C2 = 6.
Pairs are : AB, AC, AD, BC, BD, CD.
Distances between the masses in these pairs are a, √2 a, a, a, √2 a and a respectively.
Total PE = - G m * m * [ 1/a + 1/√2a + 1/a + 1/a + 1/√2a + 1/a ]
U = - G m²/a * [ 4 + √2 ]
Side = a or T ?
Potential energy exists for each pair of the masses.
U = - G m1 * m2 / d
Number of pairs: 4C2 = 6.
Pairs are : AB, AC, AD, BC, BD, CD.
Distances between the masses in these pairs are a, √2 a, a, a, √2 a and a respectively.
Total PE = - G m * m * [ 1/a + 1/√2a + 1/a + 1/a + 1/√2a + 1/a ]
U = - G m²/a * [ 4 + √2 ]
Side = a or T ?
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