Four 6.5 kg spheres are located at the corners of a square of side 0.66 m. Calculate the magnitude and direction of the gravitational force exerted on one sphere by the other three.
Magnitude
?N
Magnitude
?N
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By symmetry, the direction is directly towards the one diagonally opposite. The charge diagonally opposite creates a force directly towards the test charge, the other two have to be added in via vector arithmetic.
Gravitational attraction in newtons
F = G m₁m₂/r²
G = 6.67e-11 m³/kgs²
m₁ and m₂ are the masses of the two objects in kg
r is the distance in meters between their centers
For the one diagonally opposite, the distance is 0.66 x 1.414
F₁ = (6.67e-11)(6.5)² / (0.66•1.414)²
For the other two, the component parallel to the diagonal is the force x cos 45º = 0.707
F₂ = (0.707)(6.67e-11)(6.5)² / (0.66)²
and double that for the total.
F = F₁ + 2•F₂
you can do the math
.
Gravitational attraction in newtons
F = G m₁m₂/r²
G = 6.67e-11 m³/kgs²
m₁ and m₂ are the masses of the two objects in kg
r is the distance in meters between their centers
For the one diagonally opposite, the distance is 0.66 x 1.414
F₁ = (6.67e-11)(6.5)² / (0.66•1.414)²
For the other two, the component parallel to the diagonal is the force x cos 45º = 0.707
F₂ = (0.707)(6.67e-11)(6.5)² / (0.66)²
and double that for the total.
F = F₁ + 2•F₂
you can do the math
.