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# The masses and coordinates of three spheres are as follows: 20 kg, x = 0.50 m, y = 1.0 m; 40 kg, x = -1.0 m, y = -1.0 m; 60 kg, x = 0 m, y = -0.50 m. What is the magnitude of the gravitational force on a 20 kg sphere located at the origin due to these three spheres?

Solution

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$\textrm{First, we need to state the equations and rules we will use in this problem}$

$\Huge \color{#c34632} \boxed{F = \dfrac{Gm_1m_2}{d^2}} \;\Rightarrow \; (1)$

$\Huge \color{#c34632} \boxed{F_{x} = \dfrac{F \times x}{d}} \;\Rightarrow \; (2)$

$\Huge \color{#c34632} \boxed{F_{y} = \dfrac{F\times y}{d}} \;\Rightarrow \; (3)$

$\Huge \color{#c34632} \boxed{d_{origin} = \sqrt{x^2 + y^2 + z^2}} \;\Rightarrow \; (4)$

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