[tex]\large\boxed{ \bold{ F_{g}= 1.102 \cdot 10^{-8} \ N }}[/tex]
Datos:
[tex]\bold{m_{1} = 50 \ kg}[/tex]
[tex]\bold{m_{2} = 162 \ kg}[/tex]
[tex]\bold{d= 7 \ m}[/tex]
[tex]\large\boxed{ \bold{ F_{g} = G\ \frac{m_{1} \cdot m_{2} }{ d^{2} } } }[/tex]
Donde
[tex]\bold{ F_{g} } \ \ \ \ \ \ \ \ \ \ \ \ \large\textsf{Fuerza gravitacional atracci\'on masas}[/tex]
[tex]\bold{ G} \ \ \ \ \ \ \ \ \ \ \ \ \ \large\textsf{Constante de gravitaci\'on universal}[/tex]
[tex]\bold{ m_{1},\ \ m_{2}} \ \ \ \large\textsf{Masa de los cuerpos }[/tex]
[tex]\bold{ d} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \large\textsf{Distancia }[/tex]
Donde
[tex]\large\boxed {\bold {G = 6.67 \cdot 10^{-11} \ \frac{N \ m ^{2} }{kg^{2} } }}[/tex]
[tex]\large\textsf{Reemplazamos los valores }[/tex]
[tex]\boxed{ \bold{ F_{g}= \left[6.67 \cdot 10^{-11} \ \frac{N \ m ^{2} }{kg^{2} }\right ] \frac{(50 \ kg) \cdot (162 \ kg) }{(7 \ m)^{2} } }}[/tex]
[tex]\boxed{ \bold{F_{g}= \left[6.67 \cdot 10^{-11} \ \frac{N \not m ^{2} }{\not kg^{2} }\right ] \frac{ 8100 \not kg^{2} }{49 \not m^{2} } }}[/tex]
[tex]\boxed{ \bold{ F_{g}=[6.67 \cdot 10^{-11} ] \cdot \frac{8100}{49} \ N }}[/tex]
[tex]\textsf{Agrupamos t\'erminos y exponentes}[/tex]
[tex]\boxed{ \bold{ F_{g}=6.67 \cdot \frac{ 8100}{49} \cdot 10^{-11} \ N }}[/tex]
[tex]\textsf{Dividiendo}[/tex]
[tex]\boxed{ \bold{ F_{g}=6.67 \cdot 165.3061224489796 \cdot 10^{-11} \ N }}[/tex]
[tex]\boxed{ \bold{ F_{g}= 1102.591836734693877 \cdot 10^{-11} \ N }}[/tex]
[tex]\textsf{Reescribimos en notaci\'on cient\'ifica}[/tex]
[tex]\boxed{ \bold{ F_{g}= 1.102591836734693877 \cdot 10^{-8} \ N }}[/tex]
[tex]\large\boxed{ \bold{ F_{g}= 1.102 \cdot 10^{-8} \ N }}[/tex]
