Question

two masses are 125 m apart. mass 1 is 2.36 kg and mass 2 is 4.06 kg. what is the gravitational force between the two masses? \\(\vec{f} = ? \times 10^{?} \\, n\\) \\(\vec{f} = g \frac{m_1 m_2}{r^2}\\) \\(g = 6.67 \times 10^{-11} \\, n \cdot m^2 / kg^2\\)

Explanation:

Step1: List given values

$m_1=2.36\ \text{kg}$, $m_2=4.06\ \text{kg}$, $r=125\ \text{m}$, $G=6.67\times10^{-11}\ \text{N·m}^2/\text{kg}^2$

Step2: Calculate product of masses

$m_1m_2=2.36\times4.06=9.5816\ \text{kg}^2$

Step3: Calculate squared distance

$r^2=125^2=15625\ \text{m}^2$

Step4: Substitute into gravity formula

$F=6.67\times10^{-11}\times\frac{9.5816}{15625}$

Step5: Compute coefficient and exponent

First calculate $\frac{6.67\times9.5816}{15625}\approx\frac{63.909}{15625}\approx4.09\times10^{-3}$
Then combine with $10^{-11}$: $F=4.09\times10^{-3}\times10^{-11}=4.09\times10^{-14}$

Answer:

$\vec{F} = 4.09 \times 10^{-14}\ \text{N}$