a turtle has a mass of 10kg. if earths mass is 6 x 10^{24} kg and its radius is 6.4 x 10^{6} kg, what is the weight of the turtle?

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Accepted Answer

# Explanation: ## Step1: The formula for gravitational force $F = G\frac{Mm}{r^{2}}$, where $G = 6.67\times10^{- 11}\space Nm^{2}/kg^{2}$, $M = 6\times10^{24}\space kg$, $m = 10\space kg$, $r=6.4\times 10^{6}\space m$ ## Step2: $$ \begin{align*} F&=6.67\times 10^{-11}\times\frac{6\times 10^{24}\times10}{(6.4\times 10^{6})^{2}}\ &=6.67\times 10^{-11}\times\frac{6\times 10^{25}}{40.96\times 10^{12}}\ &=6.67\times 10^{-11}\times\frac{6}{40.96}\times10^{13}\ &=\frac{6.67\times6}{40.96}\times10^{2}\ \end{align*} $$ $$ \begin{align*} \frac{6.67\times6}{40.96}&=\frac{40.02}{40.96}\approx0.977\ F&\approx0.977\times 10^{2}=97.7\space N \end{align*} $$ # Answer: The weight of the turtle is approximately $97.7\space N$

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Explanation:

Step1: <Use Newton's law of gravitation>

Step2: <Substitute the values into the formula>

Answer: