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What is the distance between the Moon and the Earth if the mass of the moon is 7.34 x 1022 kg, the mass of the Earth is 5.98x1024 kg and the force of attraction between the two is 2.00 x 1020 N?

User Simon David
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1 Answer

14 votes
14 votes

Answer:


r=3.83*10^8m

Step-by-step explanation: We need to find the distance between the moon and earth provided the force between them and their masses. the equation used to solve this problem is as follows:


\begin{gathered} F=(m_1m_2)/(r^2)G\Rightarrow(1) \\ G=6.674*10^(-11)m^3kg^(-1)s^(-2)_{} \end{gathered}

Using the known values, and plugging in the equation (1) results in:


\begin{gathered} m_1=7.34*10^(22)\operatorname{kg} \\ m_2=5.98*10^(24)\operatorname{kg} \\ F=2.00*10^(20)N \\ \end{gathered}

The final step is as follows:


\begin{gathered} (2.00*10^(20)N)=\frac{(7.34*10^(22)\operatorname{kg})\cdot(5.98*10^(24)\operatorname{kg})}{r^2}\cdot(6.674*10^(-11)m^3kg^(-1)s^(-2)_{}) \\ \text{ Rearranging} \\ r^2=\frac{(7.34*10^(22)\operatorname{kg})\cdot(5.98*10^(24)\operatorname{kg})\cdot(6.674*10^(-11)m^3kg^(-1)s^(-2)_{})}{(2.00*10^(20)N)} \\ r^2=1.4647*10^(17)m^2 \\ r=\sqrt[]{1.4647*10^(17)m^2}=3.83*10^8m \\ r=3.83*10^8m \end{gathered}

Therefore the distance between the moon and the earth is:


r=3.83*10^8m

User Plastique
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