QuestionMay 2, 2025

4. Winston the Corgi is standing 5 meters from Cheddar the 10 kg Corgi. What is Winston's mass in kg if the gravitational force of attraction between them is 2.1times 10^-10N

4. Winston the Corgi is standing 5 meters from Cheddar the 10 kg Corgi. What is Winston's mass in kg if the gravitational force of attraction between them is 2.1times 10^-10N
4. Winston the Corgi is standing 5 meters from Cheddar the 10 kg Corgi. What is Winston's mass in kg if the gravitational force of attraction between them is 2.1times 10^-10N

Solution
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Answer

7.86 \, \text{kg} Explanation 1. Use the gravitational force formula The formula for gravitational force is F = \frac{G \cdot m_1 \cdot m_2}{r^2}, where F is the force, G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2, m_1 and m_2 are the masses, and r is the distance. 2. Rearrange to solve for m_1 Rearrange the formula: m_1 = \frac{F \cdot r^2}{G \cdot m_2}. 3. Substitute values Substitute F = 2.1 \times 10^{-10} \, \text{N}, r = 5 \, \text{m}, G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2, and m_2 = 10 \, \text{kg} into the equation: m_1 = \frac{(2.1 \times 10^{-10}) \cdot (5)^2}{(6.674 \times 10^{-11}) \cdot 10}. 4. Perform calculations m_1 = \frac{(2.1 \times 10^{-10}) \cdot 25}{(6.674 \times 10^{-11}) \cdot 10} = \frac{5.25 \times 10^{-9}}{6.674 \times 10^{-10}} \approx 7.86 \, \text{kg}.

Explanation

1. Use the gravitational force formula<br /> The formula for gravitational force is $F = \frac{G \cdot m_1 \cdot m_2}{r^2}$, where $F$ is the force, $G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$, $m_1$ and $m_2$ are the masses, and $r$ is the distance.<br />2. Rearrange to solve for $m_1$<br /> Rearrange the formula: $m_1 = \frac{F \cdot r^2}{G \cdot m_2}$.<br />3. Substitute values<br /> Substitute $F = 2.1 \times 10^{-10} \, \text{N}$, $r = 5 \, \text{m}$, $G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$, and $m_2 = 10 \, \text{kg}$ into the equation:<br />$m_1 = \frac{(2.1 \times 10^{-10}) \cdot (5)^2}{(6.674 \times 10^{-11}) \cdot 10}$.<br />4. Perform calculations<br /> $m_1 = \frac{(2.1 \times 10^{-10}) \cdot 25}{(6.674 \times 10^{-11}) \cdot 10} = \frac{5.25 \times 10^{-9}}{6.674 \times 10^{-10}} \approx 7.86 \, \text{kg}$.
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