Respuesta :
Answer:
The gravitational force between the two masses is 1.668575 × 10⁻¹¹ N
Explanation:
The given parameters are;
The mass of the two asteroids having gravitational attraction, are m₁ = m₂ = m = 50,000 kg
The separation distance between their centers, r = 1,000 m
The gravitational attraction force, F, between the two masses is given as follows;
[tex]F =G\dfrac{m_{1}m_{2}}{r^{2}}[/tex]
Where;
G = The universal gravitational constant = 6.67430 × 10⁻¹¹ N·m²/kg²
m₁ = m₂ = m
Substituting the values gives;
[tex]F =6.67430 \times 10^{-11} \times \dfrac{50,000 \times 50,000}{1000^{2}} = 1.668575 \times 10^{-7} \ N[/tex]
The gravitational force, F, between the two masses = 1.668575 × 10⁻¹¹ N.
The gravitational force between the two identical asteroids is 1.67 × 10⁻⁷ Newton.
Given the data in the question
Since the asteroids are identical
- Mass of the asteroids; [tex]m_1 = m_2 = 50000kg[/tex]
- Distance between the centers of the masses; [tex]r = 1000m[/tex]
Gravitational force; [tex]F =\ ?[/tex]
To determine the gravitational force between two identical asteroids, we use the Newton's law of universal gravitation:
[tex]F = G\frac{m_1m_2}{r^2}[/tex]
Where [tex]m_1[/tex] is mass of object 1, [tex]m_2[/tex] is mass of object 2, r is the distance between centers of the masses and G is the Gravitational constant ( [tex]6.67408 * 10^{-11} m^3/kgs^2[/tex] )
We substitute our values into the equation
[tex]F = (6.67408 * 10^{-11} m^3/kgs^2) \frac{50000kg*50000kg}{(1000m)^2} \\\\F = \frac{0.166852kgm^3/s^2}{1000000m^2}\\\\ F = 1.67 * 10^{-7}kg.m/s^2\\\\F = 1.67 * 10^{-7}N[/tex]
Therefore, the gravitational force between the two identical asteroids is 1.67 × 10⁻⁷ Newton.
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