Object A in space has a mass of 30,000 kg. It is about 200,000 m away from object B, which has a mass of 10,000 kg. Which object is exerting a stronger force of gravity on the other? How do you know?
The Correct Answer and Explanation is:
To determine which object exerts a stronger force of gravity on the other, we can apply Newton’s law of universal gravitation, which states that the gravitational force ( F ) between two objects is given by the equation:
[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
]
where:
- ( F ) is the gravitational force,
- ( G ) is the gravitational constant (( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 )),
- ( m_1 ) and ( m_2 ) are the masses of the two objects,
- ( r ) is the distance between the centers of the two objects.
In this scenario, let:
- ( m_1 = 30,000 \, \text{kg} ) (mass of object A),
- ( m_2 = 10,000 \, \text{kg} ) (mass of object B),
- ( r = 200,000 \, \text{m} ) (distance between the two objects).
According to the formula, both objects exert gravitational forces on each other. However, the magnitude of the gravitational force is the same regardless of which object is considered the source or the target of the force.
When calculating the gravitational force exerted by object A on object B (and vice versa), we see:
[
F = \frac{(6.674 \times 10^{-11}) \cdot (30,000) \cdot (10,000)}{(200,000)^2}
]
The same equation applies when switching the roles of the objects, as the forces are equal in magnitude but opposite in direction due to Newton’s third law of motion (for every action, there is an equal and opposite reaction).
Thus, object A and object B exert equal gravitational forces on each other. In conclusion, neither object is exerting a stronger force of gravity; they exert equal gravitational forces, which are calculated to be the same based on their masses and the distance between them. This phenomenon illustrates the fundamental principles of gravitational interaction in physics.