What happens to the force between two objects if I) the mass of object...
Effect of Doubling the Mass of One Object
When the mass of one object is doubled, the gravitational force between the two objects changes according to Newton's law of universal gravitation. This law states that the force is directly proportional to the product of their masses.
- Force Increases: If mass M1 is doubled (2M1), the force becomes F = G(2M1 * M2)/r². Thus, the force doubles.
Effect of Doubling and Tripling the Distance
Changing the distance between two objects significantly affects the gravitational force. The force is inversely proportional to the square of the distance.
- Doubling the Distance: If the distance r is doubled (2r), the force becomes F = G(M1 * M2)/(2r)² = G(M1 * M2)/4r². Thus, the force is reduced to one-fourth of the original force.
- Tripling the Distance: If the distance is tripled (3r), the force becomes F = G(M1 * M2)/(3r)² = G(M1 * M2)/9r². Thus, the force is reduced to one-ninth of the original force.
Effect of Doubling the Masses of Both Objects
When both masses are doubled, the gravitational force is affected similarly to the first scenario.
- Force Increases: If both masses M1 and M2 are doubled (2M1 and 2M2), the new force becomes F = G(2M1 * 2M2)/r² = 4G(M1 * M2)/r². Thus, the force quadruples.
In summary, doubling one mass doubles the force, while doubling both masses quadruples the force. Doubling the distance reduces the force to one-fourth, and tripling the distance reduces it to one-ninth.
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