Question

suppose that two objects attract each other with a gravitational force of 32 newtons. if the distance between the two objects is doubled, what is the force of attraction betweenthem?

Answer 1

Taking into account the Universal Law of Gravitation, the force of attraction between the tow objects is 8 N.

Universal Law of Gravitation

The Universal Law of Gravitation establishes that bodies, by the simple fact of having mass, experience a force of attraction towards other bodies with mass, called gravitational force.

The Universal Law of Gravitation states that the gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance that separates them.

Mathematically it is expressed as follows:

$F=G\frac{Mm}{d^{2} }$

where:

• G is the universal gravitational constant, with a value of 6.67×10⁻¹¹ $\frac{Nm^{2} }{kg^{2} }$.
• M and m are the masses of the bodies that interact.
• d is the distance that separates them.

Force of attraction in this case

In this case, two objects attract each other with a gravitational force of 32 newtons. The distance between the two objects is doubled.

Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases.

Then, if the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (d²= 2²= 4). The new force is then $\frac{1}{4}$ of the original:

F=$\frac{1}{4}$×Foriginal

F=$\frac{1}{4}$×32 N

F= 8 N

Finally, the force of attraction between the tow objects is 8 N.

Learn more about the Universal Law of Gravitation:

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