To determine the new gravitational force between the objects, we can use Newton's law of universal gravitation, which states that the force of gravity between two objects is inversely proportional to the square of their distance.
First, let's assign some variables:
- F1 is the original gravitational force,
- F2 is the new gravitational force,
- r1 is the original distance between the objects,
- r2 is the new distance between the objects.
We are given that F1 = 360 N. Now, we need to determine the relationship between F1 and F2 when the distance changes.
According to Newton's law of universal gravitation, we can write the equation as:
F1 = G * (m1 * m2) / r1^2,
where G is the gravitational constant and m1, m2 are the masses of the objects.
Since we are only interested in the change in gravitational force, we can set up a ratio between the original and new gravitational forces:
F1 / F2 = (G * (m1 * m2)) / (r1^2) / (G * (m1 * m2)) / (r2^2).
Now, let's substitute the given information in the equation:
360 N / F2 = (G * (m1 * m2)) / (r1^2) / (G * (m1 * m2)) / (3 * r1)^2.
Simplifying the equation:
360 N / F2 = (r2^2) / (r1^2 * 9).
Now, we know that the distance is now three times the original distance, so r2 = 3 * r1.
Substituting this into the equation:
360 N / F2 = ((3 * r1)^2) / (r1^2 * 9).
Simplifying further:
360 N / F2 = 9 / 9.
Therefore:
360 N / F2 = 1.
To find F2, we can rearrange the equation:
F2 = 360 N / 1.
Therefore, the new gravitational force between the objects is 360 Newtons.