The gravitional force between two objects is 360 Newton s. The objects move such that their distance is now three times their original distance. What is the new gravitational force between the objects
The gravitational force between two objects is inversely proportional to the square of the distance between them.
Let's assume that the original distance between the objects is represented by d. Therefore, the original gravitational force can be denoted as F.
Using the inverse-square law, we know that if the distance is multiplied by 3, the new distance would be 3d. The new gravitational force can be denoted as F'.
According to the inverse-square law:
(F/F') = (d'²/d²)
Substituting the given values:
(F/360) = ((3d)²/d²)
(F/360) = 9(d²/d²)
(F/360) = 9
F = 360 * 9
F = 3240 Newtons
Therefore, the new gravitational force between the objects is 3240 Newtons.
The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Let's assume that the original distance between the objects is represented by 'd', and the original gravitational force is 360 Newtons. According to the inverse square law, if the distance between the objects is now three times the original distance (3d), the new gravitational force can be calculated.
Since the distance has changed to three times the original distance, the new distance (3d) will be squared (3d)^2 = 9d^2.
Now, applying the inverse square law, we can calculate the new gravitational force:
(Original force) / (New force) = (Original distance)^2 / (New distance)^2
360 N / (New force) = d^2 / (9d^2)
To isolate the New force on one side, we can cross multiply:
360 N * (9d^2) = d^2 * (New force)
3240d^2 = d^2 * (New force)
Now divide both sides by d^2 to find the New force:
3240 = New force
Therefore, the new gravitational force between the objects is 3240 Newtons.
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.