The gravitational force between two objects is 360 Newtons. 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 call the original distance between the objects "d". The original gravitational force between them is 360 Newtons.
If the distance between the objects is now three times the original distance, then the new distance is 3d.
According to the inverse square law, the new gravitational force (F') can be calculated using the formula:
F' = (F * d^2) / (3d)^2
Where F is the original gravitational force, d is the original distance, and F' is the new gravitational force.
Simplifying the equation:
F' = (F * d^2) / (9d^2)
F' = F / 9
So the new gravitational force between the objects is 360 Newtons divided by 9, which is 40 Newtons.
To find the new gravitational force between the objects, we need to use the inverse-square law of gravitation. According to Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.674 x 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the objects
r is the distance between the centers of the objects
Since we know that the force is 360 Newtons, we can rearrange the equation to solve for the original distance (r).
360 = G * (m1 * m2) / r^2
Multiplying both sides by r^2 and dividing by F gives:
r^2 = G * (m1 * m2) / 360
Taking the square root of both sides gives:
r = sqrt(G * (m1 * m2) / 360)
Now, to find the new distance (r') between the objects, which is three times the original distance, we have:
r' = 3 * r
Substituting the value of r from the previous equation into this equation, we get:
r' = 3 * sqrt(G * (m1 * m2) / 360)
To find the new gravitational force (F'), we can once again use the inverse-square law of gravitation with the new distance (r'):
F' = G * (m1 * m2) / (r')^2
Substituting the value of r' we just found into this equation:
F' = G * (m1 * m2) / (3 * sqrt(G * (m1 * m2) / 360))^2
Simplifying this equation gives:
F' = G * (m1 * m2) / (9 * (G * (m1 * m2) / 360))
Canceling out common terms gives:
F' = 360 / 9
Therefore, the new gravitational force between the objects is:
F' = 40 Newtons.
To solve this problem, we can use Newton's law of universal gravitation, which states that 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 the original distance between the objects be represented by "d", and the new distance be represented by "3d". The ratio of the original distance to the new distance is 1:3.
According to the law of universal gravitation, the gravitational force is inversely proportional to the square of the distance. Therefore, if the distance is tripled, the force is reduced by a factor of 3^2 = 9.
So, if the original gravitational force between the objects was 360 Newtons, the new gravitational force can be calculated as follows:
New gravitational force = (Original gravitational force) / (Distance ratio)
= 360 N / 9
= 40 N
Therefore, the new gravitational force between the objects is 40 Newtons.