The gravitatioinal force between two metal sphere in outer space is 2000 N. How large would the force be if the two spheres were four times farter apart?
The gravitational force between two objects is inversely proportional to the square of the distance between them. If the two spheres were four times farther apart, the distance between them would be multiplied by a factor of 4.
Let's represent the original distance between the spheres as "d". If the original force is 2000 N, the equation for the force-distance relationship can be expressed as:
F = k / d^2
Where F is the force, d is the distance, and k is the constant of proportionality.
Let's call the new distance between the spheres "4d". To find the new force, we can substitute the new distance into the equation:
F' = k / (4d)^2
Simplifying this equation, we get:
F' = k / 16d^2
Since k is a constant, we can ignore it for this comparison.
Therefore, the new force would be 1/16th (or 1/4^2) of the original force:
F' = 1/16 * 2000 N = 125 N
So, if the two spheres were four times farther apart, the force between them would be 125 N.
To determine how the force between two spheres changes when the distance between them is altered, we can rely on the inverse square law of gravity. According to this law, the gravitational force between two objects is inversely proportional to the square of the distance between their centers. Mathematically, it can be expressed as:
F ∝ 1/r²
Where F represents the force and r denotes the distance between the centers of the spheres.
To find out how the force changes when the distance is altered, we can use the following equation, where F1 is the initial force and F2 is the force when the distance is modified:
F2 = F1 × (r1/r2)²
In our scenario, the initial force (F1) is given as 2000 N, and we need to find the force (F2) when the distance between the spheres is four times greater.
Let's denote the initial distance between the spheres as r1 and the new distance as r2. Since the initial force (F1) and the new distance (r2) are unknown, we need to determine them before calculating the new force (F2).
Given that the initial force (F1) is 2000 N, we do not need to calculate it. However, let's assume that the initial distance (r1) between the spheres is "x" units.
Using the inverse square law of gravity, we have:
F1 = 2000 N
r1 = x
To find the new distance (r2), we know that it is four times greater than the initial distance (r1). Therefore:
r2 = 4 × r1
= 4 × x
Now, substituting the known values into the formula for F2:
F2 = F1 × (r1/r2)²
= 2000 N × (x/(4 × x))²
= 2000 N × (1/4)²
= 2000 N × 1/16
= 2000 N/16
= 125 N
Therefore, the force between the two spheres would be 125 N if the distance between them is four times greater.