Gravitational force of attraction “F” exists between two point masses A and B when a fixed distance separates them. After mass A is doubled and mass B is quartered, the gravitational attraction between the two masses is
wouldn't the gravitational attraction stay the same and be 6.67 E -11 N*m2/kg2
as stated in the equation?
I'm sorry I'm having a really hard time with this
To determine the gravitational attraction between two point masses A and B after their masses are changed, 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 their centers.
Let's denote the initial masses of A and B as mA and mB, respectively, and the initial gravitational force between them as F.
According to the problem, after mass A is doubled (2mA) and mass B is quartered (mB/4), we need to find the new gravitational force, let's call it F_new.
We can express Newton's Law of Universal Gravitation mathematically as:
F = G * (mA * mB) / d^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.6743 × 10^-11 N m^2 / kg^2)
mA and mB are the masses of the two objects
d is the distance between the centers of the masses
To find the new gravitational force, we substitute the new masses for mA and mB in the formula:
F_new = G * ((2mA) * (mB/4)) / d^2
= G * (2mA * mB) / (4 * d^2)
= (1/2) * (G * (mA * mB) / d^2)
Therefore, the gravitational force of attraction between the two masses A and B, after mass A is doubled and mass B is quartered, is half (1/2) of the initial gravitational force F.