object A exerts a gravitational force of magnitude 8.2 x 10^-10 N on object B. determine the magnitude of the gravitational force if, simultaneously, the separation distance is tripled, mA increased by 4 times and m8 is halved. explain your reasons and show all calculations.
the product of masses is 4*1/2 or twice. Separatdion is tripled, so Force is 1/9
new force= old force* 2/9
To determine the magnitude of the gravitational force in the given scenario, we can use the formula for gravitational force:
F = (G * mA * mB) / r^2
where:
F is the gravitational force,
G is the gravitational constant (approximately 6.674 × 10^-11 N*m^2/kg^2),
mA and mB are the masses of objects A and B, respectively, and
r is the separation distance between objects A and B.
Let's calculate the magnitude of the gravitational force after the given changes are applied.
1. Tripled separation distance (r):
If the separation distance is tripled, it becomes 3r, where r is the initial separation distance.
2. 4 times increase in mass mA:
If mA is increased by 4 times, the new mass would be 4mA.
3. Halved mass mB:
If mB is halved, the new mass would be mB/2.
Now, let's substitute these values into the formula and solve step by step:
F' = (G * (4mA) * (mB/2)) / (3r)^2
First, let's simplify the equation:
F' = (G * 4mA * mB/2) / (9r^2)
= (2G * 2mA * mB) / (9r^2)
= (4G * mA * mB) / (9r^2)
= (4 * (8.2 x 10^-10 N) * mA * mB) / (9r^2)
Substituting the values into the equation gives:
F' = (4 * (8.2 x 10^-10 N) * (4mA) * (mB/2)) / (9(3r)^2)
= (4 * (8.2 x 10^-10 N) * (4 * mA) * (mB/2)) / (9 * (3r)^2)
Now, multiply and divide as needed:
F' = (4 * 8.2 x 10^-10 N * 4 * mA * mB) / (9 * 3^2 * r^2)
= (2 * 8.2 x 10^-10 N * mA * mB) / (9 * r^2)
Finally, we can substitute the given values into the equation.