2 objects are .25m apart and exert a force of 2.5x10^-10 N on each other. Thier total mass is 4 kg. what is the mass of each?
Apply Newton's Universal Law of Gravity and solve for M1*M2.
F = 2.5*10^-10 = G M1*M2/(0.25)^2
Once you know M1*M2 and M1 + M2 (= 4 kg), you can solve for M1 and M2 separately.
To solve this problem, we need to apply 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.
The formula for Newton's law of universal gravitation is:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (6.67 × 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
In this case, we are given the force (F = 2.5 × 10^-10 N), the distance (r = 0.25 m), and the total mass (4 kg).
First, we can rearrange the formula to solve for the product of the masses (m1 * m2):
m1 * m2 = (F * r^2) / G
Substituting the given values:
m1 * m2 = (2.5 × 10^-10 N) * (0.25 m)^2 / (6.67 × 10^-11 N m^2/kg^2)
m1 * m2 = 2.5 × 10^-10 N * 0.0625 m^2 / 6.67 × 10^-11 N m^2/kg^2
m1 * m2 = 0.000000000016 N m^2 / kg
Now, since the total mass of both objects is given as 4 kg, we can assume that each object has half of this mass (2 kg).
So, m1 = 2 kg and m2 = 2 kg.
Therefore, the mass of each object is 2 kg.