Two objects attract each other gravitationally with a force of 2.9 10-10 N when they are 0.29 m apart. Their total mass is 4.0 kg. Find their individual masses.
To find the individual masses of the two objects, we can use Newton's law of universal gravitation, which states that the attractive 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 to calculate the gravitational force (F) is given by:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (6.67430 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between their centers.
From the problem, we know that the gravitational force between the objects is 2.9 * 10^-10 N and the distance between them is 0.29 m. Also, the total mass of the two objects is given as 4.0 kg.
Substituting the given values in the formula, we get:
2.9 * 10^-10 = (6.67430 × 10^-11 * m1 * m2) / (0.29)^2
Simplifying, we get:
m1 * m2 = (2.9 * 10^-10 * (0.29)^2) / (6.67430 × 10^-11)
Next, we need to find the individual masses. Since the total mass of the two objects is given as 4.0 kg, we can express one mass in terms of the other. Let m1 be the mass of one object and m2 be the mass of the other object.
We can write:
m1 + m2 = 4.0 kg
Rearranging the equation, we get:
m2 = 4.0 kg - m1
Now, substitute this value of m2 in the equation m1 * m2 = (2.9 * 10^-10 * (0.29)^2) / (6.67430 × 10^-11):
m1 * (4.0 kg - m1) = (2.9 * 10^-10 * (0.29)^2) / (6.67430 × 10^-11)
This is a quadratic equation. Solve it to find the value of m1. Once you have the value of m1, substitute it back into m2 = 4.0 kg - m1 to find the value of m2.