Find the resultant force on (a) the mass m1 = 0.183 kg and (b) the mass m2 = 0.106 kg (the masses are isolated from the earth)..
The first mass is 400kg and its 10 cm from the second mass which is 0.183 kg (m1). the second mass is 10 cm away from the third mass which is 0.106 kg (m2).
Not enough info. You need to specify the directions of the masses from each other. The answer is very different if they're in a straight line, as opposed to at the vertices of an arbitrary triangle.
In any case, recall that F = GmM/r^2
Those are the magnitudes of the vectors. You just need to point them in the right direction and add them up.
To find the resultant force on the masses, we need to consider the gravitational forces acting on each mass due to the other masses. The formula for the gravitational force between two masses is given by Newton's Law of Universal Gravitation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 x 10^-11 N(m/kg)^2), m1 and m2 are the masses of the objects, and r is the distance between the masses.
Let's break down the problem into parts:
(a) Resultant force on m1 (0.183 kg):
We have two masses acting on m1, one with a mass of 400 kg and another with a mass of 0.106 kg.
We can calculate the gravitational forces between m1 and both masses using the formula mentioned above.
1. Gravitational force between m1 and the mass of 400 kg:
F1 = G * ((m1 * m_mass2) / r^2)
= 6.67430 x 10^-11 * ((0.183 kg * 400 kg) / (0.1 m)^2)
= 3.67423 x 10^-5 N
2. Gravitational force between m1 and the mass of 0.106 kg:
F2 = G * ((m1 * m_mass3) / r^2)
= 6.67430 x 10^-11 * ((0.183 kg * 0.106 kg) / (0.1 m)^2)
= 2.68295 x 10^-6 N
The resultant force on m1 will be the vector sum of the forces F1 and F2. Since they are acting in the same direction, we can simply add them:
Resultant force on m1 = F1 + F2
= 3.67423 x 10^-5 N + 2.68295 x 10^-6 N
= 4.94252 x 10^-5 N
Therefore, the resultant force on m1 is approximately 4.94252 x 10^-5 Newtons.
(b) Resultant force on m2 (0.106 kg):
We only have one mass acting on m2, which is the mass of 0.183 kg.
Using the same formula mentioned above, we can calculate the gravitational force between m2 and m1:
F3 = G * ((m2 * m_mass1) / r^2)
= 6.67430 x 10^-11 * ((0.106 kg * 0.183 kg) / (0.1 m)^2)
= 1.22974 x 10^-5 N
Therefore, the resultant force on m2 is approximately 1.22974 x 10^-5 Newtons.