Three masses that are 10 kg each are located at the corners of an equilateral triangle, with side length of 0.55m. What is the magnitude of the total force acting on one mass due to the other two masses?

The answer is supposed to be 3.82e-08 N. Any help is appreciated. I'm not sure where to even start this question.

Let the mass m3 be in the origin of the coordinate system, m2 be on x-axis (separated by 0.55 m from origin), and m1 is above x-axis. m1=m2=m3=m=10 kg, a=0.55 m.

The gravitational constant is
G =6.67•10^-11 N•m²/kg²,

F2 =F2x=G•m2•m3/a²,
F1x = (G•m1•m3/a²)•cos60º,
F1y=(G•m1•m3/a²)•sin60º,
F(net)x= F2x+F1x= G•m2•m3/a² +(G•m1•m3/a²)•cos60º=1.5•G•m2•m3/a²,
F(net)y = F1y=(G•m1•m3/a²)•sin60º= 0.866• G•m2•m3/a²,
F(net) =sqrt[(F(net)x)²+( F(net)y)²] = G•m²/a² •sqrt(1.5²+0.866²)=
=1.73•6.67•10^-11•100/0.55²=3.82•10^-8 N.

To find the magnitude of the total force acting on one mass due to the other two masses, you can use Newton's law of universal gravitation. This law states that the gravitational force between two masses is given by:

F = (G * m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2), m1 and m2 are the masses, and r is the distance between the centers of the two masses.

In this case, all three masses are equal to 10 kg, and the distance between them is the side length of the equilateral triangle, which is given as 0.55 m.

To calculate the force exerted on one mass by the other two masses, you need to consider the gravitational force between each pair of masses individually and then sum them up.

Let's calculate the force between mass m1 and m2:

F12 = (G * m1 * m2) / r^2

F12 = (6.67430 × 10^-11 N m^2/kg^2 * 10 kg * 10 kg) / (0.55 m)^2

F12 = (6.67430 × 10^-11 N m^2/kg^2 * 100 kg^2) / (0.55 m)^2

F12 = 1.2126 × 10^-10 N

Since the triangle is equilateral, the distance between any two masses is the same. So, the magnitude of the total force acting on one mass due to the other two masses is twice the force between any two masses:

Ftotal = 2 * F12

Ftotal = 2 * 1.2126 × 10^-10 N

Ftotal = 2.4252 × 10^-10 N

This result is not equal to the given answer of 3.82e-08 N. There might be some additional information or assumptions in the problem that could lead to the correct answer.