To calculate the magnitude of the gravitational force exerted on one sphere by the other three, we can use Newton's Law of Universal Gravitation. According to this law, the magnitude of the gravitational force between two objects is given by the equation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.
In this case, we have four 9.0 kg spheres located at the corners of a square. Let's refer to the sphere in the left and down corner as sphere A and the other three spheres as spheres B, C, and D. Since the distance between each sphere and the sphere A is the same (the side length of the square, 0.60 m), we can calculate the gravitational force between each pair of spheres and then sum them up to find the total gravitational force on sphere A.
First, let's calculate the gravitational force between sphere A and each of the other three spheres. Using the given mass of each sphere (9.0 kg) and the distance between them (0.60 m), we can substitute these values into the formula:
F_AB = G * (m_A * m_B) / r^2
F_AC = G * (m_A * m_C) / r^2
F_AD = G * (m_A * m_D) / r^2
Now we can calculate each of these forces:
F_AB = G * (9.0 kg * 9.0 kg) / (0.60 m)^2
F_AC = G * (9.0 kg * 9.0 kg) / (0.60 m)^2
F_AD = G * (9.0 kg * 9.0 kg) / (0.60 m)^2
Next, we can sum up these forces to find the total gravitational force on sphere A:
F_total = F_AB + F_AC + F_AD
Now, we need to substitute the values of the gravitational constant and the other variables into the equation and calculate the total force. The gravitational constant G is approximately 6.674 * 10^(-11) N(m/kg)^2.
Plugging in the values, we get:
F_total = (6.674 * 10^(-11) N(m/kg)^2) * [(9.0 kg * 9.0 kg) / (0.60 m)^2] + [(9.0 kg * 9.0 kg) / (0.60 m)^2] + [(9.0 kg * 9.0 kg) / (0.60 m)^2]
Calculating this expression will give us the magnitude of the gravitational force exerted on sphere A by the other three spheres.