Four identical masses of 2.6 kg each are located at the corners of a square with 1.5 m sides. What is the net force on any one of the masses?
This question is not well enough explained. Are the masses in empty space and attracted only by the gravitational attraction of the other three masses? Or are they sitting on the ground somewhere? In the latter case, if they don't move, the net force on each mass is zero. In the former case, use Newton's universal law of gravity
F = G M1 M2/R^2
and add up the forces due to the other three masses, treating them as vectors. There will be a VERY small net force of attraction towards the center of the square. R = 1.5 meters for the adjacent two masses and 1.5 sqrt2 meters for the mass located diagonally across. For the two adjacent masses, the vector sum is along the diagonal.
To find the net force on any one of the masses, we need to calculate the gravitational force exerted by the other three masses on it.
First, let's calculate the gravitational force between two masses. The gravitational force between two objects can be calculated using Newton's law of universal gravitation:
F = (G * m₁ * m₂) / r²
Where:
F is the gravitational force between the masses
G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N m²/kg²)
m₁ and m₂ are the masses of the two objects
r is the distance between the centers of the two objects
In our case, all the masses are identical (2.6 kg) and located at the corners of a square with 1.5 m sides. The distances between the corners are equal to the length of one side of the square, which is 1.5 m.
Now, let's calculate the force exerted by the other three masses on any one of the masses.
1. Calculate the distance between two masses (diagonal of the square):
d = √(s² + s²)
d = √(1.5 m)² + (1.5 m)²
d = √(2.25 m² + 2.25 m²) = √4.5 m²
d ≈ 2.12 m
2. Calculate the gravitational force between two masses:
F = (G * m₁ * m₂) / r²
F = (6.674 × 10⁻¹¹ N m²/kg²) * (2.6 kg) * (2.6 kg) / (2.12 m)²
F ≈ (6.674 × 10⁻¹¹ N m²/kg²) * (6.76 kg²) / (4.5 m²)
F ≈ 10⁻¹¹ N
3. Since there are three other masses, we need to multiply the force calculated in step 2 by 3:
net force = 3 * F
net force ≈ 3 * 10⁻¹¹ N
net force ≈ 3 * 0.00000000001 N
net force ≈ 0.00000000003 N
Therefore, the net force on any one of the masses is approximately 0.00000000003 Newtons.