Final answer:
To find the net gravitational force on each mass at the corners of the equilateral triangle, Newton's law of universal gravitation should be applied, and the net force would have to consider the contributions from both of the other two masses along with the angles involved due to the shape of the triangle.
Step-by-step explanation:
The question asks for the magnitude of the net force exerted on each of the three masses placed at the corners of an equilateral triangle in space. We are given that each mass is 7.50 kg and the length of each side of the triangle is 1.41 m. To solve this, we can apply Newton's law of universal gravitation, which states that the force of attraction between any two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The force exerted on one mass by another is given by:
F = (G ⋅ m1 ⋅ m2) / r^2
Where G is the gravitational constant (6.674 × 10^-11 N⋅m^2/kg^2), m1 and m2 are the masses, and r is the distance between the masses.
Since each mass is the same and is experiencing the gravitational pull from two other masses, we can calculate the gravitational force from one mass to another and then find the net force at the angle which will be 60 degrees because the forces act along the sides of an equilateral triangle.
However, without doing the complete calculation, we cannot provide the numerical value of the net force. But the method described here is how you would go about calculating it.