Final answer:
The net gravitational force on the mass at the origin can be calculated by using Newton's Law of Universal Gravitation and considering the forces from each of the other two masses separately before summing them to find the net force.
Step-by-step explanation:
The magnitude of the net gravitational force (Fgrav) on the mass at the origin can be calculated using Newton's Law of Universal Gravitation, which states that the force between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Considering the masses are on the x-axis, the forces due to the other two masses will be along this line, and since they are of equal magnitude and opposite direction, we can subtract the force due to the closer mass from the force due to the farther mass to find the net force on the mass at the origin.
To calculate this, you would use the gravitational constant G (6.674 × 10-11 N.m2/kg2), the mass of the weights (7500 kg each), and their positions (x1 = -100 cm and x2 = 420 cm from the origin). The force from each mass on the mass at the origin is computed separately, and then the net force is found by taking the vector sum of these two forces.