Answer :
Final answer:
The question involves using Newton's law of universal gravitation to calculate the specific point at which a 64 kg mass feels no net gravitational force due to the presence of two other masses. It requires equating the gravitational pull from both masses on the 64 kg object and finding the distance at which these forces balance out. Detailed calculations would follow by setting up and solving an equation derived from the law of gravitation.
Explanation:
The question involves using Newton's law of universal gravitation to determine at which distance from a 579 kg mass a 64 kg mass experiences a net force of zero, given the presence of another mass (215 kg) at a fixed distance. Newton's law states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them (F = GmM/r²) where G is the gravitational constant.
To find the point where the 64 kg mass experiences no net force, we need to set the forces exerted on it by the two other masses to be equal in magnitude but opposite in direction. The complexity of the question lies in balancing these forces, acknowledging that the 64 kg mass will be in equilibrium when the gravitational pull from the 579 kg mass is exactly counteracted by the pull from the 215 kg mass.
Comprehensive calculation or derivation steps would involve setting up an equation based on the gravitational forces ( F1 = Gm1m3/r1² and F2 = Gm2m3/r2²), where m1 and m2 are the masses of 579 kg and 215 kg objects, m3 is the mass of the 64 kg object, and r1 and r2 are the respective distances from the 579 kg and 215 kg masses to the 64 kg mass. Due to the complexity and specific numerical values required, this setup leads to an equation that can be solved using mathematical techniques not detailed here.
