High School

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Leaving the distance between the 193 kg and the 348 kg masses fixed, at what distance from the 348 kg mass (other than infinitely remote ones) does the 61.2 kg mass experience a net force of zero?

Answer in units of meters (m).

Answer :

Final answer:

The problem is solved by equating the gravitational forces exerted on a 61.2 kg mass by two fixed masses, 193 kg and 348 kg, and finding the distance from the 348 kg mass where these forces cancel each other out.

Explanation:

The student's question involves finding the specific point where a third object, of mass 61.2 kg, experiences a net gravitational force of zero when placed at a certain distance from two other masses, one of 193 kg and the other of 348 kg. The gravitational force acting on the object due to both masses must be equal and in opposite directions for the net force to become zero.

To solve this problem, we use Newton's law of universal gravitation, which is given by the formula F = GmM/r², where F is the force of gravity between two masses, G is the universal gravitational constant (6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²), m and M are the masses of the two objects, and r is the distance between their centers.

The condition for the net force on the 61.2 kg mass to be zero is that the gravitational forces due to both the 193 kg and 348 kg masses are equal in magnitude. By setting up the equation for gravitational force due to each mass and solving for the distance from the 348 kg mass, we can find the spot where the net force on the 61.2 kg mass is zero.

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