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Objects with masses of 116 kg and 364 kg are separated by 0.42 m. A 57.1 kg mass is placed midway between them. Find the magnitude of the net gravitational force exerted by the two larger masses on the 57.1 kg mass.

Answer :

Final answer:

The net gravitational force on a 57.1 kg mass placed midway between masses of 116 kg and 364 kg separated by 0.42 m can be found using Newton's law of universal gravitation. The forces exerted by the two larger masses on the smaller mass are calculated separately using the gravitational formula and then summed vectorially to find the net force.

Explanation:

To calculate the net gravitational force exerted by two larger masses on a 57.1 kg mass that is placed midway between them, we use Newton's law of universal gravitation. The formula to find the gravitational force between two masses is F = G∙(m1∙m2) / r², where F is the force, G is the gravitational constant (6.674 × 10⁻¹¹ N∙m²/kg²), m1 and m2 are the masses, and r is the distance between the centers of the two masses.

The mass of the objects are 116 kg and 364 kg, and the distance between them is 0.42 m, hence the 57.1 kg mass is 0.21 m from each of the larger masses. We calculate the gravitational forces separately due to each mass and then find their vector sum, since they will be exerting the forces from opposite sides.

However, the details of the calculations are not included here, and you will need to perform the computations using the formula provided and the values given to find the magnitude of the net gravitational force acting on the 57.1 kg mass.

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