Answer :
Final answer:
By calculating the forces exerted by the two larger bodies on the smaller body separately using Newton's Law of Gravitation, and subtracting them due to their opposite directions, the net force for part (a) can be found. For part (b), by setting these forces equal, the position at which the smaller body experiences zero net force can be found.
Explanation:
To solve this problem, we need to utilize Newton's Law of Universal Gravitation and the Law of Force and Acceleration (Newton's second law). To find the net gravitational force of the 195 kg and 495 kg objects on the 46.0 kg object when it is placed midway, each force should be calculated separately and then subtracted since they act in opposite directions.
The force exerted on the 46.0 kg object by the 195 kg object (or Mass1) is calculated using the formula F1 = G*M1*m/R², and similarly, the force exerted by the 495 kg object (or Mass2) is F2 = G*M2*m/R², where G is the gravitational constant, m is the mass of the 46.0 kg object, and R is the separation. Using the given values and subtracting F2 from F1 will provide the net force in magnitude (N).
To answer part (b), net force will be zero where forces from Mass1 and Mass2 are equal. We can solve the equation F1 = F2, where R represents Mass1's distance from the 46 kg object and 0.480 - R is the distance from Mass2. Solving this equation would provide the position where net force is zero.
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Final answer:
The 46.0 kg object placed midway between a 195 kg and a 495 kg object would experience a net gravitational force of zero because the forces exerted by the two larger masses are equal and opposite. To find another position with zero net force, one would solve for a distance that equates the forces exerted by the two masses.
Explanation:
To find the net gravitational force exerted by two objects on a third object placed midway between them, we can use Newton's law of universal gravitation. The force between two masses is given by the equation F = Gm1m2/d², where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), m1 and m2 are the masses of the two objects, and d is the separation distance between their centers.
To calculate the net force on a 46.0 kg object placed midway between a 195 kg and a 495 kg object separated by 0.480 m, we need to consider that the gravitational force exerted by each mass will be equal and opposite, as they are equidistant from the 46.0 kg object, thus canceling each other out, resulting in a net force of zero.
For part (b), the 46.0 kg object can be placed at a position where the gravitational forces exerted by the two larger masses are equal and opposite. This requires solving the equation F1 = F2 for the unknown distance from one of the masses such that the product of the distance squared and the mass for both objects is equal, accounting for the differing masses of the two larger objects. Typically, this position will not be at the halfway point, as the masses are unequal.
