High School

Objects with masses of 157 kg and 768 kg are separated by 0.342 m. A 28.7 kg mass is placed midway between them.

Mass arrangement:
- 157 kg ---- 28.7 kg ---- 768 kg

Find the magnitude of the net gravitational force exerted by the two larger masses on the 28.7 kg mass.

The value of the universal gravitational constant is [tex]6.672 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2[/tex].

Answer :

Final answer:

The magnitude of the net gravitational force exerted by the two larger masses on the 28.7 kg mass is approximately 1.25 × 10^-6 N.

Explanation:

The force of gravity, or gravitational force, pulls objects with mass toward each other. We often think about the force of gravity from Earth. This force is what keeps your body on the ground. But any object with mass exerts a gravitational force on all other objects with mass.

To find the magnitude of the net gravitational force exerted by the two larger masses on the 28.7 kg mass, we can use Newton's law of universal gravitation. The formula for the gravitational force is: F = G * ((m1 * m) / r^2) + G * ((m2 * m) / r^2). Plugging in the given values, we get: F = 6.672 × 10^-11 * ((157 * 28.7) / (0.342/2)^2) + 6.672 × 10^-11 * ((768 * 28.7) / (0.342/2)^2). Simplifying the equation and calculating, the magnitude of the net gravitational force is approximately 1.25 × 10^-6 N.


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