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What will be the potential energy of a body of mass 67 kg at a distance of \(6.6 \times 10^{10}\) m from the center of the Earth?

Find the gravitational potential at this distance.

Answer :

Final answer:

The potential energy of the body at the given distance is 4.5 * 10^13 J and the gravitational potential at that distance is 5.7 * 10^7 J/kg.

Explanation:

The potential energy of a body at a distance from the center of the Earth can be calculated using the formula:

Potential Energy = mass * gravitational acceleration * distance

In this case, the mass of the body is 67 kg, the distance from the center of the Earth is 6.6 * 1010 m, and the gravitational acceleration is approximately 9.8 m/s2.

Substituting the values into the formula, we get:

Potential Energy = 67 kg * 9.8 m/s2 * 6.6 * 1010 m

= 4.5 * 1013 J

The gravitational potential at a distance from the center of the Earth can be calculated using the formula:

Gravitational Potential = gravitational constant * mass / distance

In this case, the mass of the Earth is approximately 5.97 * 1024 kg, the distance from the center of the Earth is 6.6 * 1010 m, and the gravitational constant is approximately 6.6743 * 10-11 N m2/kg2.

Substituting the values into the formula, we get:

Gravitational Potential = (6.6743 * 10-11 N m2/kg2) * (5.97 * 1024 kg) / (6.6 * 1010 m)

= 5.7 * 107 J/kg

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