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How much gravitational potential energy (relative to the ground on which it is built) is stored in an Egyptian pyramid, given its mass is about 4 ✕ 10⁹ kg and its center of mass is 20.0 m above the surrounding ground?

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Final answer:

The gravitational potential energy of the Great Pyramid of Cheops is calculated to be about 2.2 x 10^12 J. This energy is much larger than the daily food intake of a person.

Step-by-step explanation:

The gravitational potential energy of an object can be calculated using the formula E = mgh, where E is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the ground. In the case of the Great Pyramid of Cheops, with a mass of about 7 × 109 kg and a center of mass 36.5 m above the surrounding ground, the gravitational potential energy can be calculated as:



E = (7 × 109 kg) × (9.8 m/s2) × (36.5 m) = 2.2 × 1012 J



This energy is a measure of the work done to lift the pyramid to its current height. To compare it with the daily food intake of a person, which is typically around 2000-2500 kcal (equivalent to about 8.4-10.5 MJ), we can see that the gravitational potential energy stored in the pyramid is much larger.

The amount of gravitational potential energy (GPE) stored in an object, such as a pyramid, can be calculated using the formula GPE = mgh, where 'm' is the mass of the object, 'g' is the acceleration due to gravity (9.8 m/s² on Earth), and 'h' is the height of the object's center of mass above the reference point, in this case, the ground.

For the Egyptian pyramid with a mass of about 4 × 10⁹ kg and its center of mass 20.0 m above the ground, the calculation would be:

GPE = mgh

GPE = (4 × 10⁹ kg) × (9.8 m/s²) × (20.0 m)

GPE = 7.84 × 10±¹ J (joules)

This gives us the gravitational potential energy of the pyramid relative to the ground on which it is built.

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