(a) How much gravitational potential energy (relative to the ground on which it is built) is stored in the Great Pyramid of Cheops, given that its mass is about 7×109kg and its center of mass is 36.5 m above the surrounding ground? (b) How does this energy compare with the daily food intake of a person? [assuming that one regular calorie is 4.184 J and that a person’s daily food intake is 2,500 food calories – note a food calorie is 1,000 regular calories]

(b) The gravitational energy stored in the Great Pyramid of Cheops is [tex]2.38 * 10^5[/tex] times greater than the daily food intake of a person (in Joules).

Explanation:

(a) Gravitational potential energy (with respect to the earth) is the energy possessed by an object due to its position from the surface of the earth.

It is given as:

[tex]PE = mgh[/tex]

where m = mass of object

g = acceleration due to gravity

h = height above the ground

∴ [tex]PE = 7 *10^9 * 9.8 * 36.5\\\\\\PE = 2.503 * 10^{12} J[/tex]

(b) A person's daily food intake = 2500 food calories

1 food calorie = 1000 regular calories

∴ 2500 food calories = 2500 * 1000 regular calories = 2500000 regular calories

We are given that :

1 regular calorie = 4.184 J

∴ 2500000 regular calories = 2500000 * 4.184 J = [tex]1.05 * 10^7 J[/tex]

Comparing this with the answer in (a) above:

[tex]\frac{2.503 * 10^{12} J}{1.05 * 10^7 J}\\\\\\\frac{2.38 * 10^5}{1}\\ \\\\2.38 * 10^5 : 1[/tex]

The gravitational energy stored in the Great Pyramid of Cheops is [tex]2.38 * 10^5[/tex] times greater than the daily food intake of a person (in Joules).