Question

(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$\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{\text{kg}}$and its center of mass is 36.5m above the surrounding ground?

(b) How does this energy compare with the daily food intake of a person?

Short answer

(a) The gravitational potential stored in the Great Pyramid of Cheops is $2.50\times {10}^{12}\text{J}$.

(b) The gravitational potential energy of the Great Pyramid of Cheops is 208333.33 times greater than the energy of food intake of an adult.

Step-by-step solution

Definition of Concept

Gravitational potential: The gravitational potential energy is stored in the body due to virtue of its position.

The expression of gravitational energy is given as,

$E_p=mgh$ (1.1)

Here, m is the mass of the object, g is the acceleration due to gravity, h is the height the object is lifted up from the surface of Earth.

The Gravitational potential energy stored in the Great Pyramid of Cheops

(a)

Considering the given values,

Putting$7\times {10}^9\text{kg}$ for m,$9.8\text{m}/{\text{s}}^2$ for g, and 36.5 m for h in equation (1.1),

$\begin{array}{rcl}{E}_p& =& \left(7\times {10}^9\text{kg}\right)\times \left(9.8\text{m}/{\text{s}}^2\right)\times \left(36.5\text{m}\right)\\ & =& 2.50\times {10}^{12}\text{J}\end{array}$

Therefore, the required gravitational potential stored in the Great Pyramid of Cheops is $2.50\times {10}^{12}\text{J}$.

Comparing energies

(b)

The energy contain of the daily food intake of an adult is,

$E_f=1.2\times {10}^7\text{J}$

Comparing energies,

$\begin{array}{rcl}\frac{E_p}{E_f}& =& \frac{2.50\times {10}^{12}\text{J}}{1.2\times {10}^7\text{J}}\\ \frac{E_p}{E_f}& =& 208333.33\\ E_p& =& 208333.33\end{array}$

Therefore, the gravitational potential energy of the Great Pyramid of Cheops is 208333.33 times greater than the energy of food intake of an adult.