Calculate the gravitational potential energy of the interacting pair of the Earth and a 14kg block sitting on the surface of the Earth. You would need to supply the absolute value of this result to move the block to a location very far from the Earth (actually, you would need to use even more energy than this due to the gravitational potential energy associated with the Sun-block interacting pair).

The gravitational potential energy is

8.74 ×10^8Joules

Explanation:

To find the gravitational potential energy between ANY two objects that have mass, such as the Earth and the moon, you need to know the universal gravitational constant (G), the mass of the two objects (M and m), and the center to center distance between them (r).

The equation for determining gravitational potential energy Ug = - GMm/r

Where G = gravitational constant 6.67×10^-11

r = radius of the earth = 6.378×10^6m

M = mass of the earth = 5.97 ×10^24kg

m = mass of object = 14kg

Substituting into the equation

Ug = [( 6.67×10^11)(5.97×10^24)(14)] / (6.378×10^6)

Ug = (5.575×10^15)/(6.378×10^6)

Ug = 8.74 ×10^8 Joules

U = 8.75×10⁸J

Explanation:

U = gravitational potential energy = GMm/Re

G = Gravitational constant = 6.67×10-¹¹ Nm²/kg²

M = mass of the earth = 5.98×10²⁴kg

m = mass of the block = 14kg

Re = distance of the object from the center of the object = radius of the earth = 6.38×10⁶m

U = (6.67×10-¹¹ ×5.98×10²⁴×14)/(6.38×10⁶)

U = 8.75×10⁸J