Question

How much energy would be needed for a 100kg body to escape from the earth?radius of earh=6400 km

Answer 1

Answer:

Energy = 6400000 Joules

Explanation:

Given the following data;

Mass = 100kg

Radius of earth = 6400 km

To find the amount of energy required by the object to escape the velocity of the earth, we would apply the Law of Conservation of Energy.

This law states that energy cannot be destroyed but can only be converted or transformed from one form to another. Therefore, the sum of the initial kinetic energy and potential energy is equal to the sum of the final kinetic energy and potential energy.

Mathematically, it is given by the formula;

Ki + Ui = Kf + Uf .......equation 1

Where;

Ki and Kf are the initial and final kinetic energy respectively.

Ui and Uf are the initial and final potential energy respectively.

At the earth surface, potential energy with respect to the radius of the earth is given by the formula;

$Ui = - \frac {GM}{R}$ ......equation 2.

Also, at the earth surface, kinetic energy is given by the formula;

$K.E = \frac{1}{2}MV^{2}$ .......equation 3.

After escaping the earth, the object wouldn't have both kinetic and potential energy; Kf = Uf = 0

Substituting eqn 2 & 3 into eqn 1, we have;

$\frac{1}{2}MV^{2} - \frac {GM}{R} = 0$

$\frac{1}{2}MV^{2} = \frac {GM}{R}$

Making "V" the subject of formula;

$RMV^{2} = 2GM$

$V^{2} = \frac {2GM}{RM}$

$V^{2} = \frac {2G}{R}$

Therefore, energy = gmR

Energy = 10 * 100 * 6400

Energy = 6400000 Joules