Question

Earth has a large mass. If you have a mass of 100 pounds (convert to kilograms) What is the gravitational force that you exert on earth? (the acceleration due to earth’s gravity is 9.8m/s^2).

Answer 1

We are asked to find the gravitational force that you exert on earth.

First, convert the mass of 100 pounds into kg.

1 kg is equal to 2.205 pounds.

`(100)/(2.205)=45.36\; kg`

Recall Newton's Universal law of gravitation given by

`F_G=G(M\cdot m)/(R^2)`

Where M is the mass of Earth, m is the mass of the person, G is the gravitational constant, and R is the radius of the Earth.

G = 6.67×10⁻¹¹ m³/kg⋅s²

M = 5.97×10²⁴ kg

R = 6.37×10⁶ m

m = 45.36

Let us substitute all the given values into the above formula

`\begin{gathered} F_G=G(M\cdot m)/(R^2) \\ F_G=6.67*10^(-11)\cdot(5.97*10^(24)\cdot45.36)/((6.37*10^6)^2) \\ F_G=445.14\; N \end{gathered}`

Therefore, the gravitational force that you exert on earth is 445.14 N