Question

Using Equation 3, what is the force of gravity between you and Earth, assuming all of the Earth's mass is at its center and you are standing at sea level? The mass of the Earth is approximately 5.900 x 1024 kg. At sea level, the distance to the center of the Earth is approximately 3,959 miles. Be mindful of your units, and show your work. Report your answer with four significant figures.

Answer 1

679.1N

Explanation:

Assuming equation 3 is Newton's universal law of gravity:

`F_g = G(m_1m_2)/(d^2)`

Where G is the universal gravity constant:

`G=6.673 x10^(-11)(Nm^2)/(kg^2)`

You need to express the radius of earth in m:

`3959mi*(1609m)/(1mi)=6.370*10^6m`

If you weight 70Kg, just replace the values in the equation:

`F_g = 6.673 *10^(-11)*(70*5.900*10^(24))/((6.370*10^6)^2)= 6.673 *10^(-11)*(4.13*10^(26))/(4.058*10^(13))=\\6.673*10^(-11)*1.018*10^(13)= 679.1N`