Question

Predict the magnitude of the gravitational force a 66.5 kg person would experience while standing on the surface of each of Earth
Mass: 5.97 × 10^24 kg Radius 6.38 × 10^6 m.
a. 246 Nb. 651 N.c. 38.5 N.d. 0.692 N.

Answer 1

Answer:

651 N

Explanation:

m = Mass of person = 66.5 kg

M = Mass of Earth = $5.97\times 10^{24}\ kg$

G = Gravitational constant = $6.67\times 10^{-11}\ m^3/kgs^2$

R = Radius of Earth = $6.38\times 10^6\ m$

The acceleration that the person is experiencing will balance the gravitational force

$ma=G\frac{Mm}{r^2}\\\Rightarrow a=G\frac{M}{r^2}\\\Rightarrow a=6.67\times 10^{-11}\frac{5.97\times 10^{24}}{(6.38\times 10^6)^2}\\\Rightarrow a=9.7827\ m/s^2$

The acceleration due to gravity is 9.7827 m/s² = g

The gravitational force would be

$W=mg\\\Rightarrow W=66.5\times 9.7827\\\Rightarrow W=650.54955\ N=651\ N$

The magnitude of the gravitational force on the person is 651 N