Question

1. Find the magnitude of the gravitational force a 66.5 kg person would experience

Answer 1

Answer:

Gravitational forces: Earth: $W = 650.969\,N$, Mars: $W = 246.449\,N$, Pluto: $W = 38.504\,N$

Explanation:

The weight ($W$), measured in newtons, experimented by the person on the surface of the planet is defined by Newton's Laws of Motion:

$W = m\cdot g$ (1)

Where:

$m$ - Mass, measured in kilograms.

$g$ - Gravitational acceleration, measured in meters per square second.

From Newton's Law of Gravitation we derive this expression for gravitational acceleration:

$g = \frac{G\cdot M}{R^{2}}$ (2)

Where:

$G$ - Gravitational constant, measured in cubic meters per kilogram-square second.

$M$ - Mass of the planet, measured in kilograms.

$R$ - Radius of the planet, measured in meters.

By (2) we calculate the gravitational acceleration for each planet:

Earth ($G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}$, $M = 5.97\times 10^{24}\,kg$, $R = 6.38\times 10^{6}\,m$)

$g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (5.97\times 10^{24}\,kg)}{(6.38\times 10^{6}\,m)^{2}}$

$g = 9.789\,\frac{m}{s^{2}}$

Mars ($G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}$, $M = 6.42\times 10^{23}\,kg$, $R = 3.40\times 10^{6}\,m$)

$g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (6.42\times 10^{23}\,kg)}{(3.40\times 10^{6}\,m)^{2}}$

$g = 3.706\,\frac{m}{s^{2}}$

Pluto ($G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}$, $M = 1.25\times 10^{22}\,kg$, $R = 1.20\times 10^{6}\,m$)

$g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (1.25\times 10^{22}\,kg)}{(1.20\times 10^{6}\,m)^{2}}$

$g = 0.579\,\frac{m}{s^{2}}$

Lastly, we calculate the gravitational force for each case by (1):

Earth ($m = 66.5\,kg$, $g = 9.789\,\frac{m}{s^{2}}$)

$W =(66.5\,kg)\cdot \left(9.789\,\frac{m}{s^{2}} \right)$

$W = 650.969\,N$

Mars ($m = 66.5\,kg$, $g = 3.706\,\frac{m}{s^{2}}$)

$W = (66.5\,kg)\cdot \left(3.706\,\frac{m}{s^{2}} \right)$

$W = 246.449\,N$

Pluto ($m = 66.5\,kg$, $g = 0.579\,\frac{m}{s^{2}}$)

$W = (66.5\,kg)\cdot \left(0.579\,\frac{m}{s^{2}} \right)$

$W = 38.504\,N$