Question

Question #5: On the moon, what would be the force of gravity acting on an object that has a mass of 7 kg?

Answer 1

$F=11.375\text{ Newtons}$

Explanation

the acceleration due to gravity formula is given by:

$\begin{gathered} g=\frac{GM}{R^2}^{} \\ \text{where} \\ G\text{ is the universal gravitational constatn G=6.674 }\cdot10^{-11}\frac{m^3}{\operatorname{kg}\cdot s^2} \\ R\text{ is the radius of the massive body ( in meters)} \\ g\text{ is the acceleration due to gravity} \\ M\text{ is the mass of the massive body ( kg)} \end{gathered}$

Step 1

Find g(acceleration due to gravity)

Let

$\begin{gathered} M=\text{ mass of the moon=7.35}\cdot10^{22}\operatorname{kg} \\ G=\text{=6.674 }\cdot10^{-11}\frac{m^3}{\operatorname{kg}\cdot s^2} \\ R=\text{radius of the moon=}1.74\cdot10^6m \end{gathered}$

now, replace in the formula

$\begin{gathered} g=\frac{GM}{R^2}^{} \\ g=\frac{\text{6.674 }\cdot10^{-11}\frac{m^3}{\operatorname{kg}\cdot s^2}\cdot\text{7.35}\cdot10^{22}\operatorname{kg}}{(1.74\cdot10^6m)^2} \\ g=\frac{4.90539\cdot10^{12}}{(3.0276\cdot10^{12})} \\ g=1.62\frac{m}{s^2} \end{gathered}$

Step 2

to find the force , use the formula

$\begin{gathered} F=\text{mg} \\ \text{where m is the mass of the object} \\ g\text{ is the acceleration due to gravity} \end{gathered}$

replace

$\begin{gathered} F=7\operatorname{kg}\cdot1.625\text{ }\frac{m}{s^2} \\ F=11.375\text{ Newtons} \end{gathered}$

therefore, the force would be

11.375 N