Question

How do I solve this problem?Hint:earth weightTo determine her weight on earth, use W = m g (where g is 10m/s2). moon weightTo determine her weight on the moon, use F = G M m / r2. F=gravitational force or weight [N]G=gravitational constant [always 6.67 x 10-11 m3/kg s2]M=larger mass [kg]m=smaller mass [kg]r=distance between the center of the two objects [m]Remember that the two objects interacting with each other are the student and the moon.

Answer 1

the weigth of the student on earth is 610 Newtons

$\begin{gathered} F=99\text{ Newtons} \\ G=6.67\cdot10^{-11}\frac{m^3}{\operatorname{kg}s^2} \\ M=7.35\cdot10^{22}\text{ kg} \\ m=61\text{ kg} \\ r=1.74\cdot10^6m \end{gathered}$

the weigth on the moon is 99 Newtons

Explanation

Step 1

find the weigth on earth

the weigth on earth is given

let

$\begin{gathered} w=\text{ mg} \\ where \\ m\text{ is the mass and g is the acceleration of gravity} \end{gathered}$

then, let

m= 61 kg

g= 10 m/s^2

replace,

$\begin{gathered} w=\text{ mg} \\ w=61\text{ kg}\cdot10\text{ }\frac{m}{s^2} \\ w=610\text{ Newtons} \end{gathered}$

therefore, the weigth of the student on earth is 610 Newtons

Step 2

Now, the expression to gravitacional force between two objects is given by:

$\begin{gathered} F=G\frac{Mm}{r^2} \\ \text{where} \\ G\text{ is the gravitational constant} \\ G=6.67\cdot10^{-11}\frac{m^3}{\operatorname{kg}s^2} \\ M\text{ is the larger mass} \\ m\text{ is the smaller mass} \\ r\text{ is the distance betw}en\text{ the center of the objects} \end{gathered}$

then , to find the G on the moon

let

$\begin{gathered} M=7.35\cdot10^{22}\text{ kg},\text{ m=61 kg} \\ r=1.74\cdot10^6m \\ \text{replace} \\ F=G\frac{Mm}{r^2} \\ F=6.67\cdot10^{-11}\frac{m^3}{\operatorname{kg}s^2}\cdot\frac{7.35\cdot10^{22}\text{ kg}\cdot61\text{ kg}}{(1.74\cdot10^6m)^2} \\ F=6.67\cdot10^{-11}\frac{m^3}{\operatorname{kg}s^2}\frac{7.35\cdot10^{22}\text{ kg}\cdot61\text{ kg}}{(3.02\cdot10^{12}m^2^{}} \\ F=6.67\cdot10^{-11}\frac{m^3}{\operatorname{kg}s^2}\cdot1.48\cdot10^{12} \\ F=99\text{ Newtons} \end{gathered}$

Step 3

finally, we have the force and the mass, so we can get the g value on the moon

$\begin{gathered} 99N=61k\cdot g \\ g=\frac{99N}{61kg} \\ g_{on\text{ moon}}=1.62\text{ }\frac{m}{s^2} \end{gathered}$

I hope this helps you