Question

How do i solve this problem?Hint: earth To determine her mass use her weight on earth, in the equation m = W / g (where g is 10m/s2). moon weightTo determine the mass of the unknown planet, apply the equation M = F r2/ (m G) to the student and the planet of unknown mass. 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]

Answer 1

We know that the weight is given by:

`F=mg`

since the weight on earth is 715 and g=10 we plug this values in the equation and solve for the mass:

`\begin{gathered} 715=10m \\ m=(715)/(10) \\ m=71.5 \end{gathered}`

therefore the mass of the student is 71.5 kg.

We can fill the table with the values given:

F=315 N

G=6.67e(-11) m3/kgs2

m=71.5 kg

r=7.14e7 m

Now to find the mass of the second planet we use the gravitational law:

`F=G(mM)/(r^2)`

Plugging the values and solving for M we have:

`\begin{gathered} 315=(6.67*10^(-11))((71.5)M)/((7.14*10^7)^2) \\ M=((315)(7.14*10^7)^2)/((71.5)(6.67*10^(-11))) \\ M=3.37*10^(26) \end{gathered}`

Therefore the mass of the second planet is 3.37e26 kg