Question

I'm stuck on this one guys!
How many Earth radii above the Earth (not from its center) must you be located to experience an acceleration of gravity of 2.00 m/s/s. Express in terms of Earth-radii; that is, express the answer as the number of times greater than 6.38 x 106 m. you can use the formula 2 = 6.674*10^-11*mass of the earth/d^2

Answer 1

please bros

Answer 2

The generally accepted value for "g" is 9.80665 meters / second^2

Answer 3

this is universal gravitation

Answer 4

Recall the Force of gravity between 2 masses
\[F _{g}=\frac{ m*M*G }{ r^2 }=m*g\]

Answer 5

The gravitational acceleration for earth is then,
\[g=\frac{ M*G }{ r^2 }\]

figure out radius r for g=2.0

Answer 6

alright i got 14126308.7889 for r

Answer 7

what do i do next?

Answer 8

\[2.0=\frac{ 6*10^{24}*6.67*10^{-11} }{ r^2 }\]
\[r \approx 1.41457*10^7~~m\]

Answer 9

Earth radius - 6.38*10^6 m
This radius - 1.41457*10^7 m

(This radius)/Earth radius = 2.22

\[\huge r _{2.0}=2.2*r _{9.8}\]

Answer 10

So you need to be 2.2 earth radius from the center, or 1.2 earth radius above sea lvl to experience gravity accelerating at 2.0 m/s^2

Answer 11

Thanks friend.