Calculate Distance from Earth's Center: 11% Force

[physicshard22]

Homework Statement

Determine the distance from Earth's centre where the force of gravity acting on a space probe is only 11% of the force acting on the same probe at the Earth's surface. express your answer in terms of Earth's radius,

Homework Equations

F = Gm1m2/R^2

The Attempt at a Solution

i tried plugging in the values but i can't seem to get the answer

 

[ideasrule]

Write down two versions of the gravitation equation:

Fs=Gm1m2/R^2
Fp=Gm1m2/r^2

where Fs is the force of gravity on Earth's surface and Fp is the force of gravity put in space. Fp/Fs = 0.11, as the question states. See what you can do with that.

 

[rl.bhat]

The relevant equation given by you is for the force on the surface of the earth. If h is the distance of the probe from the Earth's surface, what is its distance from the center of the earth? What is the force on it? take the ratio of these forces and equate it to the given value and solve for h.

 

[physicshard22]

i don't understand

h/h' = 0.11?

then what can i do?

 

[rl.bhat]

terms of R, what is h and h' for Fs and Fp?

 

[physicshard22]

terms of R, what is h and h' for Fs and Fp?

h = 1r
h' = 2r

 

[rl.bhat]

h = 1r
h' = 2r

No.
h is r and h' = r + H where H is the height of the probe from the surface of the earth. find H.

 

[physicshard22]

so it would be r/r+h = 0.11?
how do i solve with 2 unknowns?

 

[rl.bhat]

You have to write h in terms of r.

 

[physicshard22]

this is so confusing can you give me another hint?

 

[physicshard22]

Did anyone get the answer so i can compare?

 

[bleedblue1234]

give us the radius and mass of Earth ur using

 

[physicshard22]

The question doesn't give it

 

[rl.bhat]

r/(r+h) = 0.11
r = 0.11(r+h)
Now simplify and find h.