Finding the escape speed in MArs. Problem on advanced gravitational potential energy.

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1. Jul 16, 2012

mutineer123

1. The problem statement, all variables and given/known data

The mean diameters of Mars and Earth are 6.9 10^3 km and 1.3 10^4 km, respectively.?
The mass of Mars is 0.11 times Earth's mass.
(a) What is the ratio of the mean density of Mars to that of Earth?

(b) What is the value of the gravitational acceleration on Mars?

(c) What is the escape speed on Mars?

2. Relevant equations

3. The attempt at a solution
I got 1 and 2, but am stuck in 3. ANSWER 1 is 0.74, ANSWER 2 is 3.8m/s^2.

For The escape speed on Mars, I am not sure if I entirely understand this question even! One of my friends told me that escape speed is when
1/2 m v^2 > mgh. And using this method I am getting the right answer, but his definition of escape speed is not entirely satisfying. You know the formula a=v^2/r right? Why can't we use that to get V here?? Also, is there a way of finding out the answer using formulas like g=Gm/r^2 ?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 16, 2012

azizlwl

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

For excape, r=∞

$\int_R^∞ \! f(r) \, \mathrm{d} r$

$\int_R^∞ \! \frac {GMm}{r^2} \, \mathrm{d} r$

ΔPE=GMm/R=(GMm/R2).R=mgR

Last edited: Jul 17, 2012
3. Jul 16, 2012

mutineer123

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

I have no idea what you did after your integration. Can u explain?

4. Jul 16, 2012

azizlwl

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

It is the total energy needed to take an object from the radius R to infinity.
Since the final velocity is zero, energy conservation gives
ΔKE+ΔPE=0

ΔPE=(GMm/R).(R/R)

5. Jul 17, 2012

mutineer123

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

How is the final velocity 0?
ANd uve written at the beginning "For excape, r=∞', why do we take that assumption?

6. Jul 17, 2012

mutineer123

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

Are you sure your method will works? u say ΔKE+ΔPE=0 where ΔPE=(GMm/R).(R/R). But you can't use the formula ΔPE=(GMm/R).(R/R) in this way, you don't know the mass of mars!

7. Jul 18, 2012

ehild

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

Escape means to run away. An object -a spaceship- escapes Mars if it is not confined to orbit around it, but can go away from its gravitational field, that is, to infinity.
You know how the mass of Mars is related to the mass of Earth. You also know the radii, both of Mars and Earth. And you know the gravitational acceleration at the surface of Earth.

ehild

8. Jul 18, 2012

mutineer123

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

I also know mar's gravitational acceleration. But like i said using GMm/r cannot yield anything because like you know, the masses are in ratio. So I dont know the mass! How can I proceed then??

9. Jul 18, 2012

ehild

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

Do you know the mass of Earth?
The gravitational acceleration on the Earth surface is g=GM/R2 (M is the mass of Earth and R is the radius of Earth). g=9.81 m/s2. The diameter of the Earth is given in the problem.
The mass of Mars is 0.11 Mearth.
ehild

Last edited: Jul 18, 2012
10. Jul 18, 2012

mutineer123

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

Yes yes, that substitution escaped me......I did it that way now. But i am not getting the same answer as i did in the mgh way...any suggestions on why?

11. Jul 18, 2012

ehild

Re: Finding the escape speed in MArs. Problem on advanced gravitational potential ene

PE=mgh is an approximate formula valid only very near to the surface of the Earth, and it is the potential energy with respect to the ground.

GmM/R is the general gravitational potential energy of two point-like or spherical objects.

ehild