Gravitational Potential Energy problem?

[Kitten207]

Homework Statement

Here is the problem:

http://i51.tinypic.com/6r7jts.jpg

Homework Equations

PE= mgh
KE= 1/2mv^2


I'm not sure how to go about this problem =[

 

[berkeman]

Homework Statement

Here is the problem:

http://i51.tinypic.com/6r7jts.jpg

Homework Equations

PE= mgh
KE= 1/2mv^2


I'm not sure how to go about this problem =[

The problem is not stated all that well. They say "rocket", but ask what the initial KE at the surface of Vulcan has to be to do those two things? Sounds more like a projectile which gets all of its KE from a single charge at the surface, rather than a rocket that carries fuel with it and burns it as it rises.

But whatever. You listed the Relevant Equations -- how do KE and PE trade off? The escape velocity question may be the easier of the two. What is meant by "escaping" the gravitational attraction of the planet?

 

[Kitten207]

Ok I know that escaping means 1/2 mv2 = GMm/R.

So for the first part, I'd do Sum Ki + Sum Ui = Sum Kf + Sum Uf? From that, I'll get the velocity? Do I need to use any kinematics equations?

 

[Kitten207]

bump. Help on just the first part of the problem.

 

[berkeman]

Ok I know that escaping means 1/2 mv2 = GMm/R.

So for the first part, I'd do Sum Ki + Sum Ui = Sum Kf + Sum Uf? From that, I'll get the velocity? Do I need to use any kinematics equations?

Yes, you got the escape velocity part correct:

http://en.wikipedia.org/wiki/Escape_velocity

For reaching an orbit, you do trade off KE for PE, but also remember that to stay in orbit, you need to still have enough KE to match the velocity for that orbital height...

 

[Kitten207]

I am confused. To find the needed velocity:

mgh = 1/2 mv^2

v= sqrt(6gR) because height is 3R. Where do I go from there? What do I use for g?

 

[berkeman]

I am confused. To find the needed velocity:

mgh = 1/2 mv^2

v= sqrt(6gR) because height is 3R. Where do I go from there? What do I use for g?

Yeah, like I said, this question seems poorly asked (not your fault).

In a simplistic way, you could just take the delta PE from 1R to 4R (3R above the surface of Vulcan) as the delta PE, and that could give you an initial KE. But you wouldn't be able to stay in orbit at that altitude, you would just peak at that altitude (and drag down the space station if you docked...).

EDIT -- I guess all the question asks is to "reach" the space station, not orbit with it or dock with it...