# Homework Help: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in General

1. Apr 27, 2012

### AudenCalbray

1. The problem statement, all variables and given/known data
How much work is done moving a 1500 kg spacecraft from the Earth's surface into a fixed orbit at a height of 300 km above the Earth's surface?

2. Relevant equations
Eg = -Gm1m2/r
Ek = 1\2mv^2
mass of earth: 5.98 x 10^24 kg
radius of earth: 6.38 x 10^6 m

3. The attempt at a solution
So the change in Eg plus the change in Ek is equal to 0. I solved the problem without using the 300 km or the mass of the spacecraft and I know it is wrong. I got the escape velocity (11000 m/s) and then got the kinetic energy, assuming Ek2 was 0.
I restarted the problem, and now my conservation of energy equation reads: Ek = Eg2-Eg1, again assuming Ek2 is zero, which is wrong, but I do not know how the get the change in energy otherwise. I would love some help on this. Thank you.

2. Apr 27, 2012

### LawrenceC

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Gravitational acceleration is a function of distance from the earth. Therefore the potential energy change is a calculus problem.

3. Apr 27, 2012

### AudenCalbray

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Sorry, I still don't understand how to solve this.

4. Apr 27, 2012

### LawrenceC

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

The work required equals the change in potential and kinetic energies. Both are zero on earth's surface. You have to achieve an escape velocity at a certain altitude. The escape velocity is used to compute the kinetic energy while the mass raised to an altitude is used to compute the potential energy. The sum of the two is the work required. However, the potential energy is a calculus problem necessitating an integration. Integration is calculus which you probably have not studied.

You can avoid the integration and accept some error by choosing a mean value of gravitational acceleration and treating it as a constant. This is probably not a bad idea in view of the fact that air resistance is being ignored.

5. Apr 27, 2012

### Staff: Mentor

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Why do think this?

The work done will equal the change in total energy. What's the final energy of the orbiting spacecraft? What's the initial energy?

6. Apr 27, 2012

### AudenCalbray

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

They want the kinetic work, so the change in kinetic energy is the answer. I think.

7. Apr 27, 2012

### Staff: Mentor

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

What is 'kinetic work'?

8. Apr 27, 2012

### AudenCalbray

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Change in kinetic energy, as I understand it.

9. Apr 27, 2012

### Staff: Mentor

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Work is change in total energy.

10. Apr 27, 2012

### AudenCalbray

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

If it was, wouldn't work always be 0 then?

11. Apr 27, 2012

### Staff: Mentor

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

No. Why do you think the total energy doesn't change?

12. Apr 27, 2012

### AudenCalbray

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

This is a conservation of energy question.

13. Apr 27, 2012

### Staff: Mentor

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

It's an energy problem, but energy is not conserved. Work is being done!

Work = ΔPE + ΔKE

Don't assume that ΔPE + ΔKE = 0.

14. Apr 27, 2012

### AudenCalbray

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Okay, so how do I solve it?

15. Apr 27, 2012

### Steely Dan

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Yes, but 300 km is not very large compared to the radius of the Earth (~6000 km) so if this was done without calculus it would still give a reasonable answer.

It is probably confusing to use the term "escape velocity" when the Earth's gravitational field is not actually being escaped here.

It it always clearest to remember the work-kinetic energy theorem. Work is a change in kinetic energy; if the kinetic energy does not change, that means the net work done during the process is zero. However, in this case the kinetic energy does change (since the spacecraft starts at rest and ends at orbital speed). So there is a net amount of work being done to the spacecraft. The question is slightly ambiguous; if you are being asked how much work is done only by the thrust of the spacecraft itself, then you have to subtract out the work done by the gravitational field first.

16. Apr 27, 2012

### Staff: Mentor

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Any calculus needed has already been done. Note the formula for gravitational PE in the first post.
When they ask for the work done, I highly doubt they mean to include the work done by gravity. (That's reflected in the gravitational PE term.) They mean the work that must be done by some applied force to get the spaceship into orbit. For example: If you are asked how much work is required to raise something x meters, would you think they want an answer of zero? After all, the net work would be zero (assuming the speed doesn't change).

But I admit that it is somewhat ambiguous.

It is true that the work done by all forces (including gravity) equals the change in KE. But if you want the work done by some applied force (not including gravity), it equals the change in KE+PE.

17. Apr 27, 2012

### Steely Dan

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

I tend to assume that the person who wrote the question meant what they said unless otherwise specified. At any rate, as long as you specify which question you are answering, you should be fine.

18. Apr 27, 2012

### AudenCalbray

Re: Grade 12 Conservation of Enegy Question- Gravitational Potential Energy in Genera

Thank you both very much. :)