Potential energy of particle in gravitational field of disk

In summary, the conversation discusses finding the formula for potential energy for a particle of mass m moving in the direction of axis z under the influence of a gravitational force from a homogeneous circular disk of mass M and radius a. The first task involves integrating the force formula to obtain the potential energy formula, with the condition that z>0. The second task involves finding the velocity of impact on the disk at z=4a/3, using conservation of energy. The conversation also mentions the need for a different formula for z<0 and choosing the integration constant to ensure the potential energy approaches 0 for large z.
  • #1
Oomph!
55
0

Homework Statement


I have a particle of mass m. The particle is moving in direction of axis z because of the gravitational force of a homogeneous circular disk of mass M and radius a. There is a formula for gravitational force of the disk on the picture.

Task:
1) Find the formula of potentional energy for z>0 (formula is on the picture).
2) We release the particle in z=4a/3. Find the velocity of impact on disk (formula is on the picture).

formulas.png


Homework Equations


Relevant equation is the formula for force of the disk. I just have to work with that.

The Attempt at a Solution


So, the first task is simple. I just have to integrate the force and i will get the formula of potentional energy. However, I don't understand why is important that z>0. And what about the constant? If I integrate, there is a constant C. I can just say, that C=0?

The second task is more difficult for me. I think that I have to compare kinetic energy (E=0.5mv2) and the potencional energy from first task. I have to substitute the z=4a/3 . I thought that the potentional energy at the beginning and the kinetic energy of impact on disk is same. However, probably not, because my formula was little bit different. Please, could you tell me what I have to do better?

Thank you.
 
Physics news on Phys.org
  • #2
The formula for the force is valid for z>=0 only, you would need a different formula to generalize it.

The integration constant should be chosen to get U->0 for large z.

The second part works via conservation of energy. What is the total initial energy? What is the total final energy?
 
  • #3
Now I know what was wrong. The particle has also potentional energy when it impact. So the energy at the beginning was just potentional for z=4a/3. But when the particle impacted on the disk, the total energy was kinetic and also potentional for z=0. Then I have correct result. However, how could I say that z=0? The particle falls to the center of the disk?
 
  • #4
The whole disk is at z=0, not just the center. The given formulas assume the particle moves along the symmetry axis, however, so it will hit the center of the disk.
 

1. What is potential energy of a particle in a gravitational field of a disk?

The potential energy of a particle in a gravitational field of a disk refers to the energy that the particle possesses due to its position in relation to the disk. It is a measure of the work that would be required to move the particle from its current position to a point at infinity outside the gravitational field of the disk.

2. How is potential energy of a particle in a gravitational field of a disk calculated?

The potential energy of a particle in a gravitational field of a disk can be calculated using the formula PE = -GMm/r, where G is the universal gravitational constant, M is the mass of the disk, m is the mass of the particle, and r is the distance between the particle and the center of the disk.

3. Does the potential energy of a particle in a gravitational field of a disk change as the particle moves?

Yes, the potential energy of a particle in a gravitational field of a disk changes as the particle moves. As the distance between the particle and the center of the disk changes, the potential energy also changes. The potential energy decreases as the particle moves closer to the disk and increases as it moves further away.

4. How does the mass of the disk affect the potential energy of a particle in its gravitational field?

The mass of the disk directly affects the potential energy of a particle in its gravitational field. As the mass of the disk increases, the potential energy also increases, since there is a stronger gravitational pull from the disk on the particle.

5. Can the potential energy of a particle in a gravitational field of a disk be negative?

Yes, the potential energy of a particle in a gravitational field of a disk can be negative. This occurs when the particle is closer to the disk than infinity, and in this case, the potential energy is considered to be negative. However, the potential energy is only defined up to an arbitrary constant, so the actual value of the potential energy does not have a physical significance.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
278
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
300
  • Introductory Physics Homework Help
Replies
4
Views
689
  • Introductory Physics Homework Help
Replies
1
Views
827
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
936
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
588
Back
Top