Finding the potential energy of a gravitational force?

In summary, the conversation discusses the calculation of the potential energy function and work required for increasing the separation between two particles in one dimension using the equation for gravitational force. It also points out the need for a minus sign in the equation to avoid confusion and clarifies the concept of potential energy.
  • #1
CoreanJesus
Sorry if something is wrong... this is my first ever post
1. Homework Statement
The Question:
In one dimension, the magnitude of the gravitational force of attraction between a particle of mass M1, and one of mass M2 is given by:
F(r)=GM1M2/r^2
Where G is a constant and x is the distance between the particles.

a) What is the potential energy function U(x)? Assume that U(x) -> 0 as x -> infinity.
b) How much work is required to increase the separation of the particles from x=x1 to x=x1+d?

Homework Equations


F(r)=-dU/dx

The Attempt at a Solution


For a), The answer given is -GM1M2/r but I keep getting a positive equation...
∫-dU=∫GM1M2/r^2
-U=-GM1M2/r
U=GM1M2/r
For b) I just need a clue as to how to start...
 
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  • #2
CoreanJesus said:
In one dimension, the magnitude of the gravitational force of attraction between a particle of mass M1, and one of mass M2 is given by:
F(r)=GM1M2/r^2
The force is attractive, i. e. towards smaller r. It would be better to add a minus sign here, otherwise the sign convention is confusing.
CoreanJesus said:
For b) I just need a clue as to how to start...
What is the potential energy at the described places?
 
  • #3
mfb said:
The force is attractive, i. e. towards smaller r. It would be better to add a minus sign here, otherwise the sign convention is confusing.What is the potential energy at the described places?
No potential energy is given...
 
  • #5
Oh :D Thank You!
 

FAQ: Finding the potential energy of a gravitational force?

1. What is potential energy in relation to gravitational force?

Potential energy is the energy that an object possesses due to its position or configuration in a gravitational field. It is the energy that an object has the potential to release or use when it moves from its current position to a different position in the gravitational field.

2. How is potential energy of a gravitational force calculated?

The potential energy of a gravitational force can be calculated using the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance from the reference point. This equation assumes that the gravitational field is uniform and the object is near the surface of the Earth.

3. Can potential energy change due to a change in gravitational force?

Yes, potential energy can change due to a change in gravitational force. This can happen when the mass or distance between two objects changes, or when the gravitational field strength changes. For example, potential energy would increase if an object is moved to a higher altitude, where the distance from the Earth's center increases and the gravitational force decreases.

4. How does potential energy affect the motion of objects in a gravitational field?

Potential energy is converted into kinetic energy when an object moves in a gravitational field. As an object falls towards the center of the gravitational field, its potential energy decreases while its kinetic energy increases. This is evident in the conservation of energy principle, where the total energy (potential + kinetic) of an object remains constant.

5. What are some real-world examples of potential energy of a gravitational force?

There are many real-world examples of potential energy of a gravitational force. Some common examples include a roller coaster at the top of a hill, a book on a shelf, and a pendulum at its highest point. In all of these cases, the objects have the potential to release energy as they move towards a lower position in the gravitational field.

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