Potential of Point Mass: Is V = -k/r + mgz?

In summary, the equation for the potential of a point mass is V = -k/r + mgz, where k is the gravitational constant, r is the distance from the point mass, m is the mass of the point mass, and g is the acceleration due to gravity. This potential is calculated using the formula V = -k/r + mgz, taking into account the gravitational force and the height of the point mass. The negative sign in the potential equation represents the attractive force of gravity, indicating that the potential decreases as the distance from the point mass increases. The potential can be negative when the attractive force of gravity is greater than the gravitational potential energy. Additionally, the potential of a point mass decreases with distance and increases with mass,
  • #1
Logarythmic
281
0
If I have a point mass that experiences a force

[tex]\vec{F}(\vec{r}) = - \frac{k}{r^2} \vec{e_r} -mg \vec{e_z}[/tex]

is it correct that the potential is

[tex]V = - \frac{k}{r} + mgz[/tex]

??
 
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  • #2
By the unit vectors used, apparently one uses the cylindric coordinates. Did you check that [itex] \vec{F}=-\nabla U [/itex] using cylindric coordinates ?

Daniel.
 
  • #3
Yeah that's correct. Can I interpret this as a particle next to a vertical cable or something?
 
  • #4
I ain't got a clue.

Daniel.
 

1. What is the equation for the potential of a point mass?

The equation for the potential of a point mass is V = -k/r + mgz, where k is the gravitational constant, r is the distance from the point mass, m is the mass of the point mass, and g is the acceleration due to gravity.

2. How is the potential of a point mass calculated?

The potential of a point mass is calculated using the formula V = -k/r + mgz. This equation takes into account the gravitational force and the height of the point mass.

3. What does the negative sign in the potential equation represent?

The negative sign in the potential equation represents the attractive force of gravity. This means that the potential decreases as the distance from the point mass increases.

4. Can the potential of a point mass be negative?

Yes, the potential of a point mass can be negative. This occurs when the distance from the point mass is large enough that the attractive force of gravity is greater than the gravitational potential energy.

5. How does the potential of a point mass change with distance and mass?

The potential of a point mass decreases as the distance from the point mass increases. It also increases as the mass of the point mass increases. This is because a larger mass creates a stronger gravitational force, resulting in a higher potential.

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