# Solving Problems with Attractive Inverse Cubed Force

• danai_pa
In summary, the conversation discusses a particle of mass m moving in an attractive inverse cubed force and asks for various calculations and qualitative analysis. The conversation also mentions the potential energy V(r), its shape, and its relation to velocity. The unknown terms "E" and "L" are also mentioned and clarification is requested.

#### danai_pa

A particle of mass m is moving in an attractive inverse cubed force given by

F = -K/r^3, where K>0

a) Find V(r) and plot V(r) versus r.
b) Discuss the motion qualitatively by the method of effective potential.
C) Find E and L when the particle is moving in a circular orbit.
d) Find the time period of the orbit.
e) If the orbit is perturbed slightly, what will be the period of small oscillations?

What, exactly, have you done so far?

I don't know a shape of V(r) versus r

<i>I don't know a shape of V(r) versus r</i>

V is potential energy? Then V(r) is the integral of the force with respect to displacement.

Edit: make that the negative integral of the force etc.

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I find V(r) = -k/2r^2 + L^2/2mr^2
a part of r^2 of two terms are equal. Which total graph of V(r)

I could interpret V(r) as velocity or potential energy. Also I have no idea what "E"and "L" are. Please be sure you define all terms.

## 1. What is attractive inverse cubed force?

Attractive inverse cubed force is a type of force that follows the inverse cube law, meaning that it decreases with the cube of the distance between two objects. It is an attractive force, which means that it pulls objects towards each other.

## 2. How is attractive inverse cubed force used to solve problems?

Attractive inverse cubed force can be used to solve problems related to the behavior of objects that are attracted to each other, such as planets orbiting around a star or particles coming together in a chemical reaction. By understanding the strength of this force and how it changes with distance, scientists can predict and explain the behavior of these systems.

## 3. What are some real-life examples of attractive inverse cubed force?

Some real-life examples of attractive inverse cubed force include the gravitational force between celestial bodies, such as planets and stars, and the van der Waals force between molecules. The force between two electric charges at a large distance can also follow an inverse cubed relationship.

## 4. How is attractive inverse cubed force different from other types of forces?

Attractive inverse cubed force is different from other types of forces because its strength decreases with the cube of the distance between two objects. This is in contrast to other forces, such as the gravitational force, which follows an inverse square law, where the force decreases with the square of the distance.

## 5. What are the implications of attractive inverse cubed force in the field of physics?

Attractive inverse cubed force has significant implications in the field of physics, as it is a fundamental force that plays a crucial role in understanding the behavior of matter and the universe. It helps explain how objects interact with each other and how systems evolve over time. It also allows scientists to make predictions and develop theories about the structure and behavior of various systems.