# Forces on particles and second order DE's

• dawud
In summary, the conversation pertains to a homework question involving Coulomb's interaction, spring forces, and electric forces acting on particles. The electric force, spring force, and electric field all act in different directions on the particles, with the electric force being positive for both and the spring force being opposite for each particle. The question also asks about the meaning of a constant value for d, the coordinate of the center of mass, and how to write d in terms of a cosine function.
dawud

## Homework Statement

Attached. If you don't mind I'd like to go through each part of the question to make sure I've understood correctly. Thanks a lot

## Homework Equations

F=qE
F=(γq^2)/(d^2)
F=Kx
Taylor/Maclaurin (?)

## The Attempt at a Solution

So for part (a) I know that Coulomb's interaction, the spring force, and the electric force all act on the particles, so by adding all these force vectors I will obtain the required vector equations. However, I'm not sure on the directions of the forces; why is the electric force F=qE positive for in both vector equations (do they act in the same direction and if so, which?), and why is the restoring spring force opposite for the each of the two?

As for the other parts, I don't really know where to begin.

#### Attachments

• question.png
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Electric force ##qE## is pointing the same way for both particles: both have the same charge.
The other electric force ##\gamma(q^2/d^2)## is pointing in a different direction for each particle: both have the same charge, so they repel each other. (Or: E field ##\vec E =\gamma(q/d^2)\ \hat r## of 1##\rightarrow##2 points opposite from 2##\rightarrow##1.
And the spring pulls particles towards each other, so also in opposite directions.

(b) what does d = constant mean for ##\ddot x_1-\ddot x_2##?

(c) what is the coordinate of the center of mass ?

(d) write ##d = d_{eq} + a \cos{\omega t} ## with ## d_{eq} ## from (b)

## 1. What is a force and how does it affect particles?

A force is a push or pull on an object that can cause its motion to change. Forces can affect particles by causing them to accelerate, decelerate, or change direction.

## 2. What are some examples of forces that act on particles?

Some examples of forces that act on particles include gravity, friction, tension, and electromagnetic forces.

## 3. What is a second order differential equation?

A second order differential equation is a mathematical equation that involves the second derivative of a function. It is commonly used to model physical systems, such as the motion of particles under the influence of forces.

## 4. How do we solve second order differential equations for forces on particles?

To solve second order differential equations for forces on particles, we can use mathematical techniques such as separation of variables, substitution, or using an integrating factor.

## 5. How are forces and second order differential equations related in the study of physics?

Forces and second order differential equations are closely related in the study of physics because forces are often modeled using second order differential equations. These equations allow us to understand and predict the motion of particles under the influence of various forces.

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