# Potential energy particle problem

• Hiche
In summary, a conservative force of (4.0x - 13)i N acts on a particle moving along an x axis. The potential energy U associated with this force has a value of 26 J at x = 0. The maximum positive potential energy is at x = 13/4 m, where the force is zero and the kinetic energy is 0. The potential energy is equal to zero at negative x = -13/4 m and positive x = 13/4 m. To find the maximum potential energy, we can take the indefinite integral of the given force to get U = 2x^2 - 13x + c, where c is the constant of integration. The turning point of this equation

## Homework Statement

A single conservative force F = (4.0x - 13)i N, where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 26 J at x = 0. (a) What is the maximum positive potential energy? At what (b) negative value and (c) positive value of x is the potential energy equal to zero?

## Homework Equations

Force = dU/dx where U is the potential energy.

## The Attempt at a Solution

Okay, so we find the anti-derivative of the given force then we have: U = x^2/2 - 13x. Then what? At x = 0 m, U is 26 J. At the maximum U, we know the kinetic energy is 0 (v = 0).

note:
force is zero when x=13/4, everywhere else it points away from there.

the indefinite integral of 4x-13 is actually

2x2-13x+c

Which is a quadratic (c is the constant of integration).

The turning point, is where the derivative is equal to zero :) though, in this case, it looks like a minima rather than the asked-for maxima (check the equation does not have a minus sign in front).

## 1. What is potential energy?

Potential energy is the energy an object possesses due to its position or configuration. It is the energy that is stored and can be converted into other forms, such as kinetic energy.

## 2. What is a particle in the context of potential energy?

A particle is a small, localized object that has mass and occupies a specific position in space. In the context of potential energy, particles refer to the fundamental building blocks of matter that interact with each other and possess potential energy.

## 3. How is potential energy related to particles?

In the particle problem, potential energy is the energy associated with the interactions between particles. As particles move and interact with each other, their potential energy can change, which can affect the overall system's behavior.

## 4. What are some real-life examples of potential energy particle problems?

Some real-life examples of potential energy particle problems include the behavior of molecules in a chemical reaction, the movement of objects in a gravitational field, and the interactions between charged particles in an electric field.

## 5. How do scientists use potential energy particle problems in their research?

Scientists use potential energy particle problems to study and understand various phenomena, such as the behavior of matter, the properties of materials, and the dynamics of systems. By analyzing potential energy particle problems, scientists can make predictions and design experiments to test their theories.