Problem 27 - Chemistry The Central Science In Si Units

Question

Two positively charged particles are first brought close together and then released. Once released, the repulsion between particles causes them to move away from each other. (a) This is an example of potential energy being converted into what form of energy? (b) Does the potential energy of the two particles prior to release increase or decrease as the distance between them is increased.

Step-by-Step Solution

Answer

(a) Potential energy is converted into kinetic energy. (b) Potential energy decreases as distance increases.

Step 1: Understanding the Scenario

The problem involves two positively charged particles that repel each other. Initially, when these particles are close together, they have a certain amount of potential energy due to their positions. Once released, this potential energy is transformed into another type of energy as the particles move away from each other.

Step 2: Identifying Energy Conversion

When the particles are released, the electrostatic potential energy is converted into kinetic energy. The change in position results in a reduction of potential energy, which is converted into kinetic energy as the particles move apart.

Step 3: Analyzing Potential Energy Change with Distance

As the distance between the two positively charged particles increases, the electrostatic potential energy of the system decreases. This is because the potential energy between two charges decreases with increasing distance, following Coulomb's Law.

Step 4: Conclusion from Analysis

Thus, when the positively charged particles are released and move away from each other, kinetic energy increases, and the potential energy decreases. The conversion is primarily from potential energy to kinetic energy as the particles separate.

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. For moving objects, this energy can be calculated using the formula \( KE = \frac{1}{2}mv^2 \), where \( m \) represents the mass and \( v \) denotes the velocity of the object.
In the context of the two positively charged particles, when these particles are released and start to move apart, their potential energy transforms into kinetic energy.
This kinetic energy is what allows the particles to move away from each other at increasing speeds as they continue to repel.

• When the particles are initially close together, they have high potential energy and low kinetic energy.
• As they move apart, the decrease in potential energy equals the increase in kinetic energy, according to the conservation of energy principle.
• This conversion process results in the observable motion and velocity increase of the particles moving away.

Electrostatic Potential Energy

Electrostatic potential energy, associated with charged particles, is the energy stored due to the positions of these charges in relation to each other. This energy is a result of the electrostatic forces acting between the particles. Its value depends on their charges and the distance separating them.
When the particles are near each other, they possess a significant amount of electrostatic potential energy. As these particles are released and move apart, this potential energy decreases.

• The closer the charged particles are, the higher the potential energy due to strong repulsion or attraction forces.
• As the particles move away, potential energy is converted into kinetic energy, resulting in decreasing electrostatic potential energy.
• This decrease in potential energy reflects the reduction in the electromagnetic forces acting as the distance between the charges increases.

Coulomb's Law

Coulomb's Law explains the electrostatic interaction between charged particles. This fundamental principle states that the force between two charges is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between them. Mathematically, it is expressed as:\[ F = k \frac{|q_1 q_2|}{r^2} \]where \( F \) is the force, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, \( r \) is the distance between the charges, and \( k \) is Coulomb's constant.
Applying this law to the scenario with two positively charged particles:

• The force of repulsion grows weaker as the distance \( r \) increases, leading to a decrease in electrostatic potential energy.
• Coulomb's Law provides insight into how changes in distance influence both force and potential energy between charged entities.
• It supports the explanation of energy conversion observed in the transition from potential to kinetic energy as the particles repel.