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Chapter 1: Problem 27

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.

Short Answer

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

Step by step solution

01

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.
02

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.
03

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.
04

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

(a) How many liters of wine can be held in a wine barrel whose capacity is 31 gal? \((\mathbf{b})\) The recommended adult dose of Elixophyllin \(^{\circ}\), a drug used to treat asthma, is \(6 \mathrm{mg} / \mathrm{kg}\) of body mass. Calculate the dose in milligrams for a \(185-\mathrm{lb}\) person. (c) If an automobile is able to travel \(400 \mathrm{~km}\) on \(47.3 \mathrm{~L}\) of gasoline, what is the gas mileage in miles per gallon? (d) When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee \((4\) cups \(=1 \mathrm{qt}) .\) How many \(\mathrm{kg}\) of coffee are required to produce 200 cups of coffee?

A \(32.65-g\) sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is \(50.00 \mathrm{~mL}\). The solid and toluene together weigh \(58.58 \mathrm{~g}\). The density of toluene at the temperature of the experiment is \(0.864 \mathrm{~g} / \mathrm{mL}\). What is the density of the solid?

Water has a density of \(0.997 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C} ;\) ice has a density of \(0.917 \mathrm{~g} / \mathrm{cm}^{3}\) at \(-10^{\circ} \mathrm{C} .\) (a) If a soft-drink bottle whose volume is \(1.50 \mathrm{~L}\) is completely filled with water and then frozen to \(-10^{\circ} \mathrm{C},\) what volume does the ice occupy? (b) Can the ice be contained within the bottle?

A \(10.0 \mathrm{~g}\) block of gold is hammered into a thin gold sheet which has an area of \(150 \mathrm{~cm}^{2}\). Given the density of gold is \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\), what is the approximate thickness of the gold sheet in millimeters?

Give the chemical symbol or name for the following elements, as appropriate: (a) helium, (b) platinum, (c) cobalt, (d) \(t\) in, (e) silver, (f) Sb, \((\mathbf{g}) \mathrm{Pb}\), (h) \(\mathrm{Br}\) \(\mathrm{r},(\mathbf{i}) \mathrm{V},(\mathbf{j}) \mathrm{Hg}\).
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