Ch.1 - Introduction: Matter, Energy, and Measurement

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.1 - Introduction: Matter, Energy, and Measurement

Problema 27b

Capitolo 1, Problema 27b

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. (b) Does the potential energy of the two particles prior to release increase or decrease as the distance between them is increased.

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insert step 1> Identify the type of interaction between the two particles. Since both particles are positively charged, they repel each other due to electrostatic forces.

insert step 2> Recall the concept of potential energy in the context of electrostatic forces. The potential energy between two charged particles is given by the formula: U = k * (q1 * q2) / r, where U is the potential energy, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.

insert step 3> Analyze how the potential energy changes with distance. Notice that the potential energy is inversely proportional to the distance (r) between the charges.

insert step 4> Consider the scenario where the distance between the particles increases. As r increases, the value of the potential energy U decreases because the charges are moving further apart.

insert step 5> Conclude that as the distance between the two positively charged particles increases, the potential energy decreases. This is because the repulsive force does work on the particles, converting potential energy into kinetic energy as they move apart.

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Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. For two positively charged particles, this means that as they are brought closer together, the repulsive force increases, which affects their potential energy.

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01:15

Coulomb's Law Concept 2

Potential Energy in Electric Fields

The potential energy of charged particles in an electric field is related to their positions relative to each other. For two like charges, potential energy increases as the distance between them decreases due to the work done against the electric force to separate them. Conversely, as the distance increases, the potential energy decreases, indicating that the system becomes more stable.

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00:34

Kinetic & Potential Energy

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In the context of the two charged particles, as they move apart due to repulsion, the potential energy decreases, and this energy is converted into kinetic energy as the particles accelerate away from each other.

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Percorso guidato

01:48

Law of Conservation of Mass

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