Question

How does the potential energy change (increase, decrease, or no change) for each of the following? (a) Two electrons come closer together. (b) An electron and a proton become farther apart. (c) Two atomic nuclei approach each other. (d) A ball rolls downhill.

Short answer

The potential energy increases for (a) and (c), decreases for (d), and also increases for (b) as they move farther apart.

Step-by-step solution

- Understand the concept of potential energy

Potential energy is stored energy that is related to the position of an object, especially in a field such as a gravitational field or electric field. In the context of charges, like electrons and protons, potential energy decreases as opposite charges come closer together (attractive force) and increases as like charges come closer together or opposite charges move apart (repulsive force). For gravity, potential energy decreases as an object moves closer to the Earth or downhill.

- Analyze the potential energy change for two electrons

Two electrons repel each other since they have like charges. As they come closer together, they are moving against the electric force of repulsion. This causes their potential energy to increase.

- Analyze the potential energy change for an electron and a proton

An electron and a proton attract each other due to their opposite charges. When they move farther apart, the system's potential energy increases because work is done against the attractive electric force.

- Analyze the potential energy change for two atomic nuclei

Two atomic nuclei, being positively charged, repel each other. As they approach each other, their potential energy increases due to the work done against the repulsive electrostatic force.

- Analyze the potential energy change for a ball rolling downhill

When a ball rolls downhill, it is moving in the direction of the gravitational force and hence its gravitational potential energy decreases. The ball converts potential energy to kinetic energy as it rolls downhill.

Key concepts

Electric Force

Imagine two charged particles in space, exerting an invisible pull or push on one another. This is the electric force in action. It is an integral part of the concept of potential energy change in charged particles. The electric force can be either attractive or repulsive, depending on the types of charges involved. Like charges, such as two electrons, repel each other, whereas opposite charges, like an electron and a proton, attract each other. The closer these charges get to one another, the stronger the electric force becomes.

For example, when two electrons come closer together, they exert a repulsive electric force upon each other. This force is a key player in the potential energy of the system, manifesting as an increase in electrical potential energy when the electrons move against the repulsive force.

Potential Energy in Physics

Potential energy is an essential concept in physics that you can think of as stored energy. It is the energy that an object holds because of its position relative to other objects within a force field, like a gravitational or electric field. The potential energy can transform into various forms of energy, including kinetic energy, and can also come from different sources, such as gravity or electrostatic forces.

In the scenarios of the exercise, we're primarily concerned with electric potential energy. It changes when charged particles move relative to each other. If like charges are forced closer together or opposite charges are pulled apart, the potential energy increases.

Gravitational Potential Energy

Gravitational potential energy, on the other hand, is the energy an object possesses due to its position in a gravitational field, typically relative to Earth's surface. Objects positioned higher in a gravitational field have more gravitational potential energy. If you hold a ball aloft, it has more potential energy than when it's on the ground because gravity wants to pull it down.

In the context of the ball rolling downhill, the scenario from the exercise, the ball loses gravitational potential energy because its height is decreasing. As it descends, that potential energy is not just disappearing; it's being converted into kinetic energy—the energy of motion—which propels the ball forward.

Kinetic Energy Conversion

Kinetic energy is the energy of motion. When an object moves, it has kinetic energy. There is a fascinating interplay between kinetic energy and potential energy – one can transform into the other. This transformation is evident in many natural phenomena and engineered systems.

Returning to our ball rolling downhill example, as the ball gains speed, its kinetic energy increases while its gravitational potential energy decreases. This is because potential energy is being converted into kinetic energy. The concept of energy conversion is central to understanding how energy is preserved in systems, aligning with the principle of conservation of energy which states that energy in a closed system must remain constant—it can neither be created nor destroyed, only transformed.