Summary
Highlights
Work in physics has a specific meaning: a measurable change in a system due to an applied force. If you apply force to an object and it moves, work is done. Work is calculated as force multiplied by distance and the cosine of the angle between them. It's measured in Joules (Newton-meters). Work can be positive, negative, or zero depending on the direction of force relative to displacement. Work is a scalar quantity, but its sign indicates whether energy is added to or removed from the system.
Energy is defined as the ability to do work and is also measured in Joules. It's a fundamental conserved quantity, meaning that in an isolated system, the total energy remains constant, although it can transform from one form to another. Different forms of energy include mechanical, radiant (like microwaves and light), nuclear, electrical, solar, heat, and chemical energy.
Mechanical energy is divided into kinetic energy and potential energy. Kinetic energy is the energy of motion, calculated as 0.5 * mass * velocity^2. It's always a positive scalar quantity. Potential energy is energy due to an object's position or state. The two main types discussed are gravitational potential energy (mgh) and spring potential energy (0.5 * k * x^2, where k is the spring constant and x is displacement). Gravitational potential energy can be positive or negative depending on the chosen reference point, while spring potential energy is always positive.
The energy conservation principle states that the total energy of an isolated system remains constant. Work done can also be expressed as the change in kinetic energy or the negative change in potential energy. This principle allows the total initial mechanical energy (kinetic + potential) to be equated to the total final mechanical energy, simplifying problem-solving by eliminating directional information. Examples like a stone lifted to a height and a car on a hill illustrate how potential energy converts to kinetic energy while total energy remains constant.
Power is defined as the work done per unit time, measured in Watts (Joules per second). It differentiates between doing the same amount of work over different time intervals; for instance, walking versus running up stairs involves the same work but different power outputs.
Momentum is a property of moving matter, defined as mass * velocity. It's a vector quantity, so its direction is crucial in calculations. Momentum is measured in kilogram-meters per second. Like energy, momentum is a conserved quantity in an isolated system, meaning the total initial momentum equals the total final momentum. This principle is fundamental for analyzing collisions.
During a collision, two objects exert equal and opposite forces on each other (Newton's third law). This interaction produces an impulse, which is defined as force multiplied by the time over which the force acts (measured in Newton-seconds). Impulse is also equal to the change in an object's momentum. It's important to calculate impulse for individual objects in a collision.