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4.3 Conservation of Energy, the Work-Energy Principle, and Power

Peter Apps

Daniella Garcia-Loos

257Β resources
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Law of Conservation of Energyπ¨βπ»

The energy of a system is conserved.
When a system has no work being done on or by it, the total energy of the system is constant. This total energy can be internally converted among potential, kinetic, or thermal but never changes. This idea is the Law of Conservation of Energy and is one of the 4 major conservation laws in AP 1.
A key idea here is that this law only applies when there are no outside forces acting on the system. So a system consisting of a ball and the earth would have its energy conserved as the ball falls, but a system of a car would have its energy change as friction between the tires and the road removes kinetic energy.
Common situations where youβll be asked to apply energy conservation include: falling objects, sliding or rolling down ramps, masses & springs, and planetary orbits.
To help visualize this conservation, watch the roller coaster below (no friction).

Image courtesy of PhysicsClassroom.

In this case, the TME is the total mechanical energy, or potential plus kinetic energies. Most of the time, when a question refers to the total energy, we really mean total mechanical energy.
Here are some key things to remember about the law of conservation of energy:
• The law of conservation of energy states that the total amount of energy in a closed system remains constant, regardless of the changes that may occur within the system.
• The law of conservation of energy applies to all forms of energy, including kinetic energy, potential energy, and thermal energy.
• The law of conservation of energy can be used to predict and analyze the behavior of physical systems, and to solve problems involving the transfer and transformation of energy.

The Work-Energy Principle

Here are some key things to remember about the work-energy principle:
• The work-energy principle states that the work done on an object is equal to the change in kinetic energy of the object.
• The work-energy principle can be expressed using the formula: Work = change in kinetic energy
• The work-energy principle is a consequence of the law of conservation of energy, which states that the total amount of energy in a closed system remains constant.
• The work-energy principle can be used to calculate the work done on an object, or to calculate the change in kinetic energy of an object.
• The work-energy principle is a useful tool for analyzing the motion of objects and systems, and for solving problems involving the transfer of energy.
• The work-energy principle is applicable to both linear and rotational motion, as well as to both conservative and non-conservative forces.

Power

Here are some key things to remember about power:
• Power is a measure of the rate at which work is done or energy is transferred.
• Power is usually measured in watts (W), or joules per second (J/s).
• Power is calculated using the formula: Power = Work / Time
• Power is a scalar quantity, meaning it has only magnitude and no direction.
• Power can be positive or negative, depending on the direction of the work or energy transfer.
• Power is a measure of how quickly a task is completed or how fast energy is transferred.
• The higher the power, the more work is being done or energy is being transferred in a given time period.
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