Energy conservation

Energy is the ability to do work. In physics, energy can take many forms (kinetic, potential, thermal, etc.), but the total energy in a closed system remains constant. This is the principle of conservation of energy.

Work

Work is done when a force causes an object to move in the direction of the force. The amount of work done depends on the size of the force and the distance moved in the direction of the force.

If the force is not in the same direction as the displacement, use the component of the force in the direction of displacement:

$$W = F s \cos \theta$$

where $\theta$ is the angle between the force and the displacement.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another or from one object to another. In a closed system, the total energy remains constant.

Efficiency

Not all the energy supplied to a system is usefully transferred; some is wasted (often as heat or sound).

Power

Power is the rate at which work is done or energy is transferred.

If a constant force $F$ moves an object at constant velocity $v$ in the direction of the force:

$$P = F v$$

Summary

• Work is done when a force moves an object in the direction of the force.
• Energy is conserved in a closed system.
• Efficiency measures how much input energy is usefully transferred.
• Power is the rate of doing work or transferring energy.
• Key formulas: $W = F s$, $P = W/t$, $P = F v$, $\text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}} \times 100\%$