A.3.1 Conservation of energy

Kinetic Energy

It depends on two factors:

1. Mass of the object ($m$)
2. Speed of the object ($v$)

The formula for kinetic energy is:

$$E_k=\frac{1}{2}m{v}^2$$

Potential Energy

There are two main types of potential energy:

1. Gravitational Potential Energy
2. Elastic Potential Energy

Gravitational Potential Energy

The formula for gravitational potential energy is:

$$E_p=mgh$$

where:

• $m$ is the mass of the object
• $g$ is the acceleration due to gravity (approximately 9.81 m/s² on Earth)
• $h$ is the height above the reference point

Elastic Potential Energy

The formula for elastic potential energy is:

$$E_e=\frac{1}{2}k{x}^2$$

where:

• $k$ is the spring constant (a measure of the spring's stiffness)
• $x$ is the displacement from the spring's equilibrium position

Mechanical Energy

In an ideal system (without resistive forces like friction or air drag), the total mechanical energy remains constant.

This is known as the conservation of mechanical energy.

Conservation of Mechanical Energy

Energy Losses

1. In real systems, energy is often lost due to resistive forces such as friction and air drag.
2. These forces convert mechanical energy into thermal energy, reducing the total mechanical energy of the system.

Friction

When an object slides across a surface, friction converts some of its kinetic energy into thermal energy, causing the object to slow down.

Air Drag

1. It increases with the object's speed and surface area.
2. Like friction, air drag converts kinetic energy into thermal energy, reducing the object's speed.

Reflection