Work and energy are two important ideas in how things move and interact. Even though they are related, they mean different things and are used in different ways.

What is Work?
In simple terms, work is what happens when a force moves something over a distance. You can think of it as energy being transferred from one place to another.

The formula for work ($W$) is:
$W = F \cdot d \cdot \cos(\theta)$
Here's what that means:

• $F$ is the amount of force you apply.
• $d$ is how far the object moves.
• $\theta$ is the angle between the direction you push and the direction the object moves.

Work can be positive, negative, or even zero. This depends on whether the force helps the object move, pushes it back, or doesn't affect it at all.

What is Energy?
Energy is the ability to do work. There are different types of energy. For example:

• Kinetic Energy is the energy of things that are moving.
• Potential Energy is stored energy that depends on an object's position.

To find the total mechanical energy in a system, you add up these two types:
$E_{\text{total}} = KE + PE$
Where:

• $KE$ (kinetic energy) is calculated using the formula: $\frac{1}{2}mv^2$ (m = mass, v = velocity).
• $PE$ (gravitational potential energy) is calculated using: $mgh$ (m = mass, g = gravity, h = height).

In summary, work is about what happens when a force is applied to move something, while energy is about the ability to make that movement happen. Knowing the difference helps us understand how things move and how they will behave in different situations.