In college physics, we often talk about two important ideas: work and energy. These ideas help us understand how things move and change.

Work is the effort it takes to move something. It happens when you apply a force to an object and move it over a distance. You can think of it like this:

• When you push a box across the floor, you are doing work.

We can use a simple formula to show this:

$$W = F \cdot d \cdot \cos(\theta)$$

• Here, $W$ stands for work,
• $F$ is the force you use to push,
• $d$ is how far the object moves, and
• $\theta$ is the angle between the force and the direction it's moving.

If you push directly in the same direction as the movement, then $\theta = 0$, and the formula simplifies to:

$$W = F \cdot d$$

But if you push straight sideways (perpendicular), you aren’t doing any work on the object because it doesn’t move in the direction of your push. In that case, $W = 0$.

Now, let’s talk about energy. Energy is the ability to do work. There are different types of energy:

1. Kinetic energy (KE) is the energy of movement. We can calculate it with this formula:

$$KE = \frac{1}{2} mv^2$$

• $m$ is how heavy the object is, and
• $v$ is its speed.

This means, the faster something moves or the heavier it is, the more kinetic energy it has!

On the other hand, we have potential energy (PE). This is energy stored in an object because of where it is or how it's shaped. The most common type is gravitational potential energy. We can find it using:

$$PE = mgh$$

• $m$ is the mass,
• $g$ is the pull of gravity, and
• $h$ is how high the object is.

So, an object that is higher up has more potential energy since it can fall and do work when it hits the ground.

There’s a big idea that links work and energy called the Work-Energy Theorem. It tells us that the work done on an object is equal to how much its kinetic energy changes:

$$W = \Delta KE$$

This is important because it connects the work you do with the movement of the object.

In short, knowing what work and energy mean is really important for understanding how things move. They help us figure out and predict how different things behave in the physical world.