*Feel free to modify and personalize this study guide by clicking "Customize."*

#### Kinetic Energy

**Kinetic energy** (K or KE) is the energy of motion; if an object is in motion, it has kinetic energy.

The formula to find kinetic energy is: **K = \begin{align*}\mathbf{\frac{1}{2}}\end{align*}mv ^{2}**

**Note:** in the above equation, m stands for mass in kilograms (kg), and v is the object's velocity in meters per second (m/s).

Based on this equation, what happens to the kinetic energy if you double the mass? If you double the velocity?

Knowing the units for mass and velocity, what unit is energy measured in?

The kinetic energy of an object can also be changed by doing work (W) on the object, so **W _{net} = ∆KE**.

You can check your answers and find more help with kinetic energy here.

#### Potential Energy

**Potential energy** (U or PE), on the other hand, is the energy stored in a system – it's the energy that an object can *potentially* exert!

The two formulas for potential energy are:

- Gravitational potential energy:
**U**_{g}= mgh- h is heigh above the ground in meters, g is acceleration due to gravity (9.8 m/s
^{2})

- h is heigh above the ground in meters, g is acceleration due to gravity (9.8 m/s
- Spring potential energy:
**U**_{sp}= \begin{align*}\mathbf{\frac{1}{2}}\end{align*}k∆x^{2}- k is the spring constant in Newtons per meters, x is the amount the spring is displaced from resting position in meters

Based on these equations, what happens to the potential energy when an object is high above the ground? If an object has a large mass? If a spring is barely displaced from resting position?

How does the formula for gravitational potential energy relate to work?

To find more help with potential energy and to check your answers, click here.

#### Conservation of Energy

The **law of conservation of energy** states that in a **closed system**, the total energy does not change! What is a closed system? Is energy transferred in a closed system?

Therefore, \begin{align*}\mathbf{\sum}\end{align*}**E _{initial} = \begin{align*}\mathbf{\sum}\end{align*}E**

**.**

_{final}
**Note:** \begin{align*}\sum\end{align*} is the capital Greek letter "sigma" and stands for "the sum of").

How do kinetic and potential energy relate to the total or sum of the initial energy? To **mechanical energy**? If the kinetic energy decreases in a closed system, what happens to the potential energy?

To check your answers and to find more on conservation of energy, click here.