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# Potential Energy

## Objects can store kinetic energy based on their height from a surface, springs can store energy by being compressed or stretched.

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Potential & Kinetic Energy

### Potential Energy

This diver is standing at the end of the diving board, ready to dive. After she dives and is falling toward the water, she’ll have kinetic energy, or the energy of moving matter. But even as she stands motionless high above the water, she has energy. Do you know why?

### Stored Energy

The diver has energy because of her position high above the pool. The type of energy she has is called potential energy. Potential energy is energy that is stored in a person or object. Often, the person or object has potential energy because of its position or shape.

Q: What is it about the diver’s position that gives her potential energy?

### Gravitational Potential Energy

Potential energy due to the position of an object above Earth’s surface is called gravitational potential energy. Like the diver on the diving board, anything that is raised up above Earth’s surface has the potential to fall because of gravity. You can see other examples of people with gravitational potential energy in the Figure below and below. You can also watch a cartoon introduction to gravitational potential energy by playing video #10 at this URL: http://www.animatedscience.co.uk/flv/

Gravitational potential energy depends on an object’s weight and its height above the ground

### Elastic Potential Energy

##### (information in this section adapted from http://www.physicsclassroom.com/class/energy/u5l1b.cfm)

A second form of potential energy is elastic potential energy. Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs, an arrow drawn into a bow, etc. The amount of elastic potential energy stored in such a device is related to the amount of stretch of the device - the more stretch, the more stored energy. Springs are a special instance of a device that can store elastic potential energy due to either compression or stretching. A force is required to compress a spring; the more compression there is, the more force that is required to compress it further.

### Other Forms of Potential Energy

All of the examples of potential energy described above involve movement or the potential to move. The form of energy that involves movement is called mechanical energy. Other forms of energy also involve potential energy, including chemical energy and nuclear energy. Chemical energy is stored in the bonds between the atoms of compounds. For example, food and batteries both contain chemical energy. Nuclear energy is stored in the nuclei of atoms because of the strong forces that hold the nucleus together. Nuclei of radioactive elements such as uranium are unstable, so they break apart and release the stored energy.

### Summary

• Potential energy is energy that is stored in a person or object.
• Gravitational potential energy is due to the position of an object above Earth’s surface. The object has the potential to fall due to gravity. Gravitational potential energy depends on an object’s weight and its height above the ground.
• Chemical energy and nuclear energy are other forms of potential energy.

### Kinetic Energy

$Jet Takeoff$

This military jet requires a tremendous amount of work done on it to get its speed up to takeoff speed in the short distance available on the deck of an aircraft carrier.  Some of the work is done by the plane’s own jet engines but work from a catapult is also necessary for takeoff.

### Kinetic Energy

Energy is the ability to change an object’s motion or position.  Energy comes in many forms and each of those forms can be converted into any other form.  A moving object has the ability to change another object’s motion or position simply by colliding with it and this form of energy is called kinetic energy.  The kinetic energy of an object can be calculated by the equation

KE=12 mv2\begin{align*}KE = \frac{1}{2} \ mv^2\end{align*},

where m\begin{align*}m\end{align*} is the mass of the object and v\begin{align*}v\end{align*} is its velocity.  The kinetic energy of a moving object is directly proportional to its mass and directly proportional to the square of its velocity.  This means that an object with twice the mass and equal speed will have twice the kinetic energy while an object with equal mass and twice the speed will have quadruple the kinetic energy.

The SI unit for kinetic energy (and all forms of energy) is kgm2s2\begin{align*}\text{kg} \cdot \frac{\text{m}^2}{\text{s}^2}\end{align*} which is equivalent to Joules, the same unit we use for work.  The kinetic energy of an object can be changed by doing work on the object.  The work done on an object equals the kinetic energy gain or loss by the object.

#### Summary

• Energy is the ability to change an object’s motion or position.
• There are many forms of energy.
• The energy of motion is called kinetic energy.
• The formula for kinetic energy is KE=12 mv2\begin{align*}KE = \frac{1}{2} \ mv^2\end{align*}

### Review: answer in complete sentences unless otherwise directed

1. What is potential energy?
2. Why does food have potential energy?
3. How is gravitational potential energy different from elastic potential energy?
4. What is kinetic energy?
5. What two things can change the amount of kinetic energy an object has?
6. Look at the picture at the beginning of this reading on potential energy (of the diver).  What is it about the diver’s position that gives her potential energy?

elastic potential energy graphic from How Stuff Works http://science.howstuffworks.com/crossbow2.htm

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