What do potential energy and kinetic energy make together?

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When potential energy and kinetic energy are combined, they indicate total mechanical energy.  Mechanical energy is the energy that an object has due to its motion and/or due to its position.  Energy of motion is kinetic energy, and energy of position or shape is potential energy.  Think of mechanical energy like you would an addition problem.  

Mechanical energy = kinetic energy + potential energy

All three of those energies are measured in Joules, so there is no need to even worry about converting units.  

When I teach my students about mechanical energy, I like to use a roller coaster as an example.  When the roller coaster is at the top of the highest hill, it has all gravitational potential energy (just pretend the roller coaster stops for a second before going down the hill).  Halfway down that hill, the roller coaster is moving quickly, so it has kinetic energy; however, it still has potential energy because it's only halfway down. At the bottom of the hill, all of the potential energy has been converted to kinetic energy.  Due to the law of conservation of energy, the total energy of the roller coaster system must remain the same.  That means the total mechanical energy within the system stays the same.  Let's put some numbers to it.  

At the top of the hill, the roller coaster has 5,000 J of potential energy and 0 J of kinetic energy.  

Mechanical energy = potential energy + kinetic energy

5,000 J = 5,000 J + 0 J

Halfway down the hill, the equation would look like this.  

5,000 J = 2,500 J + 2,500 J

At the bottom of the hill, it would look like this.

5,000 J = 0 J + 5,000 J

As you can see, the mechanical energy of the system is conserved, and it is the sum total of the potential energy and kinetic energy within the system. 

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