High school physics is often a combination of mathematics and science. With a good background in algebra, students can gain a deeper understanding of kinetic and potential energy. Simply defined, kinetic energy is energy in motion, and potential energy is stored energy. Potential energy is greater when an object is not moving and when it is at a greater height above the Earth. Potential energy can be converted into kinetic energy as an object begins to move. The faster an object moves, the more kinetic energy it has.
Transformation of Energy

Energy can be transformed from potential into kinetic and from kinetic to potential. For example, if a vase sitting on a shelf falls, it gains more kinetic energy and loses potential energy as it falls. When it hits the ground and comes to a stop, kinetic energy is converted to potential energy again, but the potential energy would not be as great as it was when the vase was higher on the shelf. Another example is a roller coaster at a stop at the peak of the ride, where it possesses great potential energy. As it makes its descent and gains speed, its potential energy is converted into kinetic.
Example Kinetic Energy Calculation

You can calculate kinetic energy by taking half of the mass of the object multiplied by its velocity squared. Suppose a 56.2 kg ice skater is moving across the rink at a velocity of 2.71 meters per second. You want to know the skater's kinetic energy. Take half the mass, which will equal 28.1 kg. Square the velocity, which will equal 7.34 meters per second. Now, multiply these two numbers together. The skater's kinetic energy is 205 Joules.
Example Potential Energy Calculation

To calculate an object's gravitational potential energy, multiply its mass by the gravitational pull of the Earth (a constant 9.8 meters per second squared), then multiply by its height above Earth. If you take a 6.2 kg piece of luggage at the airport and heft it onto your shoulder 1.3 meters off the ground, you can calculate the potential energy of the luggage on your shoulder: 6.2 kg is the mass of the luggage, 9.8 meters per second squared is gravity on Earth, and 1.3 meters is the height of the luggage. The equation to solve this example is 6.2 x 9.8 x 1.3 = 79 Joules of potential energy.
Potential and Kinetic Energy Combined

If no other energy is present, then the sum of kinetic and potential energy in a system is its mechanical energy. The mechanical energy that is present before an event is the same after the event. Suppose a 23.2 kg Olympic diver springs vertically into the air to a height of 10 meters above the surface of a 4meterdeep pool. You can calculate the speed of the diver as she enters the pool if air resistance is not considered. Use the surface of the pool as a reference level. Subtract the depth of the pool from the height of the diver's vertical leap: (10  4 = 6 meters). Solve for the potential energy at the top of the diver's jump by multiplying mass times gravity times height: (23.2 x 9.8 x 6) = 1,364 Joules. Because mechanical energy is conserved, the kinetic energy of the diver when she reaches the water is the same as the potential energy at the top of her jump, 1364 Joules. Use the kinetic energy formula  one half of the mass times velocity squared  to solve for velocity. Take half the mass of the diver, 11.6 kg. Divide the kinetic energy by this number, then take the square root to find velocity. The speed of the diver as she enters the pool is 10.8 meters per second.
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