Conservation of Kinetic and Potential Energy

Physics Tutorial

Conservation of Kinetic and Potential Energy

Intro

Energy comes in many different forms. It can’t be created or destroyed, but it can move between objects and change forms. The energy of motion of a moving object is called kinetic energy, and is given by the equation

KE = 0.5m(v^2)

Where m is the object’s mass, and v is the object’s velocity.

Another form of energy is called potential energy which is the energy an object has from being at a spot in a field where it would rather not be. When you lift an object up from the ground, the energy you put into lifting it becomes gravitational potential energy, given by PE = mgh, where m is mass, g is acceleration due to gravity (9.8 meters per second), and h is height. Pulling opposite poles of magnets apart or pushing identical poles close together also produces its own kind of potential energy.

When you stop holding up an object, it starts to fall, and that gravitational potential energy transforms into kinetic energy (when it actually hits the ground, the energy gets dispersed in a complicated mess of heat and mechanical deformation).

Sample Problem

If a 5 kg rock is dropped from a height of 200 meters, how fast will it be moving at the moment before it hits the ground?

62.6 m/s


24.3 m/s


42.5 m/s


200.0 m/s


123.2 m/s


Solution

Whereas we could solve this problem using kinematic equations, conservation of energy makes these kind of problems much easier.

The total energy isn’t going to change from start to finish. It will just move entirely from potential to kinetic. At the start, it’s all potential, given by mgh.

(5)(9.8)(200) = 9800 J That’s joules by the way, the basic unit of energy.

This is all going to become kinetic energy, so:

9800 = 0.5m(v^2)
9800 = 0.5(5)(v^2)
3920 = (v^2)
sqrt(3920) = v = 62.6 m/s

This is an incredibly powerful trick. Using this method, we could even find how fast the rock is moving at any particular height just by finding the potential at that height, subtracting it from the starting total, and setting the leftover equal to kinetic energy.



About The Author

Physics Guru And General Math And Science Enthusia
I've always had a passion for learning science and then turning around and teaching it to anyone who will listen. My interest led me to an undergrad degree in physics, an attempt at a teaching credential (which unfortunately imploded at 95% completion in an administrative snarl), a jump to a Masters...
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