Study Guide

# Energy and Momentum - Conservation of Energy

## Conservation of Energy

So if there's all these forms of energy, we need some way to move between them—Doc Brown figured out a way to turn the kinetic energy of a DeLorean at 88 miles per hour into time travel, so moving from gravitational potential to kinetic shouldn't be too hard in comparison. Even without a flux capacitor.

Like momentum, energy is a conserved quantity. The law of conservation of energy states that energy can never be created nor destroyed, only changed from one form to another. The battery in an electric car has stored potential chemical energy that it converts into electrical energy; this electrical energy is turned into magnetic energy in a motor, which turns it into rotational kinetic energy; spinning tires on asphalt turn that rotational kinetic energy into the kinetic energy of the car.

In purely mechanical systems, we'll often look at the transformation between spring or gravitational potential energy into kinetic energy. From the law of conservation of energy, we know that the initial energy and final energy must be equal, even if they take different forms:

Σ Ei = Σ Ef
Ui + Ki = Uf + Kf

Sometimes, an object will start with only potential energy and end with only kinetic (or vice versa); other times objects will have a mixture of both kinds of energy. If we think of the total energy in an isolated system as being contained in a bucket. The block will start off with a bucket full of gravitational potential energy. As the block falls and its height decreases, the gravitational potential energy bucket drains and the kinetic energy bucket fills. Just before the block hits the ground the kinetic energy bucket is filled and the potential energy bucket is completely drained. Note: Once the block hits the ground the energy just doesn't disappear - it becomes transformed into sound and thermal energy so we would need more buckets.

### Common Mistakes

When you pick a point in time to analyze, be sure to capture all the forms of energy at that instant—and no more. Some kinds of energy may appear and disappear as an object moves (a snowboarder in a half pipe has potential energy, then kinetic, then potential again), but the only energy that matters is what's present at the exact instant you chose to examine.

### Brain Snack

Some of the best devices for converting potential energy to kinetic are ridiculous contraptions called Rube Goldberg machines, which use elaborately set-up collections of junk to achieve a relatively simple task. The best builders of Rube Goldberg machines may be the band OK Go.