Ten Precious Joules

A Joule is a unit of work equal to one Newton of force over a distance of one meter, or

Do you know what a watt is? Sure, you have a hundred-watt bulb, a kilowatts per hour charge on your energy bill, and the like. But a watt is one Joule over one second. When Doc Brown from "Back to the Future" says he needs "One point twenty-one Gigawatts!" you don’t now how long he needs it for. It could be one Joule in a very short period of time or it could be 1.21 gigajoules over one second.

However, a bolt of lightning is only one way to get a number of Joules of energy. There are several ways to get Joules of energy, and in this report I will name several.

Section 1: Dropping things

If you use 10 m/s2 as the approximation for the acceleration of gravity, 10 Joules of kinetic energy will be produced when dropping 1 kg 1 meters because

Where E is the energy in Joules, m equals the mass, g equals the acceleration due to gravity and (delta)h equals the height.

Now if we wanted to drop a one inch, 0.15-pound steel ball bearing to produce 10 Joules of kinetic energy, we would need to first convert that to kilograms by multiplying the pounds by 0.454.

Which means the kilograms are equal to 0.15 times 0.454 or 0.068 kg. Now we need to get 10 Joules of kinetic energy by dropping 0.068 kg, so we need a new formula, where you get how far you need to drop it. Let's be more precise with the acceleration due to gravity and make it 9.8 meters per second.

So you need to drop the steel ball bearing about 15.15 meters to get ten Joules of kinetic energy.

Section 2: Rain, Rain, come right here

Let's say that water is overflowing from a one and a half foot high sink, and we want to know how many cups have to overflow to produce ten Joules of energy. Let's make a formula where given the height of the fall and the Joules of energy you need, you can find the mass you need.

Let's put this new formula to use. That water is overflowing from a sink 18 inches high, making

or 0.45 meters. G equals 9.8, and we need 10 Joules.

We need 2.267 kilograms of water or 2267 grams. Using 1 gram as one cubic centimeter, we need 9.58 cups of water, since there are 236.6 cubic centimeters in a cup.

Section 3: Balls away!

We dropped the same one inch ball bearing on a beer bottle repeatedly from atop a ladder and found that the point where the ball gets enough energy to break the bottle is 6 feet and 3 inches, or 6.25 feet. To convert that to meters, we use the formula meters equals feet divided by 3.28.

Calculating that out, we get from the last problem 1.9 meters. Let's see the amount of energy we get with that height.

So we need 1.228 Joules of kinetic energy to break a beer bottle.

Section 4: Super ball bearing

You can also get ten Joules of potential energy by stretching a spring. The energy stored in a stretched spring is

To calculate a the amount of joules you get out of a spring you must multiply the spring constant in Newtons per meter (or K) by the length of the pull in meters. Let's say the spring constant is 300N/m. Let's calculate the pull you need for 10 Joules.

You need a stretch of 0.258 meters for 10 Joules.

I made a giant slingshot once for a school project. You could pull it back 4 feet or a distance of 1.21 meters and had a spring constant of 200 N/m. Those numbers meant the slingshot was capable of generating 121 Joules of energy.

Section 5: I throw a ball in the air. It falls to the ground and I know where

You can add kinetic energy to an object by doing work on it by throwing it. The work you get is expressed in the formula

So let's throw our ball bearing.

So we need to throw our one-inch ball bearing at 17.14 meters per second to produce ten Joules of kinetic energy.

Section 6: Inductor's Energy

We can store energy in an inductor to get an amount of work equaling 10 Joules with the formula

Where I equals the amount of current in Amperes you have and L equals the inductance of the inductor in Henry's.

If you have an L of .001, you will get

So I must equal 141.4 Amps for 10 Joules of energy stored in the inductor. Once you discharge the inductor, you create sparks of heat and light from the stored energy.

I did an experiment on inductors, and they are very dangerous. They can create flashes with enough power to blind the naked eye, and can also blow pits into a screw and cover it with carbon. You use special safety goggles to view inductor experiments. The inductor we used was so powerful, we needed to use capacitors to keep it from totally destroying the power supply. A schematic is below this paragraph.

Section 7: Capacitor's Energy

You can store energy in a capacitor. The energy you store into it is calculated from the formula

Where C equals the Farads of the capacitor and V is the voltage you will store. Let's get 10 Joules of energy by discharging a 0.1 Farad capacitor.

You need around 14.14 volts.

WARNING WARNING WARNING

YOU SHOULD NOT PLAY AROUND WITH A CAPACITOR. 10 Joules is enough to punch a hole through aluminum foil and still create a lot of sparks, which could start fires. 30 Joules is enough to arcweld non-insulated wire to a ball bearing. I know this from an experiment I did with a capacitor. We wore safety goggles for this, to keep ourselves from being blinded.

Other uses for a capacitor are lighting a lightbulb for a short time. The lightbulb lights with a flare, then slowly dims down. The reaction is much longer than the short circuit, but much less intense. A slight warning is if you use too much energy, the lightbulb may burn out.

Section 8: Heating

What about heating water? The energy created when you heat up water is capable of creating Joules of heat. It takes 4186 Joules to heat a kilogram of water 1-degree Celsius. The formula for the calculation of the heat energy you need to heat up the water is

Where (delta)h is the energy in Joules and (delta)T is the temperature increase, with M being the mass. Let's see how much heat you get when you use 10 Joules of energy to heat up a gram of water.

5 over 2 degrees Celsius, or 2.5 degrees.

Another way to provide heat energy is to put a resistor across a charged capacitor. The energy in the capacitor turned into heat. You can feel ten Joules of heat energy in the resistor and it is nearly too hot to touch when 40 Joules of energy are applied.

Section 9: Comparisons

Let's make a table of all the equations and see how they compare.

Dropping something
Throwing something
Spring
Heating water
Inductor
Capacitor

You will note that most of the formulas follow the pattern

Where X is a property of a thing and Y is something that happens to the thing.

Section 10: Conclusion

In conclusion, it is rather easy to work with ten Joules of energy. A freak bolt of lightning to a clock tower isn’t the only way to provide work. A capacitor or spring may suffice. Also of note, some reactions to get Joules are mild and some are dangerous. For example, you can create a huge spark with an inductor and pull a spring back for the same amount of energy, but one can create a huge spark capable of punching a hole in aluminum foil and another can fire a ball bearing across the room.

Appendix B: Comparing Inductors and Capacitors (1)

Inductors store magnetic charges, whereas capacitors store electrical charges. Inductors have current’s going through them in order to help them store the magnetic flux, whereas capacitors have that voltage for a similar reason. The larger a capacitor, the more charge it can store for each Volt or in it. The same is true for inductors with Amperes and flux. When an inductor is being used, you can disconnect the inductor to make a spark. You can put a wire across a capacitor for the same effect. You could say the capacitor dumps its energy into a short circuit and the inductor dumps its energy into an open circuit. The capacitor can be used to smooth out voltages, and the inductor can be used for smoothing out currents.

References

  1. The comparison information for inductors and capacitors is from http://tomacorp.com/motor/lc.html
  2. Ball bearings are from Hoover Balls

10/09/2001

By toma