Power

In which we examine the difference between ...

power vs. energy.

Gravitational energy: $$\text{GravE}=mgh.$$

If a 70 kg hiker and a 70 kg Tour de France racer climb the same height, have they gained the same amount of GravE? or a different amount of GravE?

What's different between the two groups?

The quickness of energy transformation

The notion that captures this idea of how quickly work is done is...

Power = $\frac{W}{t}$ = work done / time to do it=$\frac{E}{t}$ = energy/time

SI Units 1 Joule / sec $\equiv$ 1 "watt"

Remember our comparison of the energy/gram of TNT (0.65 Cal / g) vs chocolate chip (5.0 Cal / g)? But, the energy in TNT can be released much, much faster (energy / time) than the energy in a chocolate chip cookie.

Student power

A proposal on one campus was made that the exercise machinery in their equivalent of the RFC could be hooked up to electric generators, and that power could be used to offset some of the electricity consumed on campus.

[writing assignment: download and do it with a friend].

In the student power exercise, you will climb a height $h$ equal to
$h =$ (number of steps) $\times$ (height of one step [cm]) $\times \frac{\rm 1\ m}{\rm 100\ cm}$.

Your mass is... $m$ [kg] = (weight [lbs]) $\times \frac{\rm 1\ kg}{\rm 2.2\ lbs}$.

Estimate in class before they do it...

The total gravitational energy you gained was...
GravE = $m\cdot g\cdot h=
    =$(your mass [kg]) $\times$ 9.8 m/s${}^2 \times$ (height [m]) = _____ Joules

So your power = energy / time is:
power = (GravE [J]) / (time [sec]) = _____ Watts

Light Bulb

How many light bulbs could you keep going???

100 W=100 J/s for an incandescent, '100 W' bulb.

Only About 2% of the incoming ElectricE comes out as light, 98% is heat.

Luminous efficiency

In general, efficiency is: $$\frac{\text{energy in some useful form}}{\text{total energy input}}.$$

candle	0.04%
incandescent	2%
compact fl.	10%
LED (theory)	40%

See this story about LED traffic lights (Elkhart County, winter of 2013).

2010: A european ban on selling incandescent light bulbs has gone into effect. They want citizens to buy compact fluorescents or LED fixtures which have a much higher efficiency. But a german businessman is trying to get around the ban by selling incandescents labelled as "heat balls".

Heating water

What's a calorie? [little c]

1 cal is the amount of heat (thermal energy) needed to raise 1 ml of water by 1 degree celsius.

1 cal = 4.187 J

So, how many joules per kilocalorie = Calorie?

Electric usage

Power = E/t $
\to$ Energy = Power * time.

We've been measuring energy in Joules, but many other units are possible. The electric company uses kiloWatt*hrs which typically costs about $0.13

How many Joules are there in 1 kWh?

Automobiles

150 kW

745.7 W = 1 horsepower

This 1967 Mustang had engines ranging from 115-390 horsepower.

200 horsepower $\times \frac{746 W}{1 hp} \approx 1.5 \times 10^5$ W.