## Power

In which we find out the difference between ...

**power** vs. **energy**.

If a 70 kg hiker and a 70 kg Tour de France racer climb the same distance, have they gained the same amount of gravitational potential energy? or a different amount?

What's different between the two groups?

Bring in cup, gallon container, and talk about difference between flow rate and volume of water. If you have a flow rate of 1 gallon / 3 sec, how much water (how much volume) is deposited in 1 second? in 6 seconds? in one minute?

### 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

[writing-print and do 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% |

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".

### Your powers

### Tour de France racers

**Floyd Landis**placed 6th in 21 m 53 s

Average Speed: 32.3 mph (52.1 km/h)

Estimated Total Work (energy): 582 Kjoules

Cycling power.

Time = 21 min 53 sec/

How many seconds is that?

Work = 582 Kjoules.

How many Joules is that?

Power = Work / time

What was his average power?

### Average athletes

More
typical figures for non-elite athletes: Vigorous, but sustained exercise is
output of ~ **100 W** = 100 J/s for sustained periods.

How many Joules of energy do you use while playing frisbee for 1/2 hour?...

Power (J/s) = energy / time. So, if you have power and time... how do you figure the energy?

half an hour = how many seconds?

So, how many Joules are you expending to play for 1/2 hour?

Now, it turns out that the human body is ~25% efficiency: you must eat 4 Calories for every 1 Calorie you expend. So... how many Joules of food energy do you need to eat to exercise for 1/2 hour?

But usually we talk about Calories, not Joules. What's the connection?

### 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.

How many ml (milli-liters) in 1.5 liters?

How many calories needed to raise the temperature of 1.5 liters of water by 75 C?

1 cal = 4.187 J

How many Joules needed to heat 1.5 liters up by 75 C?

This
electric kettle says **'1500 watts' **=1.5 kW=1500 J / s

1500 watts is also typical of a microwave oven.

**How long** does it take to boil 1.5 L of water at 1500 watts, starting
at room temperature (25 C) $\to$ boiling (100 C)?

Start with Power = $\frac{E}{time}$,
so what's the time, given the power and energy needed?

### Calories in food

One "Calorie" on a food label is actually 1 **kilo**calorie
in terms of our thermal definition.

1 "Calorie" = 1 kcal = $10^3$ calories = 4187 J

Humans require about 12 Cal of food / lb / day. How many calories/day for a person weighing 150 lbs?

So, 170 Calorie is **what percent** of your
daily energy needs?

This is about the same as the number of Calories (165) in a 12-oz can of Mountain Dew.

So, the number of Calories you use, just sitting around in one day....

= | / per day |

Some dieticians try topoint out the difference by writing food Calories with a capital "C". But it's better just to know this from context. Anytime you hear "food" you know that what they *really* mean is kilocalories.

### back to Exercise

**1/2 hr vigorous exercise** requires ~ 700,000 J $\times$ 1 Cal/4200 J = 167
Cal $\approx$

1/2 hr =

### Losing weight

How many Calories do we have to burn to lose 1 lb?

1 lb (~450 g) of butter has about the same number of Calories as 1 lb of body fat: 3200 Cal.

To lose 1 lb / week, you'd need to either

- reduce your Calorie intake by about
3200/7 ~
**450 Cal each day**$\approx$ - Or you could exercise more: about how much *more* exercise would do it?

### 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.

### Image credits