Sunday, September 23, 2012

How long will a Snickers bar power a Cuckoo Clock

I had decided that my life would not be complete without a hand carved German Cuckoo Clock so here we are.   The basic design of the Cuckoo Clock stretches back to before 1800.  The count of the weights hanging from the clock indicate the number of features that a clock has:  2 weights one to drive the clock and the other to drive the cuckoo.  3 weights add a music box to the mix.
The fact that the clock is entirely weight driven makes it rather easy to figure out how much energy is used up driving the clock.   This posed a question that I wanted an answer to:

For how long would a standard Snickers bar power the 2 weight Cuckoo Clock that I have ?

Let's get a rough answer !

From measurement the clock weights move about  19 inches over 2 days.
This means that over two days gravity is 'calling back' the work that was done to lift the weights 19 inches.
The 'standard' value for gravity at the surface of the earth at 45 degrees latitude is 9.80665 meters/second-squared.
Because the earth is spinning the effect of gravity is less at the equator than it is at the poles because of the centrifugal effect wanting to 'throw' the object off the surface thus it matters greatly where on earth the measurement is taken.   45 degrees latitude is close enough so we'll use that.

The weight (mass) of the 2 weights totals 3 kilograms

So the amount of energy in Newton-Meters that it takes to run the clock for a day is:

Force * distance   =  m * g * d

(3 kilograms) * (9.80775 meters/ second-squared) * (19 inches/ 2 days) * (0.0254 meters / inch) = 7.099 Newton-Meters/day

From the information on the wrapper,  a 2 oz Snickers bar contains  273 nutrition calories  (a nutrition calorie is about 1000 energy calories)

Of course the human body cannot turn all of the candy bars energy into muscle power, but estimates put the conversion efficiency at between 20-25%.   We'll take the low end and assume that 20% of the Snickers bar gets turned into the muscle power used to lift the clocks driving weights.

So the energy required per day in nutrition-calories is:

7.099 Newton-Meters/day  *  ( 1 calorie /  4186.8 Newton-Meters) = 0.001696 calories/day

at 20% efficiency the required ingestion is:

0.001696 calories/day  /  0.20   =  0.00848 calories/day

The Snickers bar  contains    273  calories

So this yields

273 calories  /  (0.00848 calories/day)  =  32193 days  =  88 years

So there we have it.

One Snickers bar is enough to run my clock, bird call and all, for about 88 years.

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