Sunday, September 23, 2012
How long will a Snickers bar power a Cuckoo Clock
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 ?
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.