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Home Newtonian Physics Scaling and OrderofMagnitude Estimates Examples Cost of transporting tomatoes  
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Cost of transporting tomatoesRoughly what percentage of the price of a tomato comes from the cost of transporting it in a truck?
The following incorrect solution illustrates one of the main ways you
can go wrong in orderofmagnitude estimates. The problem is that the human brain is not very good at estimating area or volume, so it turns out the estimate of 5000 tomatoes fitting in the truck is way off. That's why people have a hard time at those contests where you are supposed to estimate the number of jellybeans in a big jar. Another example is that most people think their families use about 10 gallons of water per day, but in reality the average is about 300 gallons per day. When estimating area or volume, you are much better off estimating linear dimensions, and computing volume from the linear dimensions. Here's a better solution:
Better solution: As in the previous solution, say the cost of the
trip is $2000. The dimensions of the bin are probably 4 m × 2 m × 1 m, for a volume of 8 m^{3}. Since the whole thing is just an order of magnitude estimate, let's round that off to the nearest power of
ten, 10 m^{3}. The shape of a tomato is complicated, and I don't know
any formula for the volume of a tomato shape, but since this is just
an estimate, let's pretend that a tomato is a cube, 0.05 m × 0.05
× 0.05, for a volume of 1.25 × 10^{4} m^{3}. Since this is just a rough
estimate, let's round that to 10^{4}m^{3}. We can find the total number
of tomatoes by dividing the volume of the bin by the volume of one
tomato: 10 m^{3}/10^{4} m^{3} = 10^{5} tomatoes. The transportation cost
per tomato is $2000/10^{5} tomatoes=$0.02/tomato. That means that
transportation really doesn't contribute very much to the cost of a
tomato.


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