Made to Order (of Magnitude)
Description:
Several unrelated order-of-magnitude calculations.
Learning Goal:
To be able to make order-of-magnitude calculations.
Imagine that a company wants to build a new factory. Such a complex project would involve significant investment
in terms of both time and money. Consequently, before construction can start the company asks for
an estimate
of the
total cost. Although estimate figures are not exact, they are still helpful: For instance, if the projected cost is three
times the amount of money that the company is willing to spend, the project will be canceled or substantially
changed.
Individuals make such estimates all the time. For instance, when you need to drive somewhere for a meeting, you can
roughly predict how much time you will spend on the road and depart accordingly. Of course, the actual travel time is
unlikely to be exactly the same as the estimated one —but it still helps to make an estimate so that you can decide
when to leave.
Physicists must frequently make such estimates—known as
order-of-magnitude calculations
—as part of their job.
Depending on the results of the estimate, a potentially lengthy and costly research project may be postponed,
canceled, or redesigned. Being able to make a quick calculation and get a "ball-park figure" of the expected result is
an important skill for a scientist, involving processes such as identifying relevant information, searching for this
information, and using your experience or background knowledge.
In this problem, you will practice making such order-of-magnitude calculations.
It is impossible, of course, to give an accurate answer to this question. However, it is quite possible to find the
order of magnitude
of the answer. All one needs to do is to use some common sense and, possibly, search for
relevant reference information. The calculation can proceed as follows:
There are about
people on earth. An average adult male weighs, say, 75
; an average adult female
weighs about 60
, and an average child will weigh considerably less than 60
. Figuring roughly one child per
adult, we can reasonably say that an average person's mass is about 50
, which gives the total mass of all humans
on our planet as