Re: [Phys-L] widget rate puzzle ... reasoning, scaling, et cetera

[Carl Mungan <mungan@usna.edu>]

>    It takes 5 minutes for 5 machines to make 5 widgets.
>    So, how many minutes does it take for 100 machines
>    to make 100 widgets?

How I would explain it.

Start with given rate data:

Divide output (widgets) by input (machines) => each machine makes 1 widget.

Divide production of each machine by total time => each widget takes 5
minutes to make.

Repeat for unknown rate data:

Divide output (widgets) by input (machines) => each machine makes 1 widget.

Multiply production of each machine by time to make each output => it take
5 minutes.

In each case, the second step is a formula of the form: total time/time per
item = number of items produced per machine. The first step is a formula of
the form: total number of items produced/total number of machines producing
items = number of items produced per machine. So we could equate these two
ratios.

Somewhat similar concepts arise in converting number of molecules, number
of moles, number of kilograms, molar mass, number and mass density, etc. In
both cases, the trick seems to be come up with a formula in words and check
it by carrying units and by putting in some sample numbers to see if it
makes sense.

-- 
Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/