Re: A weighty subject

[Arlyn DeBruyckere <arlynd@HUTCH.K12.MN.US>]

Leigh Palmer wrote:

> > Arlyn DeBruyckere wrote:
> >
> > > It is also a problem in teaching them about significant figures that 40 Lb
> > > (1 sig fig) can be equal to 18.1 Kg (3 sig figs). They don't understand
> > > why I get upset when they measure 20 ml and then decide to record 20.00 ml
> > > because I told them they should measure to the nearest .01 ml.
> >
> > I would have said that the value 40 pounds is precise to 2 sigfig. Not all
> > final zeros are insignificant; it depends on the context.
>
> I agree. I'd sure complain loudly if I bought a 40 pound bag
> of potatoes and found on weighing it that I'd got 36.5 pounds.
> The implied contents is net, and it should be *at least* 40.0
> pounds. This particular example also demonstrates the shallow
> nature of the "significant figure" idea. Surely Arlyn wouldn't
> tell his students that the "correct" label should read 20 kg.
>
> Leigh

I understand, you understand, probably all of the people on this list understand
that it depends on the context but my students do not understand.  I also
understand that the 40 Lbs is pound-mass but this is a HUGE problem for students
to understand at the high school level (and I would wager at the beginning
college level).  Consider two situations in lab:

1.  A student records that he/she puts 40 Lbs on a 25 cm square and calculates a
pressure (not including the atmosphere) of 2840.90497 N/m^2.  (or even 2841
N/m^2)  How many of you have a problem with this?  They don't understand the
difference between their 40 Lbs and the bag label of 40 Lbs.  (Hey, if the
manufacturer can say 40 Lbs is the same as 40.0 Lbs why can't I say 2800 N/m^2 is
the same as 2840.90497 N/m^2 - its what my calculator told me?)

2.  In an old physics book "One slug is defined as the mass that, when acted upon
by a 1 lb force, is given an acceleration of 1 ft/sec^2."  A student then sees
the bag labeled 40 Lbs (18.1 Kg), knows this measures weight, that a weight is
force and doesn't understand my problem when he/she puts 18.1 Kg in for whatever
force they might need to solve the problem.  Would you as his/her teacher have a
problem with it?

I remember dealing with this same problem when I was in high school.  It finally
"clicked" with me when I got an old engineering text that described mass units as
slugs or kilograms and weight and other force units as pounds or newtons.  Since
then it has always "got my blood pressure up" to see notations like 40 Lbs (18.1
Kg) because I know the great confusion it caused me.  I didn't get it figured out
until about half way through my HS senior year in physics.  That failure to
figure it out caused many problems in my 9th grade physical science class.  As a
high school teacher I see it as a HUGE wall for a student's understanding of
force and mass.  There are some students that never "get it" no matter how much I
try.  Many of these students MEMORIZE what they are supposed to do but a week or
two later when their short term memory has faded are again making the same
mistakes.
--
Arlyn DeBruyckere
Hutchinson High School