Mass and Weight

Date: 08/16/97 at 04:24:42
From: Annie
Subject: Units of measurement

Dear Dr. Math,

I would like to know why it is that mass and weight supposedly measure 
different things but they are both measured with the same unit of 
measurement. If weight is supposed to change on the moon and mass is 
not, how can you tell the difference?
    
Yours sincerely,
Annie

Date: 08/16/97 at 07:56:31
From: Doctor Anthony
Subject: Re: Units of measurement

Weight is the force with which the earth and the body attract each 
other, and it can vary depending on distance from the centre of the 
earth. This force is measured in Newtons.  

Mass is a measure of the amount of material in the body (the sum of 
the atoms and molecules in the body). The mass is measured in 
kilograms. Clearly mass cannot vary.

Newton's gravitational law states 
                                       G.m1.m2
                                 F  = ----------
                                          r^2

Here m1 and m2 are the two masses and r their distance apart.  
G is a universal constant and F is the force of attraction between 
the bodies.

Now if m2 (say) is the earth, r is the radius of the earth, and 
we are talking about bodies at the surface of the earth, the terms 
G.m2/r^2  can be thought of as a single constant, called 'g' and 
we get
                                 F = m1.g

So at the surface of the earth the force of attraction in Newtons is

                  mass x g, and g = 9.8 ms^(-2)

You will notice that F and m1 are proportional to each other, so 
it is convenient to measure mass by 'weighing' a body. That does not 
mean that weight and mass are the same thing.

Since by Newton's second law  Force = mass x acceleration, this means 
that a body falling freely under gravity at the surface of the earth 
is accelerated at 9.8 ms^(-2). Of couse if we move a long way up from 
the surface of the earth, (or we are operating on the surface of the 
moon) this value of g no longer applies, and the attractive force is 
less. The mass does not change.

It is unfortunate that historically, people talked about force in 
pounds and weight in pounds, and this has led to the confusion between 
the two. It is safer to use the S.I. units, Newton for force and 
kilogram for mass, and so avoid the confusion.

1 Newton is the force that gives a mass of 1 kilogram an acceleration 
of 1 ms^(-2).

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/