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Mass and Weight

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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
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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/
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Associated Topics:
High School Definitions
High School Physics/Chemistry
Middle School Definitions
Middle School Terms/Units of Measurement

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