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/
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