Page 14 - Module2_B1_B2_i2_Portrait

As you have probably figured out, the greater the mass of an object on the surface of the earth,
the greater is the weight of this object. These two quantities are approximately proportional to
each other as long as the body remains on the surface of the earth. The word ‘approximately’ in
the previous sentence refers to the fact that the pull of the earth on a body of a given mass
varies slightly with the position of the body on the earth’s surface. For example, a body that
weighs 57.3 lbs at the North Pole would weigh 57.0 lbs at a place on the equator. This occurs
because a body at either pole is slightly closer to the centre of the earth than it is at the equator.
Thus, the pull of the earth on the body is greater at the poles and slightly smaller at other places
on the earth. However, we usually neglect this slight difference.

Physicists and engineers measure masses of bodies in slugs or kilograms and weights in
pounds or Newtons. The equation relating mass and weight is:

w = mg

This is a form of Newton’s second law (F = ma).

In this equation, g has a definite numerical value. We will use the following relations:

There is a great source of confusion in British marketing practices. For example, we often see
on a packet of sugar the information regarding the contents:

1 kg or 2.2 lbs

We note that 2.2 lbs equals 1 kg. We have just learned that 2.2 lbs is the ‘weight’ of the sugar
and that 1 kg is the ‘mass’ of the sugar. In other words, British packaging practices list the
weight of the product if we deal with the imperial system and list the mass of the product if we
are in the metric system.

For example, suppose the weight of a piece of cheese is marked 32 oz. and we wish to know
the number of grams. First we convert the weight in ounces to 2 lbs. Then we convert from
pounds to Newtons.

Next, we use the relation:

Therefore, we write:

Note that we can convert from pounds to Newtons since both are units of weight and we can
convert from kilograms to slugs since both are units of mass. However, if we want to find a
mass if we know a weight or a weight if we know a mass we must use the equation:

m = w/g or w = mg

Issue 2 – September 2016 2-8 Total Training Support Ltd
Module 2.2 Mechanics © Copyright 2016