Professor Dave here, let's learn the
difference between mass and weight.
Most people are familiar with the terms
mass and weight, and might assume that
mass is simply a fancy word for weight.
In actuality this is not the case, and
the two terms have rather different
meanings. To put it simply, mass is a
scalar and weight is a vector. This means
that mass has only magnitude, since it is
a measure of an object's inertia, or
essentially how much matter is present
within the object. Weight, on the other hand
has magnitude but also direction because
it is a force, specifically the force
that is exerted on an object by virtue
of its position in a gravitational field.
We will learn more about gravity later,
but for now we can just operate under
the common understanding that gravity is
a force that pulls things towards Earth.
Mass and weight are related in that they
are proportional and objects with more
mass will weigh more than objects with
less mass, but they are not the same
thing, and when we discuss our weight in
common parlance we are actually
referring to our mass. Weight can be
calculated using Newton's second law or
F = ma. Take an object like a 100
kilogram person. This value represents
the mass of the person, which is more or
less constant barring any huge changes
in diet, as it is a measure of the amount
of matter in the person. But the weight
of the person will depend on their
location. On the surface of the earth the
acceleration due to gravity is 9.8
meters per second squared, so their
weight will be 980 Newtons. On the moon
acceleration due to gravity is about
one-sixth of that of earth, because the
moon is much less massive, so the person
will weigh considerably less as well. In
vacuum of space far away from any
massive object, the person will be
essentially weightless, since there will
be no appreciable acceleration due to
gravity. In all of these cases the mass
of the person does not change, but their
weight will vary depending on the
presence and strength of a gravitational
field. Since weight is a force, we will
have to include weight in any free body
diagram representing objects on earth.
This will be a vector with magnitude
equal to m times g pointing straight
down towards the center of the earth
where g represents the local
acceleration due to gravity. We learned
from Newton's third law that any force
has an equal and opposite force and so
we will often encounter something called
the normal force. The normal force is
exerted by whatever surface the object
sits on, and it points in the direction
that is perpendicular to the surface. If
this is a flat horizontal surface, the
normal force will be straight up
opposite in direction to the object's
weight. The more mass an object contains
the greater its weight and the greater
the opposing normal force. If these are
the only two forces acting on the object
they will be equal, and the object will
remain at rest. Now that we understand
the distinction between mass and weight
as well as the way that weight will be
depicted in free body diagrams, we are
ready to look at other forces that can
act upon objects. Let's check comprehension.
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