Weight vs. Mass
There is often confusion about the terms ‘weight’ and ‘mass’. This is a short description of these two
terms.
Weight is a force. It is the amount of pulling force that gravity exerts on an object. What is really
interesting is the amount of force acting on an object causes that object to accelerate at -9.8 m/s/s (if
that is the only force acting on the object). Since weight is a force, it has units of Newtons (SI units).
However, most of us are more used to units of ‘pounds’ or ‘lbs’ because we all step on a scale and see
‘weight’ in ‘lbs.’
The equation for weight looks like this:
FGravity = mg
Where ‘g’ is -9.8 m/s/s and represents the acceleration due to the force of gravity and ‘m’ represents
the object’s mass.
Mass is a measure of an object’s inertia. Inertia is a mechanical term used to describe an object’s
resistance to change motion. That means that the more inertia an object has, the harder it is to get
going (from a stopped position) and the harder it is to stop the object from moving. We already know
this … can you imagine kicking a soccer ball vs. kicking a bowling ball?! Of course we would not kick a
bowling ball … it has too much inertia (too much resistance to change motion) and it would take too
much force to change the motion (and the foot would likely be injured!).
To determine the mass of the object, we would simply take the object’s weight and divide by the
acceleration due to the force of gravity. The equation looks like this: m = FGravity/g. Remember, the force
of gravity is ‘negative’ (since it is pulling down on the object) and the acceleration due to the force of
gravity is also negative … therefore, mass is positive.
How do we measure weight? We put the object of interest on a scale. Mathematically, when an object
is on a scale (see the picture below), we have two forces acting on the object: 1) Gravity pulling down
and 2) the ground pushing up (we call that the Ground Reaction Force or ‘GRF’). Since the object is not
moving, velocity is 0 m/s and is constant. Therefore, acceleration is zero (a = Δv/Δt). Knowing that, we
can now apply Newton’s 2nd Law (ΣF = ma):
ΣF = ma
FGRF + (-FGravity) = ma
Since a = 0 m/s/s
FGRF + (-FGravity) = 0 N
FGRF = FGravity
