In this video, we’re going to learn
about weight and mass. We’ll learn what these two terms
mean, how they’re different from one another, and we’ll also get some practice using
them in examples.
To start out, imagine that as a
collector of fine works of art you are waiting with great anticipation in an auction
where some collectibles will be offered to the highest bidder. In particular, you’ve had your eye
on a statue of a monkey rumored to be hundreds of years old and made of solid
gold. When it comes time to auction off
the golden monkey, the auctioneer comes on stage and makes an unexpected
announcement. The monkey will be priced according
to its weight based on the cost of gold per unit weight. Based on this information, thinking
quickly, you raise your hand and ask the auctioneer if the auction can be moved to
some spot along the Earth’s equator. To understand the reason behind
this request, we’ll want to learn about weight and mass.
Mass and weight are two terms that
sometimes are used interchangeably as those are the same thing. Mass is defined as the amount of
material in a body, whereas weight is a measurement of how much gravity pulls on a
body. Mass is typically measured in units
of kilograms, whereas weight is measured in units of force such as newtons or
pounds. It turns out that mass and weight
are different from one another. And we can understand the
difference by looking closely at these definitions.
Looking at the definition for mass,
we can see that the amount of material in a body in theory doesn’t change regardless
of the body’s position or location. If we have a one-kilogram block for
example, then that block will have the same amount of mass one kilogram regardless
of where it is. But now, look at the definition for
weight. Weight is the measurement of how
much gravity pulls on a body. This means that if gravity changes,
the weight of an object changes as well.
Let’s say we were to take our
one-kilogram mass and set it at rest on the surface of the Earth. On Earth, the weight of this mass
would equal its mass multiplied by the acceleration due to gravity on Earth’s
surface 𝑔. Say that we change locations of our
mass. Now, we put it to rest on the
surface of the Moon. Now, the weight of the mass is
equal to its mass times the gravity of the Moon. And if the gravity on the Moon is
different from the gravity on Earth which it is, then the weight of this mass will
be different in those two locations.
All this means there are a few more
things we can say about mass and weight. An object’s mass doesn’t
change. It’s always the same no matter
where the object is located. An object’s weight on the other
hand equals its mass times acceleration due to gravity. If gravity changes, so does the
object’s weight. This by the way is the reason
behind the request to relocate the auction to a spot along the equator of the
Earth. The acceleration due to gravity 𝑔
is not constant over the Earth surface, but is highest at the poles and smallest at
the equator. So an object will weight least when
it’s located along the equator and if it’s being sold by weight will cost less.
Let’s get some practice working
with mass and weight through a couple of examples.
The mass of a particle is 15.0
kilograms. What is its weight on Earth? On the Moon, the acceleration
produced by gravity is 1.36 meters per second squared. What is the weight of the particle
on the Moon? What is its mass on the Moon? What is its weight in outer space
far from any celestial body? What is its mass at this point?
In the first part of this exercise,
after having been told that we’re working with a particle of mass 15.0 kilograms, we
want to solve for its weight on Earth. We can recall that weight 𝑤 is
equal to an object’s mass multiplied by the acceleration it experiences due to
gravity. So the weight of the particle on
Earth is equal to 15.0 kilograms times 𝑔, where 𝑔 we know to be 9.8 metres per
second squared. When we calculate this product, if
we assume that 𝑔 is exactly 9.8 metres per second squared, our answer is 147
newtons. That’s the weight of the object on
Next, we want to calculate the
weight of the particles not on Earth, but on the Moon. Here, the acceleration due to
gravity is no longer 9.8 metres per second squared, but it’s 1.63 metres per second
squared. This means that the weight of the
particle on the Moon we can call it 𝑤 sub 𝑀 is equal to its mass 15.0 kilograms
multiplied by 1.63 meters per second squared. This is 24.5 newtons. Notice how much less this particle
weighs on the Moon than the Earth. It’s about six times less.
Next, we want to solve for the
particle’s mass on the Moon. This will be simple because mass
doesn’t change regardless of our location. It’s always the same. The mass of the particle on the
Moon or anywhere else is 15.0 kilograms.
Next, we want to solve for weight
in the case of being in outer space far from any celestial body. As we think about the particle
being far away from any large mass, we consider that it’s those large masses that
the source of acceleration due to gravity 𝑔. If we’re far from any celestial
body, that means that the acceleration due to gravity is effectively zero. This means that the object’s weight
which will be equal to its mass times 𝑔 which is zero is itself zero. Far away from any mass, the
particle can truly be said to be weightless.
And, finally, far away from any
celestial body, we want to know the particle’s mass. Well, this is the same as it has
been before. Since mass is a measure of the
amount of material in an object, it doesn’t depend on the environment of the
object. This means that the mass of the
particle as before is 15.0 kilograms.
We’ve learned the equation for
calculating an object’s weight based on its mass and acceleration due to
Now, let’s look at an example that
involves solving for the object’s mass through an equation.
Astronauts in orbit are apparently
weightless. This means that a clever method of
measuring the mass of astronauts is needed to monitor their mass gains or losses and
adjust their diet. One way to do this is to exert a
known force on an astronaut and measure the acceleration produced. Suppose a net external force of
50.0 newtons is exerted and an astronaut’s acceleration is measured to be 0.893
metres per second squared, calculate her mass.
Knowing the force exerted on an
astronaut as well as the astronaut’s resulting acceleration, we want to calculate
the astronaut’s mass. If we call that mass we want to
solve for 𝑚 and record the force and acceleration as 𝐹 and 𝑎, respectively, we
can recall from Newton’s second law of motion that an object’s mass is equal to the
net force acting on it divided by its acceleration. For our scenario, we can write that
𝑚 is equal to 𝐹 divided by 𝑎. And when we plug in for these two
values and calculate this fraction, we find it’s equal to 56.0 kilograms. That’s the measured mass of the
astronaut based on the astronaut’s response to an applied force.
Let’s summarize what we’ve learnt
so far about weight and mass. We’ve seen that weight and mass are
related to one another, but they’re not the same. Mass is the amount of material in a
body and weight is the measure of how much gravity pulls on a body. And we’ve seen that weight is equal
to the product of mass times gravity. All this means that an object’s
mass is constant or another way of saying it is invariant, while weight changes with
acceleration due to gravity 𝑔.