Video Transcript
In this video, we’re talking about
measuring masses. We will learn what the mass of an
object represents and how it’s related to, but different from, an object’s
weight. We’ll also learn practically how to
go about measuring an object’s mass. To get started, let’s think about
what it means that an object has mass. All massive objects have this in
common that they’re made up of matter, that is, that they’re made up of material
stuff. On a very small scale, we could
think of matter as protons, neutrons, and electrons. So anyway, the mass that an object
has tells us just how much matter it possesses. The more matter, the greater the
mass. And the less matter, the less mass
an object has.
Now, one interesting thing about
the mass of an object is we can see, based on this definition, that it has nothing
to do with anything going on around the object we’re considering. The only thing that determines the
mass of an object is how much matter it possesses. Now, we bring this up because in
our everyday life, we may be less familiar with the mass of the objects around us
than we are with what’s called their weight. We can say that weight comes from
taking an object that has mass and putting it in a gravitational field. Any time a massive of object is on
the surface of the Earth, it experiences Earth’s gravitational field. And therefore, it has weight.
There’s even a mathematical
relationship between an object’s weight and its mass that we can write down. If we assume that we are talking
about an object near or on Earth surface, then that means the gravitational
acceleration that object experiences will be equal to what we call lowercase 𝑔. 𝑔 represents a particular
acceleration 9.8 metres per second squared. Now, this acceleration is due to
the gravitational force of the Earth on objects near its surface. And it’s this acceleration that
connects an object’s mass with its weight on Earth. We can write it this way. We can say that near Earth surface,
the weight of an object 𝑊 is equal to its mass 𝑚 multiplied by the acceleration
due to gravity 𝑔.
Now, let’s notice two things about
this relationship. First off, if we want to know the
mass of an object, say we want to measure that object’s mass, then we could figure
it out by measuring the weight of the object and combining that with our knowledge
of the acceleration due to gravity. Mathematically, if we divide both
sides of this equation by the acceleration due to gravity 𝑔, then we end up with
this relationship, which shows us that if we know an object’s weight as well as 𝑔,
then we know its mass. So that’s a way we can go about
measuring an object’s mass by measuring its weight and knowing 𝑔.
A second thing to notice about this
equation is that it depends on the strength of the gravitational field our mass 𝑚
is in. So long as our object is on or near
the surface of the Earth, we can use 9.8 metres per second squared for that
acceleration. But what if we were talking about
an object somewhere else? For example, what if our object
wasn’t on the Earth, but it was on the Moon? In that case, the acceleration due
to gravity is much smaller because the Moon’s gravitational field is weaker than
that of the Earth. And therefore, going back to our
equation, the weight of our object, 𝑊, would be less. But — and this is a vital point to
realise — the mass of the object 𝑚 would remain unchanged.
We can put that in words this
way. We can say that an object’s weight
depends on the strength of gravity that acts on it. On the other hand, its mass is
always the same. This is one of the most important
differences between mass and weight. And it also helps show why it is
that measuring an object’s mass is so useful. Once we knew its mass, we knew
something that can never change. It will always be the same
regardless of how strong the gravitational field that object is in. Knowing a bit about mass as well as
weight, let’s now look at how we measure these quantities.
Two of the most common instruments
we’ll encounter for measuring mass and weight are a digital scale and what’s called
a Newton metre. A Newton metre measures object
weight in units of newtons and in its name the word metre, rather than indicating a
distance, tells us that this is a device that helps us measure newtons, that is,
object weight in the SI system. We may encounter a Newton metre
scale in the produce section of a grocery store. This device is used to indicate the
weight of produce we might be buying, either in units of newtons or sometimes in
units of pounds. So a Newton metre is a device for
telling us how much some collection of objects weighs. But if we want to measure an
object’s mass, typically we will do that using a digital scale.
Now, let’s say we have some amount
of liquid. And we’d like to measure its mass
using a digital scale. The first thing we may realise is
that while the liquid needs to be in some container while it’s on the scale, we
don’t want to know the mass of the container, just the mass of the liquid. What we could do then is take an
empty container being enough to hold our amount of liquid and put that on the scale
by itself. Now, if we do this, the digital
readout on the scale will start to display the mass of our container. But as we saw, it’s not this mass
we want to know, but rather the mass of the liquid that’s going to go in it. To deal with situations like this,
most digital scales have a button with a word like tare or zero printed on it. When this button is pressed,
whatever the mass the scale was displaying earlier, now it goes to zero.
By taking this step, we say that
we’re zeroing the scale. Now, this is great because it means
that if we pour our liquid into this empty container, the mass displayed on the
scale will only indicate the mass of the liquid. So if we go ahead and pour our
liquid in, then as the fluid settles into its container and stabilises, we will
notice the mass read out on our scale fluctuating. Eventually, though, it too will
settle on a stable value. And because we’ve zeroed out the
scale, the mass it reads out tells us the mass just of the liquid and not of the
container the liquid is in. Digital scales can be very
sensitive, that is, very precisely tuned measurement devices. Because of that, when we measure
the mass of objects on these scales, we will want to be careful not to disrupt the
accuracy of that reading in anyway.
Here are some steps we can take for
getting accurate digital mass measurements. First, we will always want to zero
the scale before we add the mass of interest to it. In our example here, the mass of
interest was our liquid, but not the container it was in. Then, once we’ve added the mass we
want to measure, we will want to wait until that measured value reaches a steady
value, that is, until the mass read out by the scale stabilises to some constant
value. Next, we’ll want to make sure to
avoid contact with the mass or with the scale during the measurement. And we also want to make sure that
the mass is being fully supported by the scale. That is, rather than the mass being
partly supported by the scale and partly supported by something else, we want 100
percent of its weight to be acting on the scale.
Now, if we follow these three
steps, then the value that is read out by our scale will be an accurate indication
of the mass of interest. There’s still one more thing we
need to be careful about, though, and that is correctly interpreting the units that
the scale reads out. Some scales may indicate a mass in
grams. Others may indicate a mass in
milligrams or still others in kilograms. And many digital scales can output
all of these units depending on the settings we choose. So we need to be careful not just
to read out the number that is displayed, but the unit as well. Following these steps, when we make
mass measurements on a digital scale, we will help to ensure the accuracy of those
measurements. Knowing all this about measuring
masses, let’s take a moment now to work on an example exercise.
David uses a digital weighing
scale to measure the mass of a steel cube. He zeros the scale, places the
cube on the scale, and pushes down on it, as shown in the diagram. He determines that the mass of
the cube is 1.560 kilograms. Which of the following
statements explains why this answer is incorrect?
Okay, before we get to these
statements, let’s consider the diagram shown here. We see the metal cube whose
mass is being measured. And we also see the digital
scale that this mass is on. We’re told that to measure this
mass, David — and this is David’s hand — first zeroed the scale by pressing this
zero button, then placed the cube on the scale, and is now pushing down on the
cube, as we can see. With all this going on, the
scale reads out a value of 1.560 kilograms. And this, David determines, is
the mass of the cube. Let’s now look at some
statements, which may help explain why this answer is incorrect.
There are four statements in
total A, B, C, and D, but we’re only showing three of them here A, B, and C. And we’ll add in the fourth one
when we have space on screen. So before we show that final
option, option D, let’s consider these three. Now, all of these are possible
explanations for why it is that the reading of our scale 1.560 kilograms is not
an accurate indication of the mass of this cube. Option A says that the reason
it’s incorrect to conclude that the cube’s mass is 1.560 kilograms is because
the scale was not zeroed before the steel cube was placed on it. The actual mass of the cube,
option A claims, is greater than 1.560 kilograms.
Now, if we recall the process
that David followed in making this measurement, we can remember that he did
indeed zero the scale before he put the steel cube on it. So even if this second part of
statement A is correct and we haven’t evaluated whether it is or it isn’t, we
know the first part about the scale not being zeroed is incorrect. Therefore, statement A cannot
be a correct explanation of why this reading of 1.560 kilograms does not
indicate the true mass of this cube. And looking ahead to option B,
we can see that we’ll have this same reason for eliminating this choice. Option B also claims that the
scale was not zeroed before the cube was placed on it, but we know that it
was. So our first two options are
off the table.
Going on to option C, this says
that as he, that is, David, is pushing down on the block, the downward force on
the scale is greater. Therefore, the scale is going
to measure the mass as being higher than it actually is. Now, let’s think about
this. If we consider just the steel
cube itself, we know that this object experiences a gravitational force on
it. This force gives rise to what’s
called the weight force of the cube. And it’s this weight that is
experienced by the scale and then converted to a mass and read out on the
display. That’s exactly how we want this
measurement to work.
But in this case, we have David
also pushing down on the block with some amount of force. This means that the net
downward force experienced by the scale will be greater than the force created
by the weight of our cube. It will be equal to that force
plus the downward force of David’s hand on the cube. In other words, the scale is
experiencing a force greater than the force that would be created just by the
mass of the steel cube itself. And therefore, the reading on
the scale will be higher than the mass of the steel cube actually is. That’s because this reading is
indicating the mass of the cube plus the effective mass that’s simulated by the
downward force that David’s hand is exerting.
So let’s check all this against
the description offered in option C. This description says that
David is pushing down on the block — that’s correct — and that the downward
force on the scale is, therefore, greater. We saw that that’s also
correct. Therefore, this option claims
the scale is going to measure the mass as being higher than it actually is. And as we saw, that’s true as
well. So option C is looking like a
good explanation for why 1.560 kilograms is not an accurate indication of the
mass of our cube. But to check that it’s the best
description of why this is, let’s consider the last option that we haven’t seen
yet, option D.
This option says, as he is
pushing down on the block, that is, David, the downward force on the scale is
greater. Therefore, the scale is going
to measure the mass as being lower than it actually is. Now, this statement in answer
choice D is very similar to the statement in answer choice C. Both say that the downward
force on the scale will be greater thanks to David’s hand pushing down on the
block. And both say this will lead to
the scale, giving a measurement that does not match the mass of the steel
cube. In option D, though, the claim
is that the indicated mass on the scale will be lower than the actual mass of
the steel cube. In option C, we saw that the
indicated mass on the scale was higher than the actual mass of the cube.
Now, because the force created
by David’s hand is working in the same direction as the weight force of the cube
on the scale, that means these forces will add together, they’ll have a
compounding effect, and so that, indeed, the scale will read out a value, which
is artificially high. That is, it’s higher than the
actual mass of the cube. Because option D says that the
scale will read out the value that’s lower than the actual cube mass, this is
where we can’t agree with this answer option. So then our final answer is
that the reason 1.560 kilograms is not an accurate indication of the mass of a
steel cube is because, as David is pushing down on the block, the downward force
on the scale is greater. Therefore, the scale is going
to measure the mass as being higher than it actually is.
Let’s now summarise what we’ve
learned about measuring masses. As we thought about object mass, we
saw that the mass of an object tells us how much matter that is material stuff the
object is made of. Then we saw that when objects with
mass are in a gravitational field, they have what’s called weight. And as far as the relationship
between mass and weight, if an object experiences an acceleration due to gravity
that we call lowercase 𝑔, then its weight is equal to the mass of the object times
𝑔. This showed us that object weight
depends on the gravitational field the object is in, while object mass is always a
constant. Object weight and mass can be
measured using various tools. A Newton metre can be used to
measure an object’s weight, and a digital scale can be used to measure its mass.
And lastly, we learned a process
when making mass measurements using a digital scale to ensure accurate readings. First, before putting on the mass
to be measured, we’re to zero the scale. Then once the mass is on the scale,
we’re to wait until the scale indicates a stable or a steady mass value. Also during the measurement, we’re
to avoid contact with the mass being measured or the scale doing the measuring. And lastly, when reading off the
measured mass value, we’re to take care to keep track of scale units, whether they
be milligrams, grams, kilograms, or some other mass unit.
