Video Transcript
What is the mass of an object that
moves at a constant velocity of 2.2 meters per second if its momentum is 3.3
kilograms meters per second?
Okay, so we have an object. Let’s draw it here as this orange
point. The question tells us that this
object has a velocity, which we’ll call 𝑉, of 2.2 meters per second. But it doesn’t tell us which
direction this velocity is in. Remember that velocity is a vector
quantity, so it has a direction as well as a numerical value. For this question, let’s assume
that the velocity is to the right. But since the question doesn’t
specify the direction, this isn’t too important. So in this case, we’ll just talk
about the magnitude or size of the velocity of the object, which is 2.2 meters per
second. And we won’t worry about what
direction this is in.
Now we’re also told that this
object has a momentum, which we’ll call 𝑃, which is equal to 3.3 kilograms meters
per second. Remember that we use this dot here
to signify multiplication, so we’re multiplying the units of kilograms by the units
of meters per second. This is different from this point
here, which is our usual decimal point. So this is just 3.3. Given all this information, the
velocity of the object and the momentum of the object, we’re asked to calculate the
mass of the object, which we’ll call 𝑚.
Let’s remember the equation for the
momentum of an object, which is that momentum 𝑃 is equal to mass 𝑚 times velocity
𝑉. Let’s also remember that since
velocity is a vector quantity so is momentum and the direction associated with the
momentum is the same as the direction associated with the velocity. This is because to get the momentum
𝑃, we multiply the velocity, which is a vector, by mass, which is a scalar. So mass has a numerical value but
no associated direction. This means that when we do this
multiplication, the direction doesn’t change and momentum has the same direction as
the velocity.
Now for our object, we’ve been told
in the question that its momentum is 3.3 kilograms meters per second. We don’t know the mass 𝑚, so let’s
leave that exactly as it is. And we’ve also been told that the
velocity is 2.2 meters per second. So we now have an equation that
involves 𝑚, which we can solve to find the mass of our object. Let’s start by dividing both sides
of our equation by 2.2 meters per second. Let’s look at the right-hand side
of this equation first. We can see that we have 2.2 meters
per second divided by 2.2 meters per second. So this cancels out, and we’re just
left with 𝑚 on the right-hand side.
If we now look at the left-hand
side of this equation, we can see that the numerical part of this is 3.3 divided by
2.2, which is equal to 1.5. And in the units, we have kilograms
meters per second divided by meters per second. So the meters per second cancel,
and we’re just left with kilograms. This means we have our equation for
the unknown mass 𝑚. We can swap the order that this
equation is written in without changing anything. And hence, we have our final
answer. The mass of the object is equal to
1.5 kilograms.
