Video Transcript
A free-body diagram representing
the forces acting on an object is shown. What is the direction of the net
force that acts on the object?
Okay, so in this question, we’ve
been given a free-body diagram here, and we need to find the direction of the net or
resultant force acting on the object. Now, to answer this question, we
first need to realize that in a free-body diagram, the object that all of the forces
are acting on can be thought of as a point, in this case the point at which all of
the lines are intersecting. And that’s because we’ve been
showing four different forces acting on this object.
So, if this is our object here,
then there’s a force acting to the east on it. There’s a force acting to the
north. There’s a force acting to the
south. And there’s a force acting to the
west. And that’s why it looks like there
are lines intersecting at the point where the object is. In reality, they’re four separate
arrows showing four different forces. Now, if we want to find the net
force acting on the object, then the first thing that we can do is to think about
the components of the net force.
Specifically, we can find the net
force in the north-south direction and the east-west direction, separately. And then, we can combine the net
forces in these two directions afterwards, if necessary. So, starting with the north-south
component, we can see that the arrow representing the northward force has the same
length as the arrow representing the southward force. In other words then, the magnitude
or size of the force acting towards the north is the same as the magnitude or size
of the force acting towards the south.
And hence, these two forces cancel
each other out. They’re acting in opposite
directions and they have the same magnitude as each other. And so, the resultant force just in
the north-south direction is zero. This means there is no north-south
component and our net force overall on the object is only going to have an east-west
component. And so, all we need to do is to
compare the magnitudes of the westward force and the eastward force.
We can see that the arrow
representing the westward force is much longer than the arrow representing the
eastward force. And this tells us that the
magnitude of the westward force is much larger than the magnitude of the eastward
force. The force on the object acting
towards the west is much larger than the force acting towards the east. And because, as we saw earlier,
there is no north-south component to the resultant force, we can therefore say that
the direction in which the net force is acting on the object is towards the
west.
Moving on to the next part of the
question then, we are now being asked which of the lines shown correctly represents
the magnitude of the net force that acts on the object compared to the magnitude of
the force that acts towards the west.
Okay, so in the previous part of
the question, we already saw that the net force on the object only has an east-west
component. Specifically, it acts towards the
west. And so, for now we’re going to
ignore the forces acting towards the north and the south. The only thing we care about is the
force acting towards the west which has this magnitude, and the force acting towards
the east which has this magnitude. We can even draw them separately to
make things a little bit clearer. So, here’s the westward-acting
force and here’s the eastward-acting force, drawn separately to scale.
In other words, the length of the
eastward-acting force is the same as the length given in the diagram, and the same
is true for the length of the westward-acting force. This is the same length of this one
here. Now, what we’ve been asked do is to
find the magnitude of the net force compared with the force acting toward the
west. And once again to scale, we’ve been
given the westward-acting force. We need to find whether line number
one, two, three, or four correctly represents the magnitude of the net force
compared with the magnitude of the force acting towards the west.
Now, to answer this question, we
need to realize that the westward- and eastward-acting forces are acting in opposite
directions. Therefore, even though the net
force on the object is towards the west because the larger force was the westward
force compared with the eastward force. The magnitude of the net force is
going to be smaller than the magnitude of the westward force because some of that
whole westward force, some of this force with this magnitude here, is counteracted
by the eastward force with this magnitude. And it’s because they act in
opposite directions.
Therefore automatically, we can
rule out option number four because that length is actually longer than the westward
force. And hence, this is suggesting that
the net force has a larger magnitude than the westward force. In reality, the magnitude of the
net force is going to be equal to the magnitude of the westward force minus the
magnitude of the eastward force because we can think about it as adding forces
together. Firstly, we add the westward force,
and then we add the eastward force acting in the opposite direction.
And so, the vector that should
represent the final or resultant force is a vector starting here and finishing at
the end point once we’ve added both of the required forces. And therefore, the resultant force
should have this magnitude here. So essentially, what we’ve done
here is to add forces vectorially. In other words, add them together,
accounting for their directions. And so, we find our resultant force
with a size or magnitude that’s less than the magnitude of the westward force, which
makes sense because some of that is negated by the eastward-acting force, the force
acting in the opposite direction.
And if we now translate all of this
to the diagram given to us below, we can see things a bit more clearly if we add the
eastward-acting force drawn to scale to the diagram given to us. Because this tells us that the
magnitude of the resultant force is from here to here. And we can clearly see that it’s
only line number one that has the correct magnitude. Every other line is far too
long. And therefore, at this point, we
found the answer to our question. Line number one correctly
represents the magnitude of the net force that acts on the object compared to the
magnitude of the force that acts towards the west.
