Hey guys!
In our previous video, we talked about something called the normal force.
Basically, whenever an object presses against a surface, the surface will put up a resistance
against the pressure to prevent the object from sinking into the surface.
That’s the normal force.
In this video, we’re going to explore the concept of normal forces a little bit further
by looking at examples of when a surface is not perpendicular to gravity.
So, let’s get started!
Alright, let’s begin by reviewing what a normal force is.
Here’s the definition.
If an object exerts a force against a solid surface, the surface will exert a force on
the object to prevent it from passing through the surface.
This counteracting force is always perpendicular to the surface, and is called the normal force.
Okay, so that’s the definition.
Let’s take a look at a quick example.
Suppose we put a book on a table.
The book is being pulled by gravity, so it applies a force on the table.
If the table didn’t resist, the book would fall right through.
But the table counts as a solid surface, right?
So it exerts a normal force that prevents the book from falling through the table.
And the direction of the normal force is perpendicular to the table - or, as some mathematicians
would say, normal to the table.
So far so good?
Okay.
Now, instead of a table, let’s put the book on something else.
Let’s put it on a ramp!
And since the book and the ramp are kind of rough, the book stays on the ramp without
sliding.
It’s a slightly different situation now, isn’t it?
Gravity is still acting downward, but the surface of the ramp is not perpendicular to
the direction of gravity!
And now we can ask ourselves a question.
In this case, which arrow corresponds to the direction of the Normal Force?
Well, the answer is this arrow here labelled C. It’s a little strange, isn’t it?
Why should it be this slanted arrow?
After all, the book isn’t moving, so the force of gravity is evidently being cancelled
out.
Shouldn’t the normal force go upward to cancel out gravity?
Actually, if we remember the origin of the name of the normal force, we would realize
that the normal force is perpendicular to the surface.
Therefore, it has to be this slanted arrow, because the normal force must be normal, that
is, perpendicular, to the surface.
But that’s not a very satisfying explanation, is it?
Let’s look at the problem from another point of view.
To start, let’s choose a reference frame.
We can choose our origin to be right in the middle of the book.
As for the axes, should we choose the standard up-down, left-right axes?
Actually, this time we’ll do something a little more interesting.
We’re going to choose this set of axes.
Notice how one axis is parallel to the ramp, and the other is perpendicular to it.
But why this set of axes?
Well, here’s the reason.
Let’s see what happens when we slide the book along the axis parallel to the ramp.
Notice how, no matter where we position the book along this axis, the book never moves
into the ramp, or away from it?
Okay, now let’s see what happens along the other axis.
Ah hah, in this direction, the book moves directly into the ramp or directly away from
it.
So when we choose this pair of axes, we can split up any motion into a component that
points directly into or out of the ramp, and another component that is completely independent
of the ramp.
Okay, now that we’ve fixed this coordinate axis, let’s consider the physical situation
again.
Because the ramp is solid, the book can’t pass through the ramp.
In other words, it cannot move in this direction, into the ramp.
We can move the book anywhere in this direction and never worry about the book sinking into
the ramp.
So clearly, a force in this direction would be opposed by a force coming from the ramp,
but a force in this direction wouldn’t be opposed at all.
But if a force in this direction causes the ramp to produce a force that cancels it out,
the cancelling force must be in this direction.
And that direction is perpendicular to the surface of the ramp, or, as some people might
say, normal to the ramp.
So the normal force must point in that direction.
So the important idea is this.
A solid surface, no matter how it’s oriented, in fact even if it’s vertical, will only
oppose the component of the force that’s perpendicular to the surface.
That’s because any motion parallel to the surface will not cause an object to move into
the surface.
And this is the reason why the normal force is normal: because it only ever acts perpendicular
to the surface.
Awesome!
But let’s go back to the example of the book on the ramp.
Remember, that book wasn’t moving.
So there’s no net force on it.
But we know of only two forces on the book: the force of gravity and the normal force.
But if we add the two forces, we still have a net force!
So why isn’t the book sliding?
Is the concept of the normal force useless in this situation?
After all, we have a net force parallel to the ramp, but the normal force only acts perpendicular
to the ramp.
Actually, the real problem is that two forces we know about aren’t the only forces on
the book.
There’s one more force that we didn’t take into account, a force that prevents the
book from sliding.
And that force should actually be pretty familiar to us.
It’s called friction.
And it acts parallel to the surface, cancelling out the net force in this direction and preventing
the book from sliding.
If the ramp were actually frictionless, the net force would cause the book to slide along
the ramp, exactly as we might expect.
Great!
So this example actually illustrates a couple of important ideas.
First of all, the normal force is not necessarily opposite to gravity.
It’s opposite only to the component of any force that happens to be perpendicular to
the surface.
And no matter how the surface is oriented, the normal force is always perpendicular to
it.
Secondly, if the normal force doesn’t completely cancel out other forces, that is to be expected.
It only cancels out the component of forces that point perpendicularly into the surface.
If an object isn’t moving despite this, it means that the normal force is not the
only force that’s cancelling things out.
Alright, let’s test our understanding with a simple example.
Suppose we place a book that weighs 1 kilogram against a wall.
Then we let the book drop.
While the book is dropping, what do you think is the normal force that the wall exerts against
the book?
Well, the answer is zero newtons!
Are you surprised?
Let’s take a look at the physical situation.
We have a book falling along a wall.
What are the forces acting on the book?
There’s gravity, and there’s … actually, there’s nothing else, only gravity!
And gravity points downward, right?
In other words, parallel to the wall.
So there’s actually no force that pushes the book into the wall.
And if there’s no force pushing into the wall, the wall doesn’t need to exert a normal
force to keep the book out of the wall.
Therefore, there’s no normal force at all!
Awesome!
And that brings us to the end of our lesson on normal forces.
We hope you now have a strong understanding of this concept and are able to go on and
practice recognizing normal forces in various physical situations.
So, make sure to catch us in the next lessons, and until then have a good one!