Intro to Normal Forces | Part 2 - Nerdstudy Physics скачать в хорошем качестве

Intro to Normal Forces | Part 2 - Nerdstudy Physics

More about normal forces. What about if you have a book that is on a surface that is not parallel to the ground? How should we think about normal forces in that case? Let's find out how normal force is not necessarily opposite to gravity! -- 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.