So, back to my puzzle. How does the floor know to exert a force of 700 newtons? Here is a hint. How does this foam know to exert a force of 700 newtons? Yes, mechanical structures always deform under load, although in some cases, like the floor, the deformation can be very small, and it's approximately Hooke's law. Talking about forces exerted by the floor takes us to our next topic. The forces between surfaces. Now, the force exerted by the floor on me is at right angles to the floor. The angle at right angles to a surface is called the normal direction, so a force in this direction is called a normal force. Now you can tell that the force exerted by the floor is no longer at right angles to the floor. It's probably in about this direction. The force exerted by one body on another at contact is called the contact force. Of course, there's a Newton pair of contact forces. Easy enough? Well, let's check with this question. We often divide a contact force into two components. The normal component is in the normal direction. The component of a contact force in the plane of the surface is what we call friction. Fundamentally, there is only one force: the contact force. Dividing it into its normal and frictional components is arbitrary, but it turns out to be very useful. In fact, we'll find out that it's often the first step in solving problems involving contact forces. But what exactly is friction? Well, on the macroscopic scale, this looks like the interaction of two flat surfaces. But on the molecular scale, it looks like taking Austria, and putting it upside down on top of Switzerland. The surfaces are only in contact on a small number of small areas. But in these areas the force per unit area can be so large that they spontaneously weld together. When we try to slide the surfaces, these microscopic mountains bump into each other, and even shear off. So, at a molecular level, friction is complicated, and there are only approximate laws for its behavior. We'll meet a couple of these. But first, we make a distinction between two different cases. When there's no relative motion between the surfaces, we call it "static friction. " When there is relative motion, when one surface slides on another, we call that "kinetic friction." Let's do an experiment. Here's a 1.0 kilogram mass. It's not accelerating in the vertical direction, so the vertical forces add to 0. So, the magnitude of the normal force between the two surfaces is "mg," which is, to a good approximation, 10 newtons. I now apply a horizontal force, gradually increasing it until it starts to move. From the last video frame before it moves, we can read the applied force. Now I tried 2 kilograms. Same surfaces in contact. This time, the normal force is 20 newtons. Again, we read the force from the video frame. Well, we continue this to plot the limiting friction versus the normal force. Empirically, we see that the limiting friction in the static case is approximately proportional to the normal force. The constant of proportionality is called the "coefficient of static friction, mu-sub-s." Here's an important point. It's static friction whenever there is no motion, so the frictional force, "Ff," can be anything from 0 up to the limiting friction, "mu-s times N." Remember that it's an inequality not an equation. Make a note of that. Now, back to our experiment, and this time we look at the case of kinetic friction. We measure the constant horizontal force required to drag the masses at constant velocity. Constant velocity, so the total horizontal force must be zero, in this case too. So the magnitude of the frictional force equals the magnitude of the applied force, zero total force. Starting again with one mass, but now reading the force required to keep it moving at constant velocity. Let's plot those data on the same plot. As with limiting friction, we see that kinetic friction is approximately proportional to the normal force. This time, the slope gives what we call the coefficient of kinetic friction. We also notice that, for these two surfaces, mu-k is a bit less than mu-s, and that's usually the case. Coefficients of friction are rarely much greater than about one. Let's summarize that. If there is no relative motion, we have static friction, and the friction force is less than or equal to mu-s times N. If there is relative motion, i.e., sliding, then the friction force is mu-k times N. Finally, mu-s is usually a bit higher than mu-k. Limiting friction is usually larger than kinetic friction, so it takes a bigger force to get something moving, but usually a smaller force to keep it moving. Let's get quantitative. My mass is 72 kilograms. The coefficient of static friction between my shoes and the floor is 1.0. So, what is the frictional force the floor exerts on my shoes? Yes, I'm not accelerating sideways, so the horizontal force on me is 0. Remember that the condition of static friction is expressed with an inequality: "F-sub-f less than or equal to mu-sub-s times N." Zero frictional force satisfies that inequality. OK now you're ready for a quiz, but think carefully.
