[MUSIC] Newton's third law is often stated like this, to every action there is an equal and opposite reaction. The trouble with this statement is that reaction sounds as though it comes second. Usually, the two forces are completely symmetrical. So I prefer this statement. Forces always come in pairs that add to zero. If body A exerts a force on body B, then B exerts on A a force that is equal in size and opposite in direction. When I push against the bench, some electrons in my hand repel electrons in the bench, but with complete symmetry, electrons in the bench repel electrons in my hand. Note the symmetry here. The electrons in the bench exert an electric force on the electrons in my hand, and vice versa. The electrons don't care whether they belong to the bench or to me, these two forces are a Newton pair. They add to zero. Here are two electrically charged balls repelling each other. Another Newton pair. Another familiar but related force is magnetism. This magnet and this steel bolt attract each other with equal and opposite magnetic forces, as do these two wires carrying large parallel electric currents. Nearly all the forces you meet in everyday life are fundamentally electromagnetic. We'll say more about this later. The one exception is gravity. Gravity also appears in Newton pairs. The Earth attracts the moon, and the moon attracts the Earth, and these two forces add to zero. Hey, why don't they, [SOUND] collide? We'll see that in a few weeks time. Finally, here's an important consequence of the third law. The force that the right hand side of an object exerts on the left, plus the force that the left hand exerts on the right, add to zero. This means that the sum of internal forces in a body is zero. If Newton's third law did not hold, isolated objects would spontaneously, [SOUND] accelerate away, and that would be a dangerous universe with no physicists in it. Let's revise the laws of this universe before going on. If total equals ma and forces come in pairs that add to 0. We're back with the first and second laws. Remember that this equation is for the total force acting. In memory of Galileo, here's a ball on a surface. It has weight, which is a vector, which I'll call w, and its direction is down. To hold it up requires an upwards force, which I'll call the normal force, n, being supplied by the bench. I call it the normal force, because it's at right angles to the bench, in the normal direction to the bench. I could also supply this force with my hand, and then I can feel that there's a force. The normal force is one of a Newton pair, and I feel minusing the force the ball exacts on my hand, or on the bench. Now when I place the ball on the bench, it turns out the normal force has a magnitude almost exactly equal to its weight. The directions are opposite. So, w plus n equals 0. Why they're almost exactly equal is a bit subtle. And you might like to reflect on that before we discuss it next week. This is one example of the situation we call mechanical equilibrium. Total force is zero, so acceleration is zero. When the ball is rolling with constant velocity, the horizontal force is also zero, so that's also mechanical equilibrium. The diagram I've drawn here, a vector representation of all the external forces acting on an object, is called a free body diagram. Let's look at the slider. Here, the upwards force is the lift, L, provided by the compressed air underneath. It's in mechanical equilibrium at rest. At constant velocity, it's also in mechanical equilibrium. But at the ends, there are large horizontal forces and large accelerations. To solve problems in physics there are several steps, and one of the most important is making appropriate approximations. Often it's the most difficult part of solving a problem. This is a simple example, but let's be careful and concentrate. Suppose I accelerate this trolley, mass one kilogram by pulling on the string, mass two grams. What forces are acquired to give an acceleration of [SOUND] two meters per second, per second? First, we can see that it doesn't accelerate upwards or downwards. So by Newton's second law, the vertical forces add up to zero. Well, that's not very interesting. What horizontal forces are involved? Well, we can identify two Newton pairs. On your left side, the string pulls the trolley to the right, and the trolley pulls the string towards the left. They are a Newton pair, so they have the same magnitude, call it F left. And on the right, my hand pulls the string to the right, but the string pulls my hand left. These have the same magnitude, call it F right. Let's label these using Newton's third law. Now, the only external force acting on the trolley is F left. So we write, F left equals ma, equals 1 kilogram times 2 meters per second per second, equals 2 Newtons. What about the string? It's also accelerating in a. But two forces act on it, if left pulls it to the left, and if right pulls it to the right. So, Newton's second law allows us to calculate the difference between the forces on the left and right end. Now, because this string is light, this force is only 0.004 Newtons. So F left equals F right, to a very good approximation. And I'll call both of these forces the tension in the string. Now, the key to making this approximation is that the string is light. Its mass is much smaller than that of the other object. In physics problems, we often meet light strings. We wouldn't make that approximation if, instead of using a, string, I used a chain. Strings and chains are also often described as inextensible, meaning that they don't stretch. If I used a rubber band, I couldn't even assume [SOUND] that the acceleration at both ends was the same. So, if the string is light and inextensible, our problem is simple. The force I apply with my hand equals the tension in the string, and the tension in the string accelerates the trolley and the string. But because the string is light, I can write, tension equals mass plus mass of string times a, is approximately equal to mass times a. A further lesson, when I wrote tension equals, mass plus mass of string times a, what happened to the other three force vectors? Let's see that next. There's another important thing about applying Newton's laws, and it concerns internal forces, the forces that one part of a body or system exerts on the other. As we saw before, these add to zero by Newton's third law. So, when we write Newton's second law, we only need to sum the forces external to the object or to the system that we're considering. Sounds easy? [LAUGH] Well, let's see how you go here. The man says to the horse, get up! With horse language for go. The horse replies. [SOUND]. There's no point. Newton's third law says that the cart that exert a force on me equal and opposite to the force I exert on it. Sum of force is equal to zero. So the acceleration will be zero. [NOISE] Okay. How would you answer the horse? Get out your secret weapons and draw a sketch before you answer. Look at the harness. The thing that links the, the horse, and the cart. We can say that the force that horse exerts on the harness equals the force that the harness exerts on the cart, but only if the harness is light. However, for the object comprising, cart, harness and horse together, these are both internal forces. If we look just at the cart, the external horizontal force for it is the tension T in the harness. That force is internal for the horse plus cart system, but external to the cart. That's what accelerates the cart. Now if we look at the horse, the harness pulls it backwards, so what makes the horse go forwards? Let's look at the horse's hoofs and the ground. The horse pushes the ground backwards and the ground pushes the horse forward. Also a Newton pair. So the external force on the horse F horse forwards and T backwards. The total force of these is positive, so the horse can accelerate forwards. Finally, look at the force that the horse exerts on the ground. This is an external force acting on the Earth. However, the mass of the Earth is so great, that the Earth doesn't accelerate measure, measurably.