[MUSIC] >> In the quiz feedback I said that the external forces of friction was what allowed the momentum of the cradle to go north, south, north etc. Do you believe me? Let's exaggerate it. To keep the base stationary, I have to add an external force. In the case of the pendulum cradle, that external force was friction. I've talked about collisions without defining them. So, a collision is an event in which two or more bodies exert forces on each other over a relatively short time. Often the colliding bodies touch as in the collision between two billiard balls. The colliding objects don't always touch during a collision. Two electrons come close and there's a strong repulsion between them. That's still a collision. A warning here, picturing electrons as moving balls is somewhat misleading. A collision between two cars is an example of a collision. Large forces between them over a short time. What's more, I'm going to neglect the external forces acting during the collision. You might think this is stupid. After all the driver's probably had the brakes on. So the frictional force between the ground and the tires is probably about 10 kilonewton, that is, the weight of about one ton mass. However, the forces between the two vehicles is much greater than ten kilonewtons. It's enough to bend the metals, shorten cars and do lots of nasty damage. And remember, the collision lasts only for a tenth of a second or so. The brake forces can stop the cars over several seconds. The collision forces stop them in a tenth of a second. So during the collision, the impulse transmitted by the brake forces is tiny compared with the impulse transmitted between the cars. So here I can say, impulse due to external forces is negligible. So, momentum is conserved during the collision to a fair approximation. Let's leave the rest of that problem for the quiz. Here's an important point. Momentum is our vector quantity. So we can consider its components in different directions. Consider this collision, I [SOUND] toss the hammer onto the skateboard. Let's make the approximation that the wheels are light and turn freely. So, if I consider the hammer and my skateboard as my assistant, then there are no external forces in the horizontal direction. And, so, the horizontal component of momentum is conserved. Well, what about external forces in the vertical direction? During the collision, the normal force between the wheel and the bench is rather large. If I put my hand here and. Actually, perhaps not. That would not be a negligible impulse. So, momentum is not conserved in the vertical direction. Initially, the hammer has the downwards component of momentum. But after the collision, there's no vertical motion. Momentum is not conserved in the vertical direction. So let's remember, this version of the law. If impulse due to external force is negligible in one direction, then momentum in that direction is conserved. Let's put that question into the quiz. Here's an important consequence of Newton's second law or conservation of momentum. In space the only external force is usually gravity. Well that's fine if you are already in your desired orbit. Then you're in free fall and gravity is the only force, as we will see next week. But what if you are to change your orbit or move in your orbit? In space there is nothing to push against. Well, you know the answer. You use a rocket engine. Here, our frame of reference is initially in the spacecraft. Let's forget about gravity for the moment. The engines spurt out a small mass of exhaust delta m at speed u in the negative direction. The spacecraft gets lighter by delta m when the exhaust leaves. Suppose there are no external forces, so we have conservation of momentum. The momentum of the exhaust going left, exhaust mass times exhaust speed. Has the same magnitude as the momentum of the spacecraft going right. In our frame, it's now moving at delta v. I expand the righthand side and I'll note that the product of two small terms is negligible. Divide both sides by the time taken. Delta v over Delta t is the acceleration. And Delta m over Delta t is the rate of burning fuel, call it R. So rearranging, we have an expression for the acceleration of the spacecraft. Obviously, it's inversely proportional to wind. That's Newton's second law. And intuitively, it's also proportional to the rate of burning fuel and also to the speed of the exhaust gasses. But there's a warning, it's more complicated with gravity, as we'll see next week. But now, time for a quiz. [MUSIC]
