1Chapter 6Momentum22Momentum• There is inertia involved with objects in motion (once an object is in motion, it tends to stay in motion, Newton’s 1stLaw)• This inertia related to the object’s velocity• A more massive objects traveling at the same speed as a less massive object is harder to stopmv=momentumRemember, since velocity is a vector, momentum is as well and points in the same direction as the velocity.33Impulse• Like acceleration is a measure of change in velocity, impulse is a measure of change in momentum• A change in momentum produces a force• Whenever you exert a force on something, you also exert an impulsebeforeaftermvmvmvFt−=∆== ImpulseRemind everyone that F is force and ∆ represents a change in a quantity.44Bouncing• Impulses are greater if bouncing takes place because velocity is a vector and bouncing changes its direction• Consider a ball falling towards the floor– No bouncing (object comes to a stop):–Bouncing:mvvmmmv =−−=∆ )(m/s)0(mvvmmvmv 2)( =−−=∆Note that the negative velocity means that the direction is down.55Problem Solving: Impulse• Which situation will have the greatest impulse?– A: a tennis ball hitting a solid wall with a force of 1 N– B: a golf ball hitting a solid wall with a force of 1 N•B. The tennis ball will bounce off the wall with less speed than the golf ball, so the golf ball has the larger change in momentum66Crash Test DummyWhen you hit the steering wheel with your face, you bounce off more quickly than if you spend time compressing an air bag. Since the impulse is the same whether or not you have an air bag in front of you (the change in momentum is the same since you WILL come to a stop one way or another), the longer it takes you to stop, the less force you experience. The less force you experience, the less damage is done to you and you have a much greater chance of survival.77Conservation of Momentum• Just like forces come in pairs, changes in momentum come in pairs…• The momentum before and after an interaction is always the same• Sometimes this is hard to notice: a bowling ball hitting a ping pong ball give the ping pong ball lots of velocity while the loss of velocity is small in the bowling ball because it is massiveIn physics, conservation means that a quantity does not change (although it can be redistributed).88It’s a Fish-Eat-Fish WorldThis is an animation of a large fish swimming towards a small fish at rest. The large fish then swallows the small fish. Conservation of momentum is illustrated by the large fish + small fish together moving more slowly than the large fish alone. The lesson to be learned here is if the more massive object encounters a less massive object, the velocity is reduced just slightly.99It’s a Fish-Eat-Fish WorldThis is another animation (like the last) only this time the large fish is stationary and the small fish is swimming towards the large fish. Unfortunately for the small fish, it is eaten again. This time we see that the total velocity of the large fish + small fish system is much less than the small fish alone.The lesson to be learned here is if a less massive object encounters a more massive object, the velocity is reduced drastically.1010Problem Solving: Conservation of Momentum• A 1.5 kg gun is initially at rest. When the trigger is pulled a 0.01 kg bullet leaves the barrel going to the right 20 m/s. Using conservation of momentum, what is the velocity of the gun after the bullet is fired?left the tom/s13.0vm/s13.01.5kg-kg)(20m/s)01.0(vkg)(20m/s)01.0()(1.5kg)(v-kg)(20m/s)01.0()(1.5kg)(v m/s)(0.01kg)(0/s)(1.5kg)(0mafter momentum before momentumgungungungun=−===+=+=Note that the most important thing to learn from this is a reminder of algebra and you see that the gun recoils much slower than the speed of the bullet.1111Collisions• There are 2 types of collisions– Elastic – the two objects bounce off of each other– Inelastic – the two objects “stick” together• Momentum is also conserved in collisions• Where does the momentum go once a ball hits the Earth and does not bounce?–Since the Earth is so massive, the velocity the ball gave to the Earth is virtually zero1212Elastic CollisionThis is an animation of a car (low mass) hitting a truck (high mass) and bouncing off (this is an elastic collision). After the impact, the truck moves forward (to the right) and the car moves backwards (to the left) but the total momentum is conserved between the two (the momentum of the truck + the car after the collision is the same as just the car before the collision).1313Inelastic CollisionsThis is another animation of a collision between the car and the truck but this time the car sticks to the truck (this is an inelastic collision). Since the two are stuck together, they both move with the same velocity forward (to the right). But, we see again that to total momentum of the car + truck system after the collision is the same as just the car before the collision.1414Complicated Collisions• Most collisions are not head-on, so vectors need to be carefully considered…• For example, consider a duck flying through the air perfectly level when a hunter shoots the duck from directly underneath the bird (the bullet strikes the bird while the bullet is moving straight up)– The bullet and bird now moves in a combination of level and up – they move on a diagonal1515A Complicated CollisionThese cars illustrate the situation between the bullet and the duck discussed on the previous slide.1616Problem Solving: Collisions• A 1000 kg car hits a 25 kg motorcycle in an inelastic collision. The car was moving at 20 m/s E and the motorcycle was at rest before the collision. What is the speed of the car + bike system after the collision?–Before:–After:m/s*20,000kgkg)(20m/s)1000( ==momentumE