Momentum Energy Angular Momentum

Transcription

1 Notes 8 Impulse and Momentum Page 1 Impulse and Momentum Newton's "Laws" require us to follow the details of a situation in order to calculate properties of the system. Is there a simpler way? CONSERVATION LAWS! We will observe that Newton's 3 force laws can be replaced with appropriate conservation law statements. While many quantities are conserved (mass, charge.), we will be examining 3 in particular: Momentum Energy Angular Momentum These conserved quantities can be related back to forces and force laws, they are useful because they make problem solving (predicting outcomes) easier. What does it mean for a quantity to be CONSERVED? Conserved=There is the same amount of that quantity in the universe. The quantity (momentum first) can be exchanged, transferred from one system to another, but is never lost, removed, or added to. Momentum is a conserved quantity.

2 Notes 8 Impulse and Momentum Page 2 Momentum and Newton's law Start with 2nd law and revise: (integral of net external force*time Instead of stating that net external force causes an acceleration we now say that THE IMPULSE causes A CHANGE IN MOMENTUM. Like 2nd law, there is a left side (impulse, the cause) and a right side (change in momentum, the effect).

3 Notes 8 Impulse and Momentum Page 3 Impulse Momentum We have impulse J Define Momentum Consider a one dimensional situation. Let a bat hit a ball. 1.00kg ball, 1000N contact force, for a time of 20.0ms. For a ball initially at rest, what happens? Impulse =1000N x 20.0ms= 20.0 N s or 20.0 kg m/s The ball has picked up a momentum of 20.0kg m/s. Or the ball is moving p/m=20.0m/s. The picture we have is unrealistic, as if the force really remains constant for the entire COLLISION. IT DOES NOT. THE DETAILS DON'T MATTER IF THE AREA IS THE SAME

4 Notes 8 Impulse and Momentum Page 4 Collisions, Conservation During a collision we consider the forces acting on each object, and the interaction time. But first what is the simplest collision we might consider (that is still a collision)? 2 objects one dimension F(of object 2 on object 1)= F(of object 1 on object 2) During the collision (interaction) the time spent by object 1 pushing on object 2 is the same as the time spent for object 2 on object 1. THERE IS ONLY t Do we add these two forces? NO WHY? For this simple "head on" collision between only 2 objects consider the changes in momentum for the system. Add up the p

5 Notes 8 Impulse and Momentum Page 5 Conservation So, Two equations here since momentum is a vector. Each component is conserved separately/indep. It does not matter how many particles (objects) interact, the total momentum (of a closed isolated system) is the same beforehand as after.

6 Notes 8 Impulse and Momentum Page 6 Some Jargon Types of collisions Head on one dim Elastic: Kinetic Energy is conserved Inelastic: Kinetic Energy is not conserved Perfectly (completely) Inelastic: Special case, the objects stick together which can only happen if Kinetic Energy is NOT CONSERVED In one dimensional head on collisions: How many unique numbers (quantities) must we deal with in such a collision? How about in a two dimensional collision (two pool balls)?

7 Notes 8 Impulse and Momentum Page 7 Simple one dim collision If the objects stick together following the collision, what is the speed of the "lump" after the collision? There are several other one dimensional collisions to consider The car could head the other way (negative) The truck could have a load dropped on it from above Ballistic pendulum or ballistics gel A perfectly inelastic explosion Energy will come up, and rotational collisions.

8 Notes 8 Impulse and Momentum Page 8 Collision examples: Where did momentum go?

9 Notes 8 Impulse and Momentum Page 9 Reverse Collision Release spring. What happens use conservation of momentum? For this explosion p i =0.00

10 Notes 8 Impulse and Momentum Page 10 Sidenotes And if we have objects that stick, then we have v 1f =v 2f The equations above involve Energy conservation, which is coming up next. The addition of many other topics extends our ability to use conservation of momentum. (center of mass)