Impulse and Momentum

1. Impulse and Momentum Saline High School Physics

2. Have you ever wondered… • Why golfers and bowlers “follow through”? • Why skydivers bend their knees upon impact? • Why Falling on a wood floor hurts less than falling on a cement one?

3. Have you ever wondered… • What’s the best strategy to win the “water balloon toss” or the “egg toss”? • Why we make auto air bags and padded dash boards? • How the police can figure out how fast you were going BEFORE an accident by measuring your skid marks?

4. To answer all of these questions--and more--you need to understand: Impulse and Momentum! • Recall, Newton’s first law…The Law of Inertia • The study of inertia for moving objects is the study of “momentum”

5. Consider the following: • When a baseball bat hits a baseball, a force is applied OVER A SHORT PERIOD OF TIME. • How would a graph of Force vs. Time look?

6. Impulse • Defn: A force applied over a period of time is called an IMPULSE. • What are the SI units of Impulse? I = F · ∆t

7. Back to baseball...Which will have the greater speed afterward? • A large or a small ball? • A fast or a slow ball? • A large or a small bat? • A fast or a slow swing?

8. Momentum • Defn: The MOMENTUM of a body is equal to the product of its mass and its velocity. • Is momentum a vector or a scalar? • What are the SI units of momentum? p = m · v

9. Determine the following momentums… • Ex #1 - A 1200lb car moving at 60mph • Ex #2 - A 5.0g bullet moving at 900m/s • Ex #3 - A 3 ton elephant sitting down • Ex #4 - A 150g hummingbird flying at 40mph • Could the momentum of the hummingbird ever be equal to that of the elephant?

10. Making the Connection: • Look at the units of Impulse and Momentum…Do you notice anything? • Recall, F = m·a…can you rearrange the equation to say something about Impulse or Momentum?

11. The Impulse-Momentum Theorem • When a net force acts upon a body for a period of time, the Impulse applied by the force is equal to the body’s change in Momentum! • This is similar to the Work-Energy Theorem… F∆t = m∆v

12. Applying the Impulse-Momentum Theorem #1: Follow Through etc… • If your Force is limited, how can you MAXIMIZE the impulse you apply? • By increasing the time of contact! • Golfing…Baseball…

13. Applying the Impulse-Momentum Theorem #2: Maximize ∆time • If your change in momentum is constant, how can you MINIMIZE the force applied to you? • By increasing the time of contact! • Bending knees upon impact, rolling with the punches, crumple zones, running shoes, air bags…

14. Momentum Changes and Bouncing • Is it more dangerous when a flower pot falls on your head and breaks or stays in one piece and bounces back up? • When an object bounces, what happens to it’s velocity? How does that effect it’s change of momentum? • Since ∆p is greater in bouncing situations, the Impulse applied will be greater!

15. Bouncing Examples: • Rain vs. hail • Lester Pelton • Broken Bat Home runs? • Can you think of any more?

16. The Law of Conservation of Momentum • Internal forces are forces that act within a system, external forces are forces that act on a system from outside… • If a system is not affected by any net external force, it is said to be “ISOLATED”. • In an isolated system, the total linear momentum is always conserved!

17. Example - Recoil • A hunter shoots a 0.22 rifle and the 3.0 kg gun recoils with a speed of 0.042 m/s. If the bullet has a mass of 0.5 g, find the muzzle speed of the gun.

18. Example - Push off from rest • Two skaters push off each other from rest on a smooth, level ice rink. The man weighs 160lb and the woman weighs 120lb. If the woman leaves with a speed of 2.5 m/s, what is the speed of the man?

19. Elastic and Inelastic Collisions • Collisions in which the bodies crash and stick together are called “INELASTIC” Collisions • Collisions in which the bodies crash and bounce are called “ELASTIC” Collisions

20. Example - Inelastic Collision • In an accident, two cars travelling in opposite directions collide and stick together. The first car has a mass of 1000 kg and a speed of 20 m/s, the second has a mass of 1750 kg and a speed of -15 m/s. What is the speed of the two cars immediately after the crash?

21. V01 = 15 m/s V02 = 0 m/s Example - Elastic Collisions • In a pool game, two identical balls of mass 0.75 kg collide as shown below. Find their speeds right after the collision. • How far will the one on the right go if µ=0.65? • How would your answer change if the ball on the right had a speed of 12 m/s to the left?

22. Example 2 - Elastic Collisions • Two identical blocks of mass 1.0 kg collide elastically, as shown below. Find their speeds right after the collision. • How far will the one on the right go if µ=0.65? • How would your answer change if the ball on the right had a speed of 12 m/s to the left? V01 = 15 m/s V02 = 12 m/s

23. The Ballistic Pendulum • A “ballistic pendulum” is made from a block of wood of known mass. It is used to find the speed of a bullet. If the bullet has a mass of 7.5 g and the pendulum has a mass of 2.5 kg and rises to a height of 65 cm, find the speed of the bullet (Hint: use conservation of momentum and energy).

24. Collisions in Two Dimensions • A 1000kg car travels east at 35 mph and another with mass 2000 kg, travels north at 40mph. If they collide inelastically, what velocity will they have after they crash? N

25. m1 x1 + m2 x2 Xcm = m1 + m2 Center of Mass • The cneter of mass of a body is the point at which you could consider ALL the mass being if it were a point mass • It can be found geometrically… • or mathematically…we can also find it’s speed... m1 v1 + m2v2 vcm = m1 + m2

26. Example • Find the Center of Mass of the Earth-Moon system. Can you find it’s speed?

27. The End...