Momentum & Impulse

1. Momentum & Impulse

2. Momentum (p) • “inertia of motion” • p = mv • Units for momentum  Kg*m/s • Vector Quantity • One way of looking at it…How much an object in motion… wants to stay in motion • Lot of momentum  hard to stop

3. How can you change an object’s momentum?? • Newton’s 2nd Law states a net force causes an acc. • An acc. Changes the velocity • Changing the velocity, changes the momentum

4. Impulse Momentum Theorem • Applying a force over a time interval changes the momentum • F changes v, therefore (mv) changes • Never looked at a relationship between ‘F’ and ‘t’ • F x t = Impulse • Since an impulse changes ‘v’, this changes momentum • Ft = Δ(mv)  Impulse-Momentum Theorem

5. Newton’s 2nd Law reworked… • F = ma and a = (Δv/t) • F= m(Δv/t) then multiply both sides by ‘t’ • Ft = mΔv which is the same thing as • Ft = Δmv • Impulse- Momentum Theorem is just Newton’s 2nd Law written a different way

6. Examples • Boxing gloves vs. MMA gloves • http://www.yourdiscovery.com/video/future-cars-nido/ • Features on a car?? • Pillow punch vs. brick punch • Bungee jump w/ elastic cord vs. rigid cord • Egg toss competition • “rolling with a punch”

8. Bouncing? • Greater Δ(mv) than just stopping an object?? • Why??  ….greater Δv • Going from -5 m/s to 5 m/s is a greater velocity change than going from -5 m/s to 0 m/s, therefore greater Δmv and impulse

9. Pelton Wheel Example • Paddles are cups instead of just flat planks • Allows water to change directions • Greater Δmv of water which means more impulse and wheel is turned much more effectively

10. Example Problem

11. Other Examples • Karate chop • http://www.youtube.com/watch?v=pLtPUgRueTE • http://www.youtube.com/watch?v=BblbLjwZC58&feature=related • http://www.youtube.com/watch?v=lupXlg4KaRg • http://www.youtube.com/watch?v=pTmRUH0uYgw • Mr. Schober gets assaulted by strangers… Story

12. Conservation of Momentum • If no outside force is applied, then the total amount of momentum in a closed system will remain constant. • Only external forces can change momentum. • Σpi= Σpf • m1v1i +m2v2i …= m1v1f + m2v2f…

13. Conservation of Momentum pai = m(v) pbi = m(0) pbf = m(v) paf = m(0)

14. Conservation of Momentum • Momentum is conserved for all objects in the interaction, even if one doesn't stop pai + pbi = paf + pbf

15. Is momentum conserved here? Yes, due to the vector nature of momentum.

16. Is momentum conserved? A B • Initial velocities of both objects is 0. • pai = ma(0) • pbi = mb(0) • Σpi = 0

17. Is momentum conserved? A B • paf = ma(-va) • pbf = mb(vb) • pf = 0 • Σpi = Σpf, so momentum is conserved!! pf = ma(-va) + mb(vb)

18. Why do internal forces result in momentum being conserved? • When Girl A pushes on Girl B, according to Newton’s 3rd Law, Girl B pushes on Girl A • How much? • These forces are equal in magnitude and opposite in direction • The time over which these forces act is exactly the same • Only while the girls are in contact, in this case

19. How does a gun work?

20. How does the gun work? • Only forces are internal (no net external forces are adding impulse to the system) • The momentum of both will add up to zero (bullet is +, gun is -)

21. Why do internal forces result in momentum being conserved? • Impulse is equal in magnitude but opposite in direction • I = (ΣF)(Δt) • Forces are equal and opposite, times are equal • Δp is equal in magnitude, opposite in direction, resulting in Σp = 0!!

22. Collisions http://www.flixxy.com/golf-ball-slow-motion.htm - Golf Ball during a surprising inelastic collision http://www.youtube.com/watch?v=pQ9NiazPYI8 --- baseball • Inelastic • Any collision in which momentum is conserved but kinetic energy is not • Most ‘real’ collisions are of this kind • KE is not conserved because some is lost to the deformation • m1v1i+ m2v2i= m1v1f + m2v2f • Perfectly Inelastic • Objects collide and stick together • KE not conserved • m1v1i + m2v2i = (m1 + m2) vf • Elastic • Both momentum and KE are conserved • “perfectly “elastic collisions only occur in real life at the subatomic level, but will treat any collision labeled as “elastic” as being ‘perfectly’ elastic • Collisions between billiard balls or between air molecules and the surface of a container are both highly elastic • No Energy lost to deformation • m1v1i+ m2v2i= m1v1f + m2v2f And • ½m1v1i2 + ½m2v2i2 = ½m1v1f2 + ½m2v2f2 • When combining these two and reducing we get…. V1i – v2i =-(v1f – v2f)

23. Example problem

24. Problem Solving #1 • A 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is at rest. Find the velocity of the fish immediately after “lunch”. • System is both fish, and collision is perfectly inelastic so ….. • Σpi= Σpf • (m1v1i)+ (m2v2i)= (m 1+ m2)vf • 6(1) + (2)(0) = (6+2) vf • Vf =6/8 = .75 m/s

25. Problem Solving #2 • Now the 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is swimming towards it at 2 m/sec. Find the velocity of the fish immediately after “lunch”. • System is both fish, so…. • Σpi = Σpf • (Σ(mv))i= (Σ(mv))f • (m1v1i)+ (m2v2i)= (m 1+ m2)vf • (6 kg)(-1 m/s) + (2 kg)(2 m/s) = (6 kg + 2 kg)(vf) • -6 kg.m/s + 4 kg.m/s = (8 kg)(vf) • vf=-2 kg.m/s / 8 kg vf= -.25 m/s

26. Collisions in 2-D (more to be posted later) • Σpxi = Σpxf • Σpyi = Σpyf Momentum is a vector, so momentum must be conserved in the x-direction, and in the y-direction

27. Inelastic in 2-D ?? 1 kg ?? .5 kg 2.2 m/s 33° 1.5 m/s

28. Perfectly Inelastic in 2-D 1.5 kg 1 kg 2.5 m/s 1.3 m/s .5 kg