Linear Momentum & Impulse

1. Linear Momentum&Impulse

2. Define Linear Momentum = product of objects mass x velocity A measure of how hard it is to stop an object. It is like a quantity of motion. How is it different from inertia?

3. Momentum (p) depends on: mass & velocity of object. p = mvm in kg v in m/s Units are … kg m no name. s

4. Momentum is aVector Quantity Same direction as velocity All Energy KE too is a scalar

5. Change in momentumoccurs any time an object changes velocity (speed or direction).

6. Momentum Change &Newton’s 2nd Law • F = ma • F = m(Dv/Dt) • FDt =mDv m (vf - vi) for const mass. • FDt = Dp Impulse direction is same as F. • Dp = Change in momentum

7. Equations of Momentum Change • Impulse J = change momentum. • J =FDt = Dp pf – pi. • Dp = mvf – mvi • for velocity change with constant mass can factor out mass you can write, • m (vf - vi) or mDv.

8. Increased force & contact time on object give greatest Dp = mDv.

9. The more time in contact, the less force needed to change p.

10. Impulse (J) is the momentum change. It has the same units. kg m or Ns s The quantity FDt (or Ft) is called impulse (J).

11. 1. A bus driving east hits a mosquito flying west. Compare the impacts of each on the bus and the bug: • Time of impact • Force • Impulse • Dp • Acceleration • Damage done.

12. Changing momentum: bringing objects to rest with impulse. • Catch the egg without breaking vs dropping on ground. • Fall from building onto cement vs. airbag. Same impulse, more time = less force.

13. 2. Find the change in momentum of a 1 kg mass which is dropped and hits the floor with a velocity of 8 m/s. It bounces back up with 6 m/s. • Dp = m Dv. • = 1 kg( - 8 m/s – 6 m/s) • - 14 Ns

14. Stand on a skateboard catch a ball and bring it to rest or let it bounce off? • Bouncing causes bigger impulse than absorbing or giving with the motion.

15. Graphs

16. Constant force F - t graph:Dp /Impulse is area under curve FDt. Force N

17. 3. Non-Constant ForceForce vs. time graph. The area under the curve = impulse or Dp change in momentum. • How much impulse is each box on the graph? • 5 Ns.

18. 4. What is the change in velocity imparted to the 0.8 kg object below?

19. IB Style Question

20. 5. Water is poured from 0.5 m onto a pan balance at 30 L/min. Assume vf of water = 0. rWat = 1 kg/L. • 1. Estimate the velocity of the water upon hitting the pan. (Assume the stream starts from rest). • 2. Estimate the mass of water hitting the pan each second. • 3. Assuming the water’s velocity after hitting the pan goes to zero, estimate the reading on the pan balance in grams.

21. v2 = 2as. • v2 = 2(10)(0.5) = • v = 3.2 m/s • Mass water/sec, • 30 L / 60 s x 1 kg/ L = 0.5 kg/sec so in 1 second 0.5 kg mass arrives at the pan balance. • Water changes momentum FDt = mDv. • The force on the balance = mDv/t, • (0.5kg)(3.2 m/s)/ 1 s = 1.6 N • = 160 grams.

22. Hwk Kerr. • Pg 72 # 6-7

23. Newton’s First Law • Object at rest or constant velocity has not Fnet. Upward = Downward.

24. Newton’s 3rd Law • Object A exerts Force F, on object B, then object B exerts equal but opposite force on A. • F a,b = - F b,a.

25. Conservation Momentum particle interaction N3 • FAB = - FBA. • FDt = mDv • mDva = - mDvb. t t • Contact time, t, is the same they cancel. • m (vfa – via ) = - m (vfb – vib ) • Expand and rearrange, collect vi on one side, vf on the other. • S pi = Spf(Conservation of momentum).

26. Conservation of Momentum • If no external force acts on a closed system, the total momentum within the system remains unchanged even if objects interact. • Momentum can be transferred between objects.

27. What is a system? • Two or more objects that interact in motion. One may transfer part or all of its momentum to the other(s). • Common examples: collisions, explosions.

28. 6. Bounce a ball off the floor • Did the momentum of the ball change? • Was conservation of momentum obeyed?

29. What happened to the momentum? • How much momentum was gained by Earth? • The ball’s mass is 0.25-kg. It’s initial speed was 5.0 m/s, and its final speed was 3.0 m/s. • What was the change in velocity of Earth due to the collision? (mass Earth = 6.0 x 1024 kg.) • The impulse on the ball: • 0.25 (8 m/s) = 2.0 Ns. • 2.0 Ns = mDv • Dv = 2 Ns / 6 x 1024 kg

30. To Calculate: SPbefore = Spafterm1v1 + m2v2 = m1fv1f + m2fv2f • v1 and v2 velocities for objects one and two. • m1 andm2 masses of objects

31. One Ball transfers all its momentum.

32. Conservation of Momentum Calc’s • Total momentum before = total after interactions. • The direction of the total momentum is conserved as well. • Collisions. • Explosions • Pushing apart.

33. Elastic & Inelastic Collisions Elastic: no KE (velocity) lost (to heat, light, sound etc.) Usu. Involves objects that don’t make contact. KE before = KE aft. Inelastic: involves greatest loss of KE (velocity). Often objects stick together.

34. Recoil: objects initially at rest explode or push apart

35. Recoil illustrates conservation of momentum where initial and final momentum = 0.0 = p1 + p2.

36. 7. On July 4th my family likes to shoot off fireworks. One rocket was shot straight up, climbed to a height 18-m and exploded into hundreds of pieces in all directions at its highest point.Thinking about conservation laws, think about the rocket at its highest point just before & just after it explodes:How does the rocket’s momentum compare before & after the explosion?How does its KE compare before & after the explosion?

37. Throw a ball off the wall. • How is momentum conserved? • What is the system?

38. Systems, External & Internal Force • If system is single astronaut, then external force applied by astronaut 2, momentum not conserved –it changes. • If system is 2 astronauts, then the force is internal and total momentum is conserved.

39. State Newton 3 • If 2 objects interact, the force exerted by on object A by object B (Fa,b), is equal in magnitude but opposite in direction to the force exerted on object B by object A, (-Fb,a).

40. 1. A lamp of weight W is suspended by a wire fixed to the ceiling. With reference to Newton’s third law of motion, the force that is equal and opposite to W is the: • A. tension in the wire. • B. force applied by the ceiling. • C. force exerted by the lamp on the Earth. • D. force exerted by the Earth on the lamp

41. 2. A student is sitting on a chair. One force that is acting on the student is the pull of gravity. According to Newton’s third law, there must be another force which is: • A. the upward push of the chair on the student. • B. the downward force on the student. • C. the downward push of the chair on Earth. • D. the upward force on Earth.

42. 3. What is the reaction force for the following: A 0.5 kg bird glides above the earth’s surface. It’s wings push down on the air with its weight, 5-N, so:

43. How can anything have Fnet and accelerate? • Acceleration is caused by the Fnet on a single object. It is the sum of all the forces. • Action/Reaction occurs for different objects.

44. Hwk in Kerr • pg 72 # 8 – 9 Show work. • IB set momentum .