INTRODUCTION TO BIOMECHANICS SECTION 6.1: LINEAR KINETICS

1. INTRODUCTION TO BIOMECHANICS SECTION 6.1: LINEAR KINETICS

2. Impulse mom • http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Momentum/impulse-momentum.htm

3. Impulse mom • http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Momentum/impulse-momentum.htm

4. CONSERVATION OF LINEAR MOMENTUM - RECAP

5. THE TOTAL MOMENTUM OF A SYSTEM AFTER COLLISION IS EQUAL TO THE TOTAL MOMENTUM OF THE SYSTEM BEFORE COLLISION.

6. M1=90kg V1=6m/sec M2=80kg V2=7m/sec • Example: Consider that we have two skaters each heading towards one another. Each of the objects has a mass and a velocity. At some point in time the bodies collide. Applying the Conservation Principle to this situation:

7. (m1v1+m2v2) =(m1+m2)V2 (90)(6)+(80)(-7)=90+80(?) 540-560=170v V=-.12m/sec .12m/sec in direction of 80kg player Or IF THE OBJECTS REMAIN IN CONTACT

8. IMPULSE(NS) • IMPULSE is the application of force over a certain time • J=(F)(T) • Force x time

9. IMPULSE-MOMENTUM RELATIONSHIP • Impulse is responsible for changing the amount of momentum. Another way of expressing this is that impulse results in a change in momentum • Theoretically this can be best understood by examining the IMPULSE-MOMENTUM RELATIONSHIP

10. The Impulse –momentum equation can be easily derived from kinematics and Newton’s second Law.

11. Force/time record for a high vertical jump Shaded area represents impulse generated against floor during the jump

12. Force/time record for a low vertical jump

13. IMPULSE-MOMENTUM RELATIONSHIP • Impulse causes a change in momentum • J=FT M=mv • A change in momentum can be expressed as • M=m2v2-m1v1 • However the mass of an object or body rarely changes from one moment to another M = m(v2-v1) ?

14. If we increase the magnitude of the impulse what will happen to the momentum FT=m(v2-v1)

15. Momentum will also increase and since this increase will probably have nothing to so with the mass the result will be a corresponding increase in the magnitude of the velocity. Therefore, the change in resulting momentum is usually associated with a change in the resulting velocity

16. How Do We Increase The Impulse So That We Can Increase The Resulting Momentum?

17. Theoretically the same increase in velocity should be able to be achieved by applying a large force for a short period of time or a small force for a long period of time. • IMPULSE = FtorIMPULSE = Ft

18. However, In the human body muscles are able to contract more forcefully over short periods of time than when they are required to contract more slowly • important to emphasize explosive movements and short take-off times

19. Tennis example • Suppose that you are playing tennis. You don't just want to serve the ball - you want to get an ace! You want to put the ball past your opponent before she can react to it. To do this, you want the ball to have the largest possible velocity when it leaves the tennis racket. • What does impulse the impulse-momentum equation say about this?

20. Since momentum depends on mass and velocity (momentum = (mass)(velocity)), to say that you want maximum possible velocity for the ball is the same as saying that you want the largest possible momentum for the ball as it leaves the racket. • Now the ball has essentially zero momentum when you hit it, since it is moving very slowly just before the racket hits it. You want to change this momentum to a very large momentum toward the other side of the net. So, to say that you want the largest possible momentum for the ball as it leaves the bat means that you want the largest possible change in momentum for the ball.

21. So, to get the largest possible change in momentum, we want to apply the largest possible impulse to the ball. • Impulse depends directly on the force applied and the time the force is applied. (Impulse = (force)(time)). So, to get the largest possible impulse you should either: • apply the largest possible force • apply the force for the longest possible time • or both

22. So, swinging harder will hit the ball harder. (Duh?) Certainly, you want to apply maximum force by hitting the ball hard. If you hit the ball with twice the force, you will impart twice the impulse to the ball. Since impulse = change in momentum, this will double the ball's change in momentum. • Since momentum equals mass times velocity, doubling the ball's momentum will double its velocity. However, if you try to apply too much force your coordination and timing will suffer, and your serve will not be accurate - you may even miss the ball!

23. You can also increase the impulse on the ball by increasing the time that the racket exerts its force on the ball - "following through". If you hit the ball for twice as much time, you will impart twice the impulse to the ball, which means twice the change in momentum for the ball. So, following through is important. • Of course, if you hit the ball hard and follow through, you will impart the greatest impulse to the ball. If you double both the force and the time, you get four times the impulse, and four times the change in momentum!

24. The same analysis would apply to hitting a golf ball, baseball, softball - whatever: • In summary: • To get the largest possible velocity for the ball, you want the largest possible momentum for the ball, since momentum equals mass times velocity. • To get the largest possible momentum for the ball, you want to apply the largest possible impulse to the ball, since impulse equals change in momentum. • To apply the largest possible impulse to the ball, you want to apply the largest possible force, or apply a force for the longest possible time, or both.

25. JOINT RANGE OF MOTION AND IMPULSE • IN general skills which require a maximal application of force also require that the joint be moved through a large range of motion • R of M effects time

26. IMPULSE AND FORCE ABSORBTION • Force absorption is the process of gradually decelerating a moving mass. Large forces need to be absorbed during impact or landing in order to prevent injury or catch or control the object • Another way of wording this is: • The object or body has developed a certain amount of momentum which has to be dissipated over a limited amount of time.

27. Remember that impulse and momentum are intimately related. A given impulse will result in a change in momentum. • Similarly, if an object or body which is traveling with a given amount of momentum is forced to reduce the momentum and therefore, decrease the velocity(as in landing or catching movements) the subsequent change will result in an applied impulse.

28. Impulse => Ft If the time over which the velocity is decreased is very small then the force will be very large. If the time over which the velocity is decreased is very large then the magnitude of the forces will be small.

29. Therefore if we are trying to absorb forces we should try to increase the time component of the landing or a catch as much as possible in order to decrease the force per unit time.

30. Jumping off a chair example • Suppose that you are going to jump off a chair. • When you land, you certainly don't want to hurt yourself, but you know that the floor has to exert a force on you to stop you. You want this force to be as small as possible, however. How do you arrange it?

31. First of all, once you jump you are in free fall. You are accelerating toward the floor at about 9.8m/s2 ("g"), and your speed just before you hit the floor simply depends on the height of the chair. • Your momentum just before you hit the floor equals your mass times your velocity. Your mass is going to be constant during the fall, and you can't adjust your velocity (since air resistance is not going to be a factor when you jump off a chair), so you can't lessen the momentum you have just before you hit the floor, either.

32. Once the floor stops you, your momentum will be zero. So your momentum is going to change from whatever it was just before you hit (which you can't control) to zero - you have no control over how much your momentum will change when you hit the floor.

33. Now, the impulse – momentum equation says that your change in momentum will equal the impulse that the floor exerts on you. Your change in momentum is determined by the height of the chair - you can't change that - so you also have no control over the amount of impulse that the floor will exert on you. Once you left the chair, the impulse that the floor will exert on you was fixed.

34. FT = change in M • FT = mvf –mvi • Mvf =0 (body coming to stop/rest)

35. It is beginning to look like you really don't have a lot of control over this situation, doesn't it? (This might explain why people get hurt falling down, huh?) • The impulse that the floor exerts on you to stop you is determined by your mass and the height of your jump, and nothing else.

36. However, the impulse that the floor exerts on you depends on two things - the force that the floor exerts and the time that it exerts it. • You DO have some control over the stopping time! Suppose that you flex your knees when you land. This increases the time that the floor stops you, thereby decreasing the force that the floor has to exert. Most people flex their knees instinctively in this situation (or maybe they tried it with locked knees and got hurt!).

37. By doubling the stopping time, the floor can exert the same impulse on you with half the force. With five times the stopping time, the floor has to exert just one-fifth of the force to exert the same impulse on you. • The same principles explain why it is better to fall on a soft carpet or mat than on a hard floor - the stopping time is automatically increased, thereby decreasing the stopping force.

38. In Summary: • You can't change your velocity just before you hit the floor. • So you can't change your momentum just before you hit the floor. • So you can't change the amount your momentum needs to change when the floor stops you. • Since the impulse that the floor has to exert to stop you equals your change in momentum, the floor has to exert the same impulse on you no matter how you land.

39. But, since impulse equals force times time, you can decrease the force that the floor exerts on you by increasing the stopping time, by bending your knees or landing on a soft mat (or both).

40. The best shock absorbing technique is based on receiving a small force spread over a long period of time. • How do we increase the time component?

41. HOW DO WE DO THIS IN SPORTS? • JUMPING: During landing flex the joints as much as possible. If no flexion took place we would feel the extremely large forces of impact as the velocity of the mass was reduced to zero in a short period of time.

42. Flexing at the joints will increase the range of motion and the time over which the momentum is reduced. This in turn results in a small force being applied over a relatively large period of time

43. CATCHING: During the skill of catching the athlete reaches out with the glove and as the ball contacts the glove the arms flex inward to increase the time of force application. Unskilled players often keep the glove in the same place at impact and all the forces are applied over one instant - loss of control of the ball or pain

44. IMPULSE/MOMENTUM • A pitched ball with a mass of 1kg reaches a catchers glove traveling at a velocity of 28m/sec. • A) how much momentum does the ball have? • B) How much impulse is required to stop the ball? • C) If the ball is in contact with the catchers glove for .5 seconds how much average force is applied by the glove?

45. ANSWERS • A) M=mv = (1kg)(28m/sec) = 28kg.m.sec • B) J = Mfinal – Minitial= (1)(0) – (1)(28) = 28NS • C) (Force)(T) = 28NS • F = 28/.5 = 56N

46. A force of 602 N is applied to a 3613 kg object for 29 seconds. What is the change in velocity that the object experienced? • Lise Go pushed her 663 kg vehicle from rest to 2.6 m/s in 19 seconds. What is the magnitude of the impulse on the car?

47. Lee Mealone, a hermit pushes a 14 kg boulder into the wall of his cave at a speed of 3.7 m/s, the boulder is brought to a stop in 1.8 seconds. What was the magnitude of the impulse (in N-s) imparted to the boulder?

48. Example • A 50 kg gymnast dismounts from the vault and sticks her landing. • If she impacted the ground at a speed of –3.75 m/s, how would landing technique affect the forces she experienced in coming to a stop? • Hard landing: dissipating a • large force over short time • (Δt = 0.20 s) • Soft landing: dissipating a • large force over long • time (Δt = 0.60 s)

49. Short answer Do you think landing technique is related to lower extremity injury? Why or why not? From a standing position, rapidly squat down and hold this position. Draw the net force vs. time profile of this motion How would you compute the impulse generated during this task.

50. How do airbags help reduce the severity of many automobile accidents? How does the impulse-momentum relationship influence vertical jumping performance?