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Understanding Impulse and Impact in Baseball Bat Dynamics

Explore how a baseball bat, impacting a ball, functions based on time, force, and direction. Learn about realistic vs. simplified impacts and the calculation of impulse in collisions. Understand Newton's Second Law in the context of momentum and impulse. Discover how to calculate impulse and impact force in various scenarios. Maximize impact forces by adjusting duration and intensity. Examples illustrate the application of impulse-momentum principles in sports and collisions.

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Understanding Impulse and Impact in Baseball Bat Dynamics

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  1. Think of how a baseball bat _________ (comes into contact with) a ball as a function of _________. impacts time maximum ___________ force of bat on ball Fnet A Realistic Impact: t leaves ball _________ the bat bat first _________ ball touches A _________ Impact: Fnet Simplified Area = _______ FnetDt t

  2. The ________ of and ____________ (time) of impact determine the future __________ of the ball. The quantity _______ is called the _____________ It is a ______________ quantity. magnitude: J = _______ direction: same as the dir. of ______ units of J: [ ] [ ] = _______ (derived) force duration motion Fnett impulse, J vector Fnett Fnet Fnet t N · s J J direct direct Fnet t

  3. 40 kg Ex 1: A net force of 25 N to the right acts on a 40-kg snowman for 3.0 s. Calculate the impulse exerted on Frosty. Fnet = 25 N Fnett J = = = (25 N, right) (3.0 s) 75 N·s, right = + 75 N·s mag. of J same as Fnet

  4. Ex 2: Give the direction of the impulse for a: A/ ball moving up during free fall B/ ball falling down during free fall C/ ball fired up at an angle at the four points shown below: down down ignore air resistance All J's are ___________ because that is the direction of ___________ downward Fg Fg Fg gravity Fg

  5. Newton's Second Law: Fnet = Rewrite a as Dv/t: Fnet = Multiply both sides by t: Fnet = But mDv = Dp, so write: Fnet = Since Fnet t = ____, the last line can be written: ma Dv t m m Dv t Dp t J J = Fnet t = Dp Impulse momentum • _____________ changes ________________ (Historical note: Newton actually first wrote his second law using _____ , and not ____ .) a Dp

  6. If you re-write Dp = pf - pi and substitute in, you get: J = Fnett = pf – pi or: mfvf – mivi J = Fnett = units From this last equation, the _______ of impulse J can be written two ways: [J] = [ ][ ] = [ ] [ ] v Fnet t m N [J] = ( ) ( ) = ( ) ( ) s m/s kg fundamental derived N·s kg·m/s =  ____________ __________  kg·m/s2 This is true because: 1 N·s = 1 ( ) s = 1 kg·m/s

  7. Ex: An impulse of 24 N·s north is applied to a 0.15-kg baseball initially moving at an initial speed of 40 m/s south. What is the change in momentum of the baseball? Given: J = m = v = Unknown: + 24 Ns 0.15 kg -40 m/s Dp J = Fnett = Dp Equation: Answer: Dp = + 24 Ns = + 24 kg·m/s Same as J!

  8. Ex: A 0.5-kg ball is moving at 4.0 m/s to the right when it hits a wall. Afterwards, it moves 2.0 m/s to the left. Determine the impulse exerted on the ball by the wall. vi = 4.0 m/s wall m = 0.5 kg vf = -2 m/s Dp = pf – pi = mfvf – mivi = (0.5)(-2) – = - 3 kg·m/s = - 3 N·s J = Fnett = Dp To find J, find Dp (0.5)(4)

  9. J = Fnet t = Dp This can be written: J = And can be rearranged to: pf = This says, "J is what you add to ___ to get ___." pf – pi pi + J pi pf Ex. The last example found Dp = J = -3 N·s = ___ kg·m/s -3 Adding the impulse of -3 N·s from the wall to pi: Before the impulse: J = -3 pi = mvi = (0.5)(4) = 2 kgm/s pi = 2 pf = -1 kgm/s

  10. The impulse J is ______________ (to the left) in the previous example because _____ from the wall is. negative Fnet The wall in the previous example exerts its force for a time of 0.12 seconds. Calculate the net force that acts on the ball during that time. J = Fnett = Dp Fnet ( ) = Fnet = -3 N·s / 0.12 s = -25 N -3 N·s 0.12 s

  11. The equation: Ft = Dp has many applications in sports and collisions…. maximize • To ______________ (make the most of) Dp, you can: •  apply a ____________ F ___t • (hit harder) •  ____________ the impact time: F___ • (follow through) F greater Dp t  ________ increase Both of these help you to take a ball moving in one direction and allow you to send it in another direction with a _____________________ velocity. much different

  12. Suppose 2 identical cars (m=1000 kg), traveling • at the same initial vi (30 m/s) both come to rest: • a/ Car A hits a _________ wall and stops in 1 s. • b/ Car B hits _________ barrels and stops in 4 s. •  For both cars: Dp = mfvf – mivi • = = brick water 0 -(1000)(30) -30,000 Apply Ft = Dp to each car to find force on car: A: F t = Dp F ____ = -30,000 F = ________ B: F t = Dp F ____ = -30,000 F = ________ 1 4 -30,000 -7,500 less more • __________ time to stop • _________ force of impact • __________ time to stop • _________ force of impact more less

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