CH 7 Lect 2 Recoil and Elastic Collisions

I. RecoilA. Two skaters push off from each other

1) FT = 0 (f is small; W/N cancel)

2) pT = 0

3) pi = pf = 0

4) p2 = - p1 or p2 + p1 = 0

5) m2v2 = -m1v1

6) If m1 = 2m2, m2v2 = -2m2v1 v2 = -2v1

7) Recoil = brief interaction of 2 objects causing them to move in opposite directions

B. Shotgun shooting

1) Gun pushes back as it pushes shot forward

2) M(shot) small, m(gun) large: mSvS = -mGvG

3) Velocity of shot fast, recoil velocity is slower

4) Hold gun firmly, increase body/gun mass weaken recoil

C) Rockets

1) -p(gas) = p(rocket)

2) Problems in doing rocket calculations

a) Blast occurs over a long time

b) Mass of the rocket gets smaller as it burns up its fuel

c) We can treat a brief rocket blast as a recoil

3) How does a rocket work in space? nothing to push against (propeller, jet)

4) Rocket pushes against its own exhaust gases to move forward

II. Elastic and Inelastic CollisionsA) Perfectly Inelastic Collision

1) 2 objects collide and stick together: treat these using cons. of momentum

2) m1 = 20,000kg v1 = 15 m/s m2 = 80,000 kg v2 = 0

p1 = m1v1 = (20,000kg)(15m/s) = 300,000kgm/s

p2 = m2v2 = (80,000kg)(0m/s) = 0

vT?pT = 300,000kgm/s

3m/s100,000kg

/s300,000kgm

m

pv

T

TT

B) Conservation of Energy in Collisions

1) KE = ½ mv2

2) We have lost KE!!!

3) Perfectly Inelastic Collisions always lose KE to heat, sound, deformation

C) Elastic Collisions

1) Perfectly Elastic Collision has no loss of KE

2) Partially Elastic Collision loses some KE, but objects still bounce

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2

1 JxsmkgKE f

52 1050.4)/3)(000,100(2

1

PerfectlyElastic

PerfectlyInelastic

D) Pool Balls Colliding in 1 Dimension

1) Perfectly Elastic Collision

2) Cue ball stops, other ball gains same momentum

3) KE is conserved because m and v identical

E) Collisions at an Angle

1) Football Tackle: inelastic 2D collision

pT

2f1i

2f1ff2i1ii

p p

p p p p p p

21T p p p

2) Pool Balls in 2D, an Elastic 2D Collisiona) Cue hits other ball off center

b) pI = cue only = pT = pf = pC + pO

c) Force is in the direction of m1m2 line

d) Since this is the only force acting on 2nd ball,

it moves off in the same direction as F

e) PT maintains same direction as pI

f) pC + pO = pT (Vector addition)

g) How do we find the angle between 2 balls?

h) Conservation of Energy (Elastic Collision)

i) KE cue = KE cue + KE other

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1

2

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2

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222 bac

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a

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