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Momentum and Collisions Momentum and Collisions Dr. Robert MacKay Clark College, Physics

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Introduction Review Newtons laws of motion Define Momentum Define Impulse Conservation of Momentum Collisions Explosions Elastic Collisions

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Introduction Newtons 3 laws of motion 1. Law of inertia 2. Net Force = mass x acceleration ( F = M A ) 3. Action Reaction

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Law of interia (1st Law) Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. acceleration = 0.0 unless the objected is acted on by an unbalanced force

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Newtons 2nd Law Net Force = Mass x Acceleration F = M A

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Newtons Law of Action Reaction (3rd Law) You can not touch without being touched For every action force there is and equal and oppositely directed reaction force

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Newtons Law of Action Reaction (3rd Law) For every action force there is and equal and oppositely directed reaction force Ball 1 Ball 2 F 1,2 F 2,1 F 1,2 = - F 2,1

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Momentum, p Momentum = mass x velocity is a Vector has units of kg m/s

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Momentum, p (a vector) Momentum = mass x velocity p = m v p = ? 8.0 kg 6.0 m/s

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Momentum, p Momentum = mass x velocity p = m v p = kg m/s 8.0 kg V= ?

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Momentum, p Momentum is a Vector p = m v p1 = ? p2 = ? m2= 10.0 kg V= -6.0 m/s m1= 7.5 kg V= +8.0 m/s

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Momentum, p Momentum is a Vector p = m v p1 = +60 kg m/s p2 = - 60 kg m/s m2= 10.0 kg V= -6.0 m/s m1= 7.5 kg V= +8.0 m/s

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Momentum, p Momentum is a Vector p = m v p1 = +60 kg m/s p2 = - 60 kg m/s the system momentum is zero., m2= 10.0 kg V= -6.0 m/s m1= 7.5 kg V= +8.0 m/s

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Newtons 2nd Law Net Force = Mass x Acceleration F = M a F = M (V/t) F t = M V F t = M (V F -V 0 ) F t = M V F - M V 0 F t = p Impulse= Ft The Impulse = the change in momentum

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Newtons 2nd Law Net Force = Mass x Acceleration F t = p Impulse= F t The Impulse = the change in momentum

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Newtons Law of Action Reaction (3rd Law) For every action force there is and equal and oppositely directed reaction force Ball 1 Ball 2 F 1,2 F 2,1 F 1,2 = - F 2,1

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Newtons Law of Action Reaction (3rd Law) Ball 1 Ball 2 F 1,2 F 2,1 F 1,2 = - F 2,1 F 1,2 t = - F 2,1 t p 2 = - p 1

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Conservation of momentum Ball 1 Ball 2 F 1,2 F 2,1 If there are no external forces acting on a system (i.e. only internal action reaction pairs), then the systems total momentum is conserved.

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Explosions 2 objects initially at rest A 30 kg boy is standing on a stationary 100 kg raft in the middle of a lake. He then runs and jumps off the raft with a speed of 8.0 m/s. With what speed does the raft recoil? M=100.0 kg after before V=? V=8.0 m/s

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Explosions 2 objects initially at rest A 30 kg boy is standing on a stationary 100 kg raft in the middle of a lake. He then runs and jumps off the raft with a speed of 8.0 m/s. With what speed does the raft recoil? M=100.0 kg after before V=? V=8.0 m/s p before = p after 0 = 30kg(8.0 m/s) kg V 100 kg V = 240 kg m/s V = 2.4 m/s

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Explosions If V red =9.0 m/s V blue =? 9.0 m/s

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Explosions If V red =9.0 m/s V blue =3.0 m/s 9.0 m/s 3.0 m/s

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Stick together 2 objects have same speed after colliding A 30 kg boy runs and jumps onto a stationary 100 kg raft with a speed of 8.0 m/s. How fast does he and the raft move immediately after the collision? M=100.0 kg afterbefore V=? V=8.0 m/s

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Stick together 2 objects have same speed after colliding A 30 kg boy runs and jumps onto a stationary 100 kg raft with a speed of 8.0 m/s. How fast does he and the raft move immediately after the collision? M=100.0 kg afterbefore V=? V=8.0 m/s p before = p after 30kg(8.0 m/s) = 130 kg V 240 kg m/s = 130 kg V V = 1.85 m/s

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Stick together 2 objects have same speed after colliding This is a perfectly inelastic collision A 30 kg boy runs and jumps onto a stationary 100 kg raft with a speed of 8.0 m/s. How fast does he and the raft move immediately after the collision? M=100.0 kg afterbefore V=? V=8.0 m/s

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A 20 g bullet lodges in a 300 g Pendulum. The pendulum and bullet then swing up to a maximum height of 14 cm. What is the initial speed of the bullet?

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mv = (m+M) V Before and After Collision 1 / 2 (m+M)V 2 =(m+M)gh After collision but Before and After moving up

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2-D Stick together (Inelastic) Momentum Before = Momentum After P before = P after For both the x & y components of P. A 2000 kg truck traveling 50 mi/hr East on McLoughlin Blvd collides and sticks to a 1000 kg car traveling 30 mi/hr North on Main St. What is the final velocity of the wreck? Give both the magnitude and direction OR X and Y components.

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2-D Stick together (Inelastic) A 2000 kg truck traveling 50 mi/hr East (V1) on McLoughlin Blvd collides and sticks to a 1000 kg car traveling 30 mi/hr North (V2) on Main St. What is the final velocity (V) of the wreck? Give both magnitude and direction OR X and Y components. V V1 V2 P before =P after P Bx =P Ay & P By =P Ay 2000Kg(50 mi/hr)=3000KgV x & 1000kg(30mi/hr)=3000kgV y V x =33.3 mi/h & V y =10 mi/hr Or V= 34.8mi/hr = (sqrt(V x 2 +V x 2 ) & =16.7° = tan -1 (V y /V x ) 2000Kg 1000Kg 3000Kg

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Elastic Collisions Bounce off without loss of energy p before = p after & KE before = KE after v1v1 m1m1 m1m1 m2m2 m2m2 v 1,f v 2,f

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Elastic Collisions Bounce off without loss of energy p before = p after & KE before = KE after & v1v1 m m m m v 1,f = 0.0 v 2,f = v 1 if m1 = m2 = m, then v 1,f = 0.0 & v 2,f = v 1

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Elastic Collisions Bounce off without loss of energy p before = p after & KE before = KE after & v1v1 m m M v 1,f =- v 1 v 2,f 0.0 if m 1 <<< m 2, then m 1 +m 2 m 2 & m 1 -m 2 -m 2 v 1,f = - v 1 & v 2,f 0.0 M

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Elastic Collisions Bounce off without loss of energy v1v1 m m M v 1,f =- (v 1 +v 2 +v 2 ) v 2,f v 2 if m 1 <<< m 2 and v 2 is NOT 0.0 M Speed of Approach = Speed of separation (True of all elastic collisions) v2v2

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Elastic Collisions m m M v 1,f =? if m 1 <<< m 2 and v 2 is NOT 0.0 v 2,f ? M Speed of Approach = Speed of separation (True of all elastic collisions) A space ship of mass 10,000 kg swings by Jupiter in a psuedo elastic head-on collision. If the incoming speed of the ship is 40 km/sec and that of Jupiter is 20 km/sec, with what speed does the space ship exit the gravitational field of Jupiter? v 1 = 40 km/s v 2 =20 km/s

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Elastic Collisions m m v 1,f =? if m 1 <<< m 2 and v 2 is NOT 0.0 v 2,f ? Speed of Approach = Speed of seperation (True of all elastic collisions) A little boy throws a ball straight at an oncoming truck with a speed of 20 m/s. If trucks speed is 40 m/s and the collision is an elastic head on collision, with what speed does the ball bounce off the truck? v 1 = 20 m/s v 2 =40 m/s M M

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Elastic Collisions Bounce off without loss of energy p before = p after & KE before = KE after v1v1 m m mm if m1 = m2 = m, then v 1,f = 0.0 & v 2,f = v 1 90°

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Elastic Collisions Bounce off without loss of energy p before = p after & KE before = KE after v1v1 m m m m if m1 = m2 = m, then v 1,f = 0.0 & v 2,f = v 1 90° p 1 =p 1f +p 2f p1p1 p 2f p 1f 90°

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