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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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