Momentum and CollisionsMomentum and Collisions

Dr. Robert MacKay

Clark College, Physics

Introduction Introduction

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

Introduction 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)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

Newton’s 2nd LawNewton’s 2nd Law

Net Force = Mass x Acceleration

F = M A

Newton’s Law of Action Newton’s Law of Action Reaction (3rd Law)Reaction (3rd Law)

You can not touch without being touched

For every action force there is and equal and oppositely directed reaction force

Newton’s Law of Action Newton’s Law of Action Reaction (3rd Law)Reaction (3rd Law)

For every action force there is and equal and oppositely directed reaction force

Ball 1

Ball 2

F1,2 F2,1

F1,2 = - F2,1

Momentum , pMomentum , p

Momentum = mass x velocity

is a Vector

has units of kg m/s

Momentum , p (a vector)Momentum , p (a vector)

Momentum = mass x velocity p = m v p = ?

8.0 kg 6.0 m/s

Momentum , pMomentum , p

Momentum = mass x velocity p = m v p = 160.0 kg m/s

8.0 kg V= ?

Momentum , pMomentum , 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 , pMomentum , 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 , pMomentum , 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

Newton’s 2nd Law Newton’s 2nd Law Net Force = Mass x Acceleration F = M a F = M (∆V/∆t) F ∆t = M ∆V F ∆t = M (VF-V0)

F ∆t = M VF- M V0

F ∆t = ∆p Impulse= F∆t The Impulse = the change in momentum

Newton’s 2nd Law Newton’s 2nd Law Net Force = Mass x Acceleration F ∆t = ∆p Impulse= F ∆t The Impulse = the change in momentum

Newton’s Law of Action Newton’s Law of Action Reaction (3rd Law)Reaction (3rd Law)

For every action force there is and equal and oppositely directed reaction force

Ball 1

Ball 2

F1,2 F2,1

F1,2 = - F2,1

Newton’s Law of Action Newton’s Law of Action Reaction (3rd Law)Reaction (3rd Law)Ball 1

Ball 2

F1,2 F2,1

F1,2 = - F2,1 F1,2∆t = - F2,1 ∆t ∆p2 = - ∆p1

Conservation of momentumConservation of momentumBall 1

Ball 2

F1,2 F2,1

If there are no external forces acting on a system (i.e. only internal action reaction pairs), then the system’s total momentum is conserved.

““Explosions”Explosions”2 objects initially at rest2 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 M=100.0 kg

after

before

V=?

V=8.0 m/s

““Explosions”Explosions”2 objects initially at rest2 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 M=100.0 kg

after

before

V=?

V=8.0 m/s

p before = p after

0 = 30kg(8.0 m/s) - 100 kg V100 kg V = 240 kg m/s V = 2.4 m/s

ExplosionsExplosions

If Vred=9.0 m/sVblue=?

9.0 m/s

ExplosionsExplosions

If Vred=9.0 m/sVblue=3.0 m/s

9.0 m/s 3.0 m/s

““Stick together”Stick together”2 objects have same speed after colliding2 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 M=100.0 kg

afterbefore

V=?

V=8.0 m/s

““Stick together”Stick together”2 objects have same speed after colliding2 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 M=100.0 kgafterbefore

V=?V=8.0 m/s

p before = p after

30kg(8.0 m/s) = 130 kg V240 kg m/s = 130 kg V V = 1.85 m/s

““Stick together”Stick together”2 objects have same speed after colliding2 objects have same speed after colliding

This is a perfectly inelastic collisionThis 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 M=100.0 kgafterbefore

V=?V=8.0 m/s