Impulse and Momentum

• Chapter problems Serway– 5,6,10,13,16,17,18,27,29,33,43,44,52,54,59,60

– cw.prenhall.com/~bookbind/pubbooks/giancoli

Linear momentum & impulse

• Linear momentum is defined as the product of mass and velocity– p=mv, px=mvx , py= mvy

– units of momentum are kgm/s

• From Newtons 2nd law• F= ma F=mdv/dt F= dp/dt

• The rate of momentum change with respect to time is equal to the resultant force on an object

• The product of Force and time is known as IMPULSE

• J= Fdt

• units of impulse are Ns

Linear momentum & impulse

Examples of impulses being applied on everyday objects

Impulse Momentum Theorem

Fdt=mdv

You apply an impulse on an object and you get an equal change in momentum

IFdtmdvdppf

pi

tf

ti

vf

vi

tf

ti

Fdt Area under a Force vs time graph

v m t F

Impulse Graph

Linear Momentum and Impulse

Example problems 1,2,3

Chapter questions 5,6,10,13,16

Conservation of momentum2 particle system

For gravitational or electrostatic force

m1m2

F12

F21

F12 is force of 1 on 2

F21 is force of 2 on 1

F12 =dp1/dt F21 = dp2/dt

Conservation of momentum2 particle system

From Newton’s 3rd Law

F12 = - F21 or F12 + F21 = 0

m1m2

F12

F21

F12 is force of 1 on 2

F21 is force of 2 on 1

F12 + F21 =dp1/dt + dp2/dt = 0

d(p1 + p2)/dt= 0

Since this derivative is equal to 0

Conservation of momentum2 particle system

d(p1 + p2)/dt= 0then integration yieldsp1 + p2 = a CONSTANT

m1m2

F12

F21

F12 is force of 1 on 2

F21 is force of 2 on 1

Since this derivative is equal to 0

Thus the total momentum of the system of 2 particles is a constant.

Conservation of linear momentum

m1

m2

F12

F21

Simply stated: when two particles collide,their total

momentum remains constant.

pi = pf

p1i + p2i = p1f + p2f

(m1v1)i + (m2v2)i = (m1v1)f + (m2v2)f

Provided the particles are isolated from external forces, the total momentum of the particles will remain constant regards of the interaction between them

Conservation of linear momentum

Serway problems 9.2

17 & 18

Collisions

Collisions

Event when two particles come together for a short time producing impulsive forces on each other., No external forces acting. Or for the enthusiast: External forces are very small compared to the impulsive forces

Types of collisions

1) Elastic- Momentum and Kinetic energy conserved

2) Inelastic- Momentum conserved, some KE lost

3) Perfectly(completely) Inelastic- Objects stick together

Collisions in 1 d

Perfectly Elastic

1) Cons. of mom.

2) KE lost in collision

3) KE changes to PE

Elastic C

ollis ion Calculation

2 objects

Collisions - Examples

Computer Simulations

example 2, problems 5,24,29

Serway Problems 27,29,33,37

Collisions in 2 dimensions

mavax

mb

vel=0

p=0

Before collision

After Collision

mavaf

mbvbf

mavafx

mbvbxf

x momentum before collision equals x momentum after the collision

xfxi pp

1

2

Collisions in 2 dimensions xfxi pp

mavax= mavafx + mbvbxf

or

mavax= mavaf cos1 + mbvbf cos2

Collisions in 2 dimensions

mavax

mb

vel=0

p=0

Before collision

After Collision

mavaf

mbvbf

mavayf

Mbvbyf

y momentum before collision equals y momentum after the collision

yfyi pp

Velocity

y axis =0

py=o

2

1

Collisions in 2 dimensions yfyi pp

0= mavafy - mbvbfy

or

0= mavaf sin1 -mbvbf sin2

Collisions in 2 dimensions

xfxi pp

0= mavaf sin1 -mbvbf sin2

yfyi pp

mavax= mavaf cos1 + mbvbf cos2

Problems ex 9.9

43,44