Transcript Impulse and Momentum

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
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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
Ft  mv
Fdt=mdv
You apply an impulse on an object and you
get an equal change in momentum
pf
vf
tf
pi
vi
ti
 dp   mdv   Fdt I
tf
 Fdt 
ti
Area under a Force vs
time graph
Impulse Graph
Linear Momentum and Impulse
Example problems 1,2,3
Chapter questions 5,6,10,13,16
Conservation of momentum
2 particle system
For gravitational or electrostatic
force
m1
m2
F12
F21
F12 =dp1/dt
F21 = dp2/dt
F12
is force of 1 on 2
F21
is force of 2 on 1
Conservation of momentum
2 particle system
From Newton’s 3rd Law
F12 = - F21
m1
or
F12 + F21 = 0
m2
F12
F21
F12 + F21 =dp1/dt + dp2/dt = 0
d(p1 + p2)/dt= 0
F12
is force of 1 on 2
F21
is force of 2 on 1
Since this
derivative is
equal to 0
Conservation of momentum
2 particle system
Since this
derivative is
d(p1 + p2)/dt= 0
then integration yields equal to 0
p1 + p2 = a CONSTANT
F12
m2
m1
F12
F21
F
21
Thus the total momentum of the
system of 2 particles is a constant.
is force of 1 on 2
is force of 2 on 1
Conservation of linear
momentum
Provided the particles are isolated from external forces,
the total momentum of the particles will remain constant
regards of the interaction between them
F12
m1
F21
m2
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
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
Collisions - Examples
Computer Simulations
example 2, problems 5,24,29
Serway Problems 27,29,33,37
Collisions in 2 dimensions
 pxi   pxf
After Collision
x momentum before
collision equals x
momentum after the
collision
mavax
Before
collision
mb
vel=0
p=0
mavaf
1
mavafx
mbvbxf
2
mbvbf
Collisions in 2 dimensions
 pxi   pxf
mavax= mavafx + mbvbxf
or
mavax= mavaf cos1 + mbvbf cos2
Collisions in 2 dimensions
 pyi   pyf
After Collision
y momentum before
collision equals y
momentum after the
collision
mavax
Before
collision
Velocity
y axis =0
py=o
mavaf
1
mavayf
mb
vel=0
p=0
2
mbvbf
Mbvbyf
Collisions in 2 dimensions
 pyi   pyf
0= mavafy - mbvbfy
or
0= mavaf sin1 -mbvbf sin2
Collisions in 2 dimensions
p p
yi
yf
0= mavaf sin1 -mbvbf sin2
p p
xi
xf
mavax= mavaf cos1 + mbvbf cos2
Problems ex 9.9
43,44