impulse and momentum chapter problems serway –5,6,10,13,16,17,18,27,29,33,43,44,52,54,59,60...
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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
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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
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Linear momentum & impulse
Examples of impulses being applied on everyday objects
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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
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Impulse Graph
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Linear Momentum and Impulse
Example problems 1,2,3
Chapter questions 5,6,10,13,16
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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
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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
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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.
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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
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Conservation of linear momentum
Serway problems 9.2
17 & 18
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Collisions
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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
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Collisions in 1 d
Perfectly Elastic
1) Cons. of mom.
2) KE lost in collision
3) KE changes to PE
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Elastic C
ollis ion Calculation
2 objects
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Collisions - Examples
Computer Simulations
example 2, problems 5,24,29
Serway Problems 27,29,33,37
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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
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Collisions in 2 dimensions xfxi pp
mavax= mavafx + mbvbxf
or
mavax= mavaf cos1 + mbvbf cos2
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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
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Collisions in 2 dimensions yfyi pp
0= mavafy - mbvbfy
or
0= mavaf sin1 -mbvbf sin2
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Collisions in 2 dimensions
xfxi pp
0= mavaf sin1 -mbvbf sin2
yfyi pp
mavax= mavaf cos1 + mbvbf cos2
Problems ex 9.9
43,44