phys2014 lecture15 xie 2010 ch9 multi
TRANSCRIPT
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OSU PHYS2014 Lecture 15 (Xie) 1
Lecture 15
Chapter 9: System of Particles
Rigid body and flexible bodies
Center of Mass
Conservation of Momentum
Inelastic collision
Todays Topics:
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OSU PHYS2014 Lecture 15 (Xie) 2
Motion of Many Particle Systems
Flexible systems:
Olympic skaters, Olympic skiers, & us!!!
Solar system, two colliding cars
Exploding fireworks on July 4
th
, exploding bombsRigid systems (rigid body):
Earth (Approximately), golf ball, basket ball (in air)
Windmill, airplane, car
What are systems of particles?What are systems of particles?
How to analyze the motions of many particleHow to analyze the motions of many particle
systems?systems?
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OSU PHYS2014 Lecture 15 (Xie) 3
Center of Mass
!! iii
cm mMM
rmr where
TT
2
2
dt
rda&aMF cm
cmcmextnet
TTTT
!!
iinet
i
aTT
!,
For any one particle in a many particle system:
For the entire many particle system:
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OSU PHYS2014 Lecture 15 (Xie) 4
Find the Center of Mass
(1) Two identical masses ofm
(2) Two unequal masses, m & M
(3) Three identical masses ofm
!! iiicr
r here
TT
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OSU PHYS2014 Lecture 15 (Xie) 5
The Center of Mass
for Continuous Matter
Center of Mass and Stability
masstotaldmr
rcm here !!T
T
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OSU PHYS2014 Lecture 15 (Xie) 6
Concept Question 1
The center of mass of a uniform ring with radius R
is located:
(A) On the ring(B)A distance R/2 from the center
(C)A distance R/3 from the center
(D)A distance 2R/3 from the center
(E)At the center
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OSU PHYS2014 Lecture 15 (Xie) 7
Linear Momentum
Linear momentum of a particle:
Linear momentum of a system:
vmpTT
!
!! iii vmpPTTT
dt
PdF extnet
TT
!
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OSU PHYS2014 Lecture 15 (Xie) 8
Conservation of Momentum
Linear momentum of a system:
!! iii vmpPTTT
dt
PdF extnet
TT
!0 !extnetF
Tconstant!P
T
When the net external force on a system is zero:
The total momentum of the system is conserved!
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OSU PHYS2014 Lecture 15 (Xie) 9
Motion of the Center of Mass
The center of mass remains the same:
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OSU PHYS2014 Lecture 15 (Xie) 10
Exercise 1
Two boys, with masses of4040--kgkgand 6060--kgkg respectively,
stand on a horizontal frictionless surface holding the
end of a light 10m10m long rod. The boys pull themselves
together along the rod. When they meet the 4040--kgkgwill
have moved what distance.
(A) 4 m
(B) 5 m
(C) 6m
(D)10m
(E) Need to know the force they exert
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OSU PHYS2014 Lecture 15 (Xie) 11
Clicker Question 1Clicker Question 1
The center of mass of a system of particles remains
at the same place if:
(A) it is initially at rest and the external forces sum to zero.
(B) it is initially at rest and the internal forces sum to zero.
(C) the sum of the external forces is less than the
maximum force of static friction.
(D) no friction acts internally(E) none of the above
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OSU PHYS2014 Lecture 15 (Xie) 12
Totally Inelastic Collision
(2D))( 212211 fii vmmvmvmTTT
!
fiivmmvmvmTTT)(
212211!
xfxixi vmmvmvm )( 212211 !
Conservation of Momentum
Totally inelastic collision:
yfyiyi vmmvmvm )( 212211 !Or
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OSU PHYS2014 Lecture 15 (Xie) 13
ExamplesExamples for many particle systems
A 42-kg child stands at rest on ice skates. She catches a
1.1-kg ball moving horizontally at 9.5 m/s. What is her
speed after shes caught the ball?
Two identical trucks have mass 5500 kg when empty.
One truck carries a 9500-kg load and is moving at 65
km/h. It collides inelastically with the second truck, which
is initially at rest, and the pair movies off at 40 km/h. What
is the load of the second truck?
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OSU PHYS2014 Lecture 15 (Xie) 14
Clicker Question 2Clicker Question 2
BlockA, with mass of 4 kg, is stationary while block
B, with a mass of 8 kg, is moving at 3 m/s. The center of
mass of the two block system has a speed of(A) 0 m/s
(B)1.5 m/s
(C)2 m/s
(D)3 m/s
(E)12 m/s