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OSU PHYS2014 Lecture 15 (Xie) 1
Lecture 15Chapter 9: System of Particles
Rigid body and flexible bodies
Center of Mass
Conservation of Momentum
Inelastic collision
Today’s Topics:
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 4th, exploding bombs
Rigid 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 particle How to analyze the motions of many particle systems?systems?
OSU PHYS2014 Lecture 15 (Xie) 3
Center of Mass
iii
cm mMM
rmr where
2
2
dt
rda & aMF cm
cmcmext net
iinetiamF
,
For any one particle in a many particle system:
For the entire many particle system:
OSU PHYS2014 Lecture 15 (Xie) 4
Find the Center of Mass
(1) Two identical masses of m
(2) Two unequal masses, m & M
(3) Three identical masses of m
iii
cm mMM
rmr where
OSU PHYS2014 Lecture 15 (Xie) 5
The Center of Mass for Continuous Matter
Center of Mass and Stability
masstotalMM
dmrrcm where
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
OSU PHYS2014 Lecture 15 (Xie) 7
Linear Momentum
Linear momentum of a particle:
Linear momentum of a system:
vmp
iii vmpP
dt
PdF extnet
OSU PHYS2014 Lecture 15 (Xie) 8
Conservation of Momentum
Linear momentum of a system:
iii vmpP
dt
PdF extnet
0 extnetF
constantP
When the net external force on a system is zero:
The total momentum of the system is conserved!
OSU PHYS2014 Lecture 15 (Xie) 9
Motion of the Center of Mass
The center of mass remains the same:
OSU PHYS2014 Lecture 15 (Xie) 10
Exercise 1
Two boys, with masses of 40-kg40-kg and 60-kg60-kg respectively, stand on a horizontal frictionless surface holding the end of a light 10 m10 m long rod. The boys pull themselves together along the rod. When they meet the 40-kg40-kg will have moved what distance.
(A) 4 m
(B) 5 m
(C) 6 m
(D) 10 m
(E) Need to know the force they exert
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
OSU PHYS2014 Lecture 15 (Xie) 12
Totally Inelastic Collision
(2D) )( 212211 fii vmmvmvm
fii vmmvmvm
)( 212211
xfxixi vmmvmvm )( 212211
Conservation of Momentum
Totally inelastic collision:
yfyiyi vmmvmvm )( 212211 Or
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 she’s 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?
OSU PHYS2014 Lecture 15 (Xie) 14
Clicker Question 2Clicker Question 2
Block A, 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
