phys2014 lecture15 xie 2010 ch9 multi

8/6/2019 PHYS2014 Lecture15 Xie 2010 Ch9 Multi

1/14

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:


2/14


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?


3/14


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:


4/14


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


5/14


The Center of Mass

for Continuous Matter

Center of Mass and Stability

masstotaldmr

rcm here !!T

T


6/14


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


7/14


Linear Momentum

Linear momentum of a particle:

Linear momentum of a system:

vmpTT

!

!! iii vmpPTTT

dt

PdF extnet

TT

!


8/14



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!


9/14


Motion of the Center of Mass

The center of mass remains the same:


10/14


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


11/14


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


12/14


Totally Inelastic Collision

(2D))( 212211 fii vmmvmvmTTT

!

fiivmmvmvmTTT)(

212211!

xfxixi vmmvmvm )( 212211 !


Totally inelastic collision:

yfyiyi vmmvmvm )( 212211 !Or


13/14


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?


14/14


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

phys2014 lecture15 xie 2010 ch9 multi

Documents