Transcript Welcome to PHYS 2014

Lecture 15
Chapter 9: System of Particles
Today’s Topics:

Rigid body and flexible bodies

Center of Mass

Conservation of Momentum

Inelastic collision
OSU PHYS2014 Lecture 15 (Xie)
1
Motion of Many Particle Systems
What are systems of particles?
How to analyze the motions 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
OSU PHYS2014 Lecture 15 (Xie)
2
Center of Mass
For any one particle in a many particle system:


Fi ,net  mi ai
For the entire many particle system:
2

d rcm


Fnet ext  Macm & acm 
dt 2

rcm 

 mi ri
M
where M   mi
OSU PHYS2014 Lecture 15 (Xie)
3
Find the Center of Mass

rcm 

m
r
 ii
M
where M   mi
(1) Two identical masses of m
(2) Two unequal masses, m & M
(3) Three identical masses of m
OSU PHYS2014 Lecture 15 (Xie)
4
The Center of Mass
for Continuous Matter

rcm 

 r dm
M
where M  total mass
Center of Mass and Stability
OSU PHYS2014 Lecture 15 (Xie)
5
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)
6
Linear Momentum
Linear momentum of a particle:


p  mv
Linear momentum of a system:



P   pi   mi vi


dP
Fnet ext 
dt
OSU PHYS2014 Lecture 15 (Xie)
7
Conservation of Momentum
Linear momentum of a system:



P   pi   mi vi
When the net external force on a system is zero:

Fnet ext

dP

dt

P  constant

Fnet ext  0
The total momentum of the system is conserved!
OSU PHYS2014 Lecture 15 (Xie)
8
Motion of the Center of Mass
The center of mass remains the same:
OSU PHYS2014 Lecture 15 (Xie)
9
Exercise 1
Two boys, with masses of 40-kg and 60-kg respectively,
stand on a horizontal frictionless surface holding the
end of a light 10 m long rod. The boys pull themselves
together along the rod. When they meet the 40-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)
10
Clicker 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)
11
Totally Inelastic Collision
Totally inelastic collision:



m1vi1  m2vi 2  (m1  m2 )v f
Conservation of Momentum



m1v1i  m2v2i  (m1  m2 )v f
(2D)
m1v1xi  m2v2 xi  (m1  m2 )vxf
Or
m1v1yi  m2v2 yi  (m1  m2 )vyf
OSU PHYS2014 Lecture 15 (Xie)
12
Examples 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)
13
Clicker 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
OSU PHYS2014 Lecture 15 (Xie)
14