Download Chapter_9a

Chapter 9: Linear Momentum &
Collisions
Reading assignment: Chapter 9.5-9.7
Homework : (due Wednesday, Oct. 5, 2005):
Problems:
32, 36, 43, 52, 69, 71
• Center of mass
• Momentum


p  mv
• Momentum is conserved
Center of mass
Center of mass for many particles:

rCM 
 ______
i
M
Black board example 9.1
Where is the center of mass of the arrangement of particles below.
(m3 = 2 kg and m1 = m2 = 1 kg)?
A method for finding the center of mass of any object.
- Hang object from two
or more points.
- Draw extension of
suspension line.
- Center of mass is at
intercept of these lines.
Center of mass of a solid body
(uniform density)
xCM
yCM
zCM
1

xdV

__
1

ydV

__
1

zdV

__
Black board example 9.2
A uniform square plate 6 m
on a side has had a square
piece 2 m on a side cut out of
it. The center of that piece is
at x = 2 m, y = 0. The center
of the square plate is at x = y
= 0. Find the coordinates of
the center of mass of the
remaining piece.
Motion of a System of Particles.
Newton’s second law for a System of Particles
The ____________ of a system of particles (combined mass M)
moves like one equivalent particle of mass M would move under
the influence of an external force.


Fnet  MaCM
Fnet , x  MaCM , x
Fnet , y  MaCM , y
Fnet , z  MaCM , z
A rocket is shot up in the air and explodes.
Describe the motion of the center of mass before and after
the explosion.
Linear Momentum
The linear momentum of a particle of mass m and velocity
v is defined as


p  __  v
The linear momentum is a vector quantity.
It’s direction is along v.
The components of the momentum of a particle:
px  m  vx
py  m  vy
pz  m  vz



dp d (m  v )
From Newton’s second law: Fnet 

 __ __
dt
dt
The time rate of change in linear momentum is equal to the net
forces acting on the particle.
This is also true for a system of particles:


P  M  vCM
Total momentum = Total mass ·velocity of center of mass
And: Net external force = ____________ in
momentum of the center of mass


dP
Fnet 
dt
Conservation of _________ momentum
Thus:
If no _________________ is acting on a particle, it’s momentum
is conserved.
This is also true for a system of particles:
If no external forces interact with a system of particles the total
momentum of the system remains constant.

  
P   p  p1  p2      constant
 
or : Pi  Pf




p1i  p2i      p1 f  p2 f    
Black board example 9.3
You (100kg) and your skinny friend
(50.0 kg) stand face-to-face on a
frictionless, frozen pond. You push
off each other. You move backwards
with a speed of 5.00 m/s.
(a) What is the total momentum of the
you-and-your-friend system?
(b) What is your momentum after you
pushed off?
(c) What is your friends speed after you
pushed off?