PHYS 81 GY 1st Sem 20092010
AKGTapia
1
Systems of Particles and
Systems of Particles and
Conservation of Momentum
Conservation of Momentum
Momentum of an Object
• Momentum (
p
)
is defined as the product of its
mass and velocity.
– Measure of the difficulty of bringing a particle
to rest.
v
p
m
=
Unit: 1 kg•m/s = 1 N•s
m
v
Problem on Linear Momentum
• A 0.100kg ball is thrown straight up into the air
with an initial speed of 15.0 m/s. Find the
momentum of the ball (a) at its maximum height
and (b) halfway up to its maximum height.
Original statement of Newton’s Second Law
v
p
Δ
=
Δ
m
t
t
m
m
Δ
Δ
=
Δ
Δ
=
=
p
v
a
F
net
The net force acting on a particle equals the time
rate of change of the particle’s linear momentum.
For systems of
particles,
∑
=
=
i
CM
i
i
MV
v
m
P
Infinitesimally,
dt
dP
F
net
=
The net force acting on a particle equals the time
rate of change of the particle’s linear momentum.
Original statement of Newton’s Second Law
The wrestling entertainment ring was designed to
cushion the fall of wrestlers.
This will lessen the impact
force by increasing the change in time.
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AKGTapia
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Conservation of Linear Momentum
• If the net external force on a system is zero, the
velocity of the center of mass of the system is
constant and the total momentum of system is
conserved; the is, it remains constant.
∑
∑
=
f
i
p
p
∑
=
=
=
i
i
i
CM
v
m
MV
P
constant
Note: Can be applied in isolated system where
there are no external forces.
Problem on Cons. of Linear Momentum
:
A man of mass 70 kg and a boy of mass 35 kg are
standing together on a smooth ice surface for
which friction is negligible.
If they push each other
apart and the man moves away with speed of 0.3
m/s relative to the ice, how far apart are they after
5 s?
Questions
:
1. If the kinetic energy of a particle is zero, what is
its linear momentum?
2. As a pendulum bob swings.
Is the momentum
conserved?
Why?
3. If the speed of a particle is doubled, by what
factor is its momentum changed? By what factor
is its kinetic energy changed?
Collisions
An isolated event where bodies exert a relatively
great amount of force to each other over a short
period of time.
M
1
M
2
v
1
v
2
System boundary
Particles
before
collision
Particles
after
collision
Collision
event
Elastic Collisions
The momenta and kinetic energies of the bodies
may change but
the total momentum and the total
kinetic energies are constant
.
∑
∑
=
f
i
p
p
∑
∑
=
f
KE
KE
i
e.g. (billiards, collision of particles,…)
System boundary
Particles
before
collision
Particles
after
collision
Collision
event
Note:
Kinetic
energy is
not
dissipated.
Note: For elastic collisions, the relative speed of
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 Spring '09
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