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Momentum
 Momentum
 What
is Inertia?
 …think
 Based
is inertia in motion
Newton’s 1st Law
on mass and velocity
Calculating Momentum
 Momentum
p
= mass x velocity
= mv
p
= momentum (kg●m/s)
 m = mass (kg)
 v = velocity (m/s)
 No
“special” unit name
Practice - Momentum

What is the momentum of a 7-kg bowling ball is
it is travelling down the bowling lane at 5 m/s?
What happens if…



What happens to momentum if you double
the mass of the object?
What happens to momentum if you double
the velocity of the object?
What kind of relationship is this?
Momentum is Conserved

The momentum of any isolated system
always remains CONSTANT, in the
absence of any external force
 This
is The Law of Conservation of
Momentum
Initial Momentum = Final Momentum

pinitial = pfinal

In general, for two objects:
m1v1i + m2v2i = m1v1f + m2v2f
Concept Check




What is momentum?
What is the symbol for momentum?
What is the unit for momentum?
What does the Law of Conservation of
momentum say?
Impulse




Impulse describes how LONG a FORCE acts
on an object
Throwing an egg… “catch” for a long time
Air bag & crumple zones… “crash” for a long
time
Dropping an eff… “land” for a long time
Calculating Impulse
 Impulse
J
= Force x Time
= Ft
J
= impulse (Ns)
 F = Force (N)
 t = time (s)
Practice - Impulse

An 8-N force acts on a-5 kg object for 3
seconds.


What impulse is imparted on the object?
What change in momentum does the impulse
cause?
Impulse – Momentum Theorem
 “Impulse
is equal to the change in
momentum it causes”
 Ft = m∆v
F
= force (N)
 ∆t = change in time (s)
 m = mass (kg)
 ∆v = change in velocity (m/s)
Concept Check



What is the symbol for impulse?
What is the unit for impulse?
How are momentum and impulse related?
Collisions & Conservation of
Momentum

When objects collide, with no external forces,
the momentum before the collision is equal to
the momentum after the collision.


total momentum before = total momentum after
But, there are different ways that objects can
collide.
Elastic Collisions - Bouncing
objects are initially separated & stay separated
KE is conserved
Before collision:
After collision:
m1v1i + m2v2i = m1v1f + m2v2f
Image from http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Elastic.html
Practice – Elastic Collision:

A 1 kg ball moves east at 5 m/s. It hits a 2 kg
ball moving at 4 m/s, west. After the collision,
the 1 kg ball has a velocity of 6 m/s, west.
What is the speed of the 2 kg ball after the
collision?
Inelastic Collisions – “Coupling”
objects moving separately, combine into one mass
KE is NOT conserved
Before collision:
After collision:
m1v1i + m2v2i = (m1+ m2)vf
Image from www.physics.us.to
Practice – Inelastic Collision:

A 40,000 kg freight car is coasting at a speed
of 5 m/s along a straight track when it strikes
a 30,000 kg stationary freight car and couples
to it. What will be their combined speed after
impact?
Separation
objects moving together separate into multiple masses
Before
After
(m1+ m2)vi = m1v1f + m2v2f
Image from www.physics.us.to
Practice - Separation

A 2000 kg rocket is traveling at 750 m/s when
it divides into 2 stages. The front stage is 250
kg and is ejected with a speed of 1250 m/s.
What is the speed of the rear section of the
rocket after separation?