Uses the Law of Conservation of Momentum and describes momentum, impulse, elastic and inelastic collisions as well as explosions. **More good stuff available at: www.wsautter.com and http://www.youtube.com/results?search_query=wnsautter&aq=f

1. Copyright Sautter 2015

2. Newton’s Second Law of Motion
Acceleration = velocity / time
Combining the two equations
Rearranging the equation
Impulse Momentum 2

3. Impulse & Momentum
• As seen on the previous slide, momentum and impulse
equations are derived from Newton’s Second Law of Motion
(F = ma). Impulse is defined as force times time interval during
which the force is applied and momentum is mass times the
resulting velocity change.
• The symbol p is often used to represent momentum, therefore p
= mv.
• The question maybe however, “why develop a momentum
equation when it is merely a restatement of F = ma which we
already know ?”
• The answer is that no conservation principles can be applied to
forces. There is no such thing as “conservation of force”.
However, Conservation of Momentum is a fundamental law
which can be applied to a vast array of physics problems.
Therefore, manipulating Newton’s Second Law into the impulse
– momentum format helps us to implement a basic principle of
physics ! 3

4. A collision is a momentum exchange.
In all collisions the total momentum before a
collision equals the total momentum after
the collision. Momentum is merely redistributed
among the colliding objects.
Momentum = Mass x Velocity
p = m x v
Σ Momentum before = Σ Momentum after
collision collision 4

5. Momentum & Kinetic Energy
• Recall the following facts about kinetic energy:
• Kinetic energy is the energy of motion. In order to
possess kinetic energy an object must be moving.
• As the speed (velocity) of an object increases its
kinetic energy increases. The kinetic energy content
of a body is also related to its mass. Most massive
objects at the same speed contain most kinetic
energy.
• Since the object is in motion, the work content is
called kinetic energy and therefore: K.E. = ½ m v2
5

6. Types of Collisions
(Momentum Transfers)
• Collisions occur in three basic forms:
• (1) Elastic collisions – no kinetic energy is lost during
the collision. The sum of the kinetic energies of the
objects before collision equals the sum of the kinetic
energies after collision.
• It is important to realize that kinetic energy is
conserved in these types of collisions. Total energy is
conserved in all collisions. (The Law of Conservation
of Energy requires it!)
• The only collisions which are perfectly elastic are
those between atoms and molecules. In the
macroscopic world some collisions are close to
perfectly elastic but when examined closely, they do
lose some kinetic energy. 6

7. Types of Collisions
(Momentum Transfers)
• (2) Inelastic collisions – the objects stick together
after collision and remain as a combined unit.
Kinetic energy is not conserved !
• (3) Partially elastic collisions – kinetic energy is
not conserved but the colliding objects do not
remain stuck together after collision. Most
collisions are of this type. In these collision some
of the energy is converted to heat energy or used
to deform the colliding objects. That which
remains is retained as kinetic energy.
7

8. Types of Collisions
(Momentum Transfers
• Example collisions:
• Elastic collisions – pool balls colliding, a golf ball
struck with a club, a hammer striking an anvil.
Remember, these collisions are not perfectly elastic
but they are close!
• Inelastic collisions – an arrow shot at a pumpkin
and remaining embedded, a bullet shot into a piece
of wood and not fully penetrating, two railroad cars
colliding and coupling together.
• Partially elastic collisions - two cars colliding and
then separating, a softball struck by a bat, a tennis
ball hit with a racket.
8

9. M1U1 + M2U2 = M1V1 + M2V2
CLICK
HERE
Σ K.E. before collision = Σ K.E. after collision e = 1.0 9

10. M1U1 + M2U2 = (M1 + M2) V
CLICK
HERE
Σ K.E. before collision = Σ K.E. after collision/ e = 0 10

11. Measuring Collision Elasticity
• The elastic nature of a collision can be measured
by comparing the K.E. content of the system
before and after collision. The closer they are to
being equal, the more elastic the collision.
• Another way to measure elasticity is to use the
Coefficient of Restitution. The symbol for this
value is e. If e is equal to 1.0 the collision is
perfectly elastic. If e is equal to zero the collision is
inelastic. If e lies in between 0 and 1.0 the collision
is partially elastic.
• The closer e is to 1.0 the more elastic the collision,
the closer e is to 0 the more inelastic.
11

12. Ball
1
Ball
2
Velocity of ball 1
Before collision u1
Velocity of ball 2
Before collision u2
Ball
1
Ball
2
Point
of
collision
Velocity of ball 1
after collision V1
Velocity of ball 2
after collision V2
12

13. Momentum – A Vector Quantity
• Momentum is a vector quantity (direction counts). In one
dimensional collisions motion lies exclusively along the x plane
or the y plane.
• One Dimensional Collisions - The direction of the momentum
vectors are identified by the usual conventions of plus on
horizontal plane (x axis) is to the right and minus is to the left.
In the vertical plane (y axis) , plus is up and minus is down.
• Two Dimensional Collisions – The momentum vectors can be
resolved into x – y components and combined using vector
addition methods to obtain the momentum sums before and
after collision.
• In two dimensional collisions the sums of the vertical
momentum components must be equal before and after
collision just as the sums of horizontal momentum components
must be equal before and after collision. 13

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