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Chapter 6
Momentum and Collisions
Section 6-1
Momentum
Momentum

Momentum describes an object’s motion.

Momentum can be defined as "mass in motion."
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All objects have mass; so if an object is moving,
then it has momentum .
The amount of momentum an object has
depends on two things :


How much stuff is moving
How fast the stuff is moving
Momentum

Momentum is a vector quantity (magnitude and
direction).

It is represented by the symbol p

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Formula :
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Comes from the word progress
P=mv
Momentum equals mass times velocity
SI Units :
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kg∙m/s
kilogram-meters per second
Examples of Momentum


Bowling ball vs. Playground ball at same speed.
Which will have more momentum?
Example of Momentum

A small object moving with a very high velocity has a
large momentum.


Hailstones
By the time they reach Earth, they have enough momentum to
hurt you or cause serious damage to cars and buildings.
Let’s Practice Together.

Determine the momentum of a ...

60-kg halfback moving eastward at 9 m/s.

1000-kg car moving northward at 20 m/s.

40-kg freshman moving southward at 2 m/s.
Impulse

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A change in momentum takes force and
time.
Momentum is closely related to force.
For a CONSTANT force, impulse is the
product of the force and time acted on an
object.
Impulse – Momentum Theorem


The impulse experienced by an object is
always equal to the change in its
momentum.
Formula
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FΔt =Δp
force x time interval = change in momentum
From this formula we can say :

A small force acting for a long time can produce the
same change in momentum as a large force acting for
a short time.
Example : Change in
Momentum
Preview of Collisions


In a collision, an object experiences a
force for a given amount of time which
results in its mass undergoing a change in
velocity.
What happens to the momentum of the
object?
Newton’s 3rd Law

The Law of Action-Reaction

Newton's 3rd Law is naturally applied to
collisions between two objects.


In a collision between two objects, both
objects experience forces which are equal
in magnitude and opposite in direction.
Such forces cause one object to speed up
(gain momentum) and the other object to
slow down (lose momentum).
Section 2 : Conservation of
Momentum Principle

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
The total momentum of all objects
interacting with one another remains
constant regardless of the nature of the
forces between the objects.
Momentum is conserved in collisions.
Momentum is conserved for objects
pushing away from each other.
Conservation of Momentum



m1v1,i + m2v2,i = m1v1,f + m2v2, f
Total Initial Momentum = Total Final
Momentum
(Same Formula for Elastic Collisions)
Section 3 :Collisions

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The total momentum remains constant in
any type of collision.
Total kinetic energy is not always
conserved.
KE is converted to internal energy when
the objects deform.
Elastic Collisions

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In elastic collisions, two objects collide
and return to their original shapes with no
change in total kinetic energy
Both momentum and kinetic energy are
conserved in an elastic collision.
Elastic Collisions
Elastic Collisions
Elastic Collisions

m1v1,i + m2v2,i = m1v1,f + m2v2, f
 (same formula as conservation of momentum)
Perfectly Inelastic Collision

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When two objects collide and move together as
one mass, the collision is called perfectly
inelastic.
The two objects become one object after the
collision.
Objects in this type of collision are deformed
during the collision and lose some kinetic
energy. KE changes to different forms of
energy.
Perfectly Inelastic Collision

When an arrow
pierces a target and
remains stuck in the
target, the arrow and
target have
undergone a perfectly
inelastic collision
(assuming no debris
is thrown out)
Perfectly Inelastic Collision


m1v1,i + m2v2,i = (m1+m2)vf
After colliding, the objects stick
together and move with the same
final velocity (Vf).