Unit 7
&
Momentum
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Any mass in motion
–
Inertia depends on mass (Newton’s 1st law)
Momentum = mass x velocity
–
Unit is kg x m/s
–
p  mv
Example 1
Impulse p
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A change in momentum
Requires a force F  ma
v
F  m( )
t
F  t  m  (v)
Impulse = force x time
p=Fxt
F  t  mvf  mvi  p
Example 2
Example
Example
Example

A 1400 kg car moving westward with a velocity of 15 m/s collides
with a utility pole and is brought to rest in 0.30 s. Find the magnitude
of the force exerted on the car during the collision.
Example

A 2250 kg car traveling to the west slows down uniformly from 20.0 m/s to
5.00 m/s. How long does it take the car to decelerate if the force on the car is
8450 N to the east? How far does the car travel during the deceleration?

When egg hits the plate
the time period is
shorter & force is
greater

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When the egg hits the
pillow the time increases
and the force decreases
As the time increase, the
force continues to
decrease
Conservation of Momentum
Newton’s Third Law of Motion

For every action (force) there is an equal and
opposite reaction (force)

... in every interaction, there is a pair of forces acting
on the two interacting objects.
–
–
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The size of the force on the first object equals the size of the
force on the second object.
The direction of the force on the first object is opposite to
the direction of the force on the second object.
Forces always come in pairs - equal and opposite actionreaction force pairs.
Conservation of Momentum

Momentum is never lost , but is simply
transferred from one object to another.
mv1i + mv2i = mv1f + mv2f
m1v1i  m2 v2i  m1v1 f  m2 v2 f

If the net force is zero then the total change
in momentum is zero
Systems


Any group of objects interacting are known
as a system.
The total momentum of the system remains
constant as long as the interactions occur
between the objects and no external force
acts on the system.
Elastic vs. Inelastic Collisions

Elastic Collisions
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two objects collide and then bounce off each other.
Both objects return to their original shape.
There is no change in the total kinetic energy.
Objects move separately after the collision.
Total momentum (and total energy) is conserved

mv1i + mv2i = mv1f + mv2f

½mv2 1i + ½mv2 2i = ½mv2 1f + ½mv2 2f
Elastic collision where a larger mass
hits a ball that is initially at rest
Elastic collision where a smaller mass
hits a larger mass
Collisions That are not Head On
Elastic vs. Inelastic Collisions

Inelastic Collisions
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–
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Two objects collide and stick together and move
as one mass.
The velocity of the two objects after the collision is
the same (obviously since they are stuck together).
Momentum is conserved but the energy is NOT
conserved.
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Some of the energy is used to deform the object.
Some of the energy is converted to sound
Some is dissipated as heat.
The kinetic energy is reduced in the end.
m1v1i  m2 v2i  (m1  m2 )v f
Example
Example
Example