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Momentum
• Inertia in motion
• momentum = mass x velocity
• P = mv
• When direction is not an important factor:
• momentum = mass x speed, still P = mv
Momentum
• A compact car traveling at 20 mph has
less momentum than a large truck
traveling at the same velocity
• Why? The truck has more mass
Example
• When would a car and a truck with 2X car’s mass have the same momentum?
• They’d have the same momentum if the car were traveling 2x as fast as the truck
• (m x 2v) car = (2m x v) truck
How Does Momentum Change?
• mass changes
• velocity changes
• both mass and velocity change
• Usually-velocity changes (it accelerates!)
Example: Long-Range Cannons
• Long barrels
• Longer the barrel,
the greater the
velocity of the
emerging cannonball
or shell
Example, continued
• The force of exploding gunpowder in a long barrel acts on the cannonball for a longer time
• Increased impulse � greater momentum
• The force is not steady though-we refer to the average force
Momentum Over a Long Time
• The brakes in your car fail! Do you aim the car
at the concrete wall or at the haystack?
• Either way your momentum decreases the
same-you come to rest
• Hitting the haystack extends your contact
time-the time during which your momentum is
brought to zero
Momentum Over a Long Time
Momentum Over a Long Time
• Longer time reduces the force and decreases
the resulting deceleration
• Time of contact is extended 10x � force of
contact is reduced 10X
• When you jump you bend your knees before
you make contact with the ground: increases
the amount of time in the collision
Examples Extending the time in which momentum is being reduced
Catching A Fastball The
hand is initially forward
so it can move
backward after contact
with the ball
Bungee Jumping
The long stretch of the cord results in a small
average force to bring the jumper to a safe halt
before hitting the ground
Example: Karate Expert Breaks Bricks
• The impulse is the force of his hand against the bricks multiplied by the time his hand makes contact
• Therefore the force is huge!
• If his hand bounces, the force is even greater
Example
If a boxer makes the
time of contact 3X as
long by riding with the
punch, by how much is
the force reduced?
The force will be 3X less
than if he didn’t pull back
Example
• If the boxer instead moves into the punch
and shortens the contact time by half, how
much is the force increased?
• The force will be 2X greater than if he held
his head still. Forces of this kind account for
many knockouts!
Impulses are Greater: Bounce
• The impulse required to bring an object to a
stop and then to “throw it back again” is
greater than the impulse required merely to
bring it to a stop
Example
• You catch a falling flower pot
• You throw it back up in the air?
• That takes greater impulse (remember:
Impulse = force x time)
Example
• Think back to the karate expert. How does
the force that he exerts on the bricks
compare with the force exerted on his hand?
• Newton’s 3rd Law…they will be equal!
Example
• How will the impulse differ if his/her hand
bounces back when striking the bricks?
• The impulse will be greater if his/her hand
bounces. If the time of contact is not
increased, a greater force is then exerted on
the bricks (and her hand).
Conservation of Momentum
• There is a fixed amount of momentum for the
entire universe
• Additional momentum cannot be gained or
lost, but only transferred from one object to
another
Momentum is Conserved
• To change the momentum of an object, exert an impulse on it
• Internal forces do not affect momentum
– You push on the dashboard and the car’s momentum does not change
– When a cannon fires a cannonball, the explosive forces are internal; the momentum of the cannon-cannonball system doesn’t change
Momentum is Conserved
• Momentum is a vector quantity (magnitude and
direction)
• Same directions � added
• Opposite directions � subtracted
• Conservation: no momentum gained or lost
Law of Conservation of Momentum
• In the absence of an external force, the
momentum of a system remains unchanged
Example
• A high-speed bus and an innocent bug have a head-on collision.
• The sudden change of momentum for the bug spatters it all over the windshield.
• Is the change in momentum of the bus greater, less, or the same as the change in momentum of the unfortunate bug?
Example
• The momentum of both bug and bus change by the same amount because both the amount of force and the time (impulse) is the same on each.
• Momentum is conserved.
• Speed is another story! Because of the huge mass of the bus, its reduction of speed is very tiny-too small for the passengers to notice.
Momentum is Conserved in Collisions
Net momentum
before collisionNet momentum
after collision=
mvbefore = mvafter
Elastic Collisions
• The first ball comes to rest and the second ball moves away at the velocity of the first ball.
• Momentum is transferred from the first ball to the second one!
• A collision in which colliding objects rebound
without lasting deformation or the generation of heat
Inelastic Collisions
• A collision in which the colliding objects
become distorted, generate heat, and
possibly stick together
• A perfect inelastic collision: the objects stick
together
• Freight trains collide with one another
• We can calculate the velocity of the coupled
cars after the impact
• [mAvA + mBvB]before = [(mA + mB)v]after
Example: Inelastic Collision
Momentum and Airbags
• Airbags expand from the
steering wheel/dashboard
• A sensor has been triggered
due to a sudden IMPULSE or
CHANGE IN MOMENTUM
Momentum and Airbags
• The airbag fills with nitrogen
gas in 1/20th of a second
• The airbag expands before
the person hits it
• After 0.3 sec, the collision
should be complete and the
airbags empty
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