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

P = mvvelocity (m/sec)

mass (kg)

Momentum (kg-m/sec)

Momentum

• P = mv

• Therefore, the units

of momentum are:

kg x m/s

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!)

Impulse

• “force x time”

• Change in momentum

• Ft � change in mv

• Ft = ∆mv

Impulse = ∆Momentum

Ft = ∆mv

(Kg)(m/s2)(s) = (kg)(m/s)

Impulse

“Force multiplied by the time during which it

acts equals change in momentum

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

Momentum Over a Short Period

• Short contact time = large force

• Momentum is quickly reduced

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

Mgvg = mbVb

(4kg) vg = (0.010kg) (300 m/s)

4vg = 3

vg = 3/4

vg = 0.75 m / s

Example

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

Example: Elastic Collision

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

Example: Inelastic Collision

Example: Inelastic Collision

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

What is the function of an airbag?

• During front-end collisions the driver and passengers have inertia and will continue forward until the dashboard, seatbelt, or airbag forces them to stop

• Airbags were created to cushion the impact by increasing the time to stop, resulting in a smaller force