IMPULSE AND MOMENTUMTest tentatively scheduled for 1/24 !!!!

WHAT IS MOMENTUM?

• Defined as the product of a body’s mass and its velocity.

• Expresses how hard it is to STOP something!!

• Vector quantity that points in the direction of the velocity.

• SI unit is the kg•m/s

• A fast moving car will have

more momentum than a slower

car with the same mass.

• ???? How could the slower car match the momentum of the larger?

mvp

EXAMPLE: HOW FAST WOULD A 2.5 KG CAT NEED TO RUN IN ORDER TO MATCH THE MOMENTUM

OF A 9.25 KG DOG CHASING IT AT 6.25 M/S?

IMPULSE AND MOMENTUM

• This means that a force applied over time results in a change in momentum.

• This force applied over time is called Impulse! (J)

• Impulse has the same units as momentum - kg•m/s

• Impulse is also a vector quantity.

• I can only exert so much force, so I can increase time to get more velocity!

• Follow through in a golf swing

• Follow through on a basketball shoot

• Follow through on a baseball hit

• Longer barrel of a cannon or rifle

pJ

tFJ

A TENNIS RACKET EXERTS 35 N OF FORCE ON A BALL FOR 0.05 SECONDS. WHAT

CHANGE IN MOMENTUM IS DELIVERED TO THE BALL?

• If the 150 g ball started with an initial velocity of 10.0 m/s to the left, what would its velocity be after the impulse was applied?

A 0.25 KG BALL HITS A TENNIS RACKET WITH A SPEED OF 17.5 M/S TO THE RIGHT AND REBOUNDS WITH A SPEED OF 25 M/S. WHAT IMPULSE WAS DELIVERED

TO THE BALL?

CONSERVATION OF MOMENTUM

• In an isolated system of bodies, the momentum remains constant.

• Generally, momentum is NOT conserved:

• In the presence of friction (object loses KE because it gains thermal energy)

• When the object is working against gravity (object loses KE because it gains PE)

ab pJp

WRITE CONSERVATION OF MOMENTUM EQUATIONS FOR THE FOLLOWING:

• 1. A bowling ball rolls to a stop because of friction.

• 2. A moving car speeds up.

• 3. Two billiard balls hit and bounce off of each other.

• 4. A moving ball hits a stationary ball. Both move afterward.

• 5. A cannonball is fired from a cannon.

• 6. A man jumps into a stationary raft. The raft drifts away.

• 7. A car starts to move.

• 8. Two moving objects collide and stop.

• 9. Two stationary ice skaters push off of each other.

F VS T - FINDING IMPULSE VIA A GRAPH

• Impulse (J) = area under the curve

• ∆p = Impulse (J) = area under the curve

• If a 500 g object going 4.0 m/s

experienced this impulse, how fast

would it be going after?

TYPES OF COLLISIONS

• Elastic: momentum and kinetic energy are conserved

• The only true elastic collisions are atomic particles and subatomic particles

• We use billiard balls to model elastic collisions because they lose very little KE.

• Inelastic: momentum is conserved but KE is lost due to deformations, sound, etc.

• Most collisions fall into this category

• If I lose ANY KE (due to friction, sound energy, etc)

• Perfectly Inelastic: momentum is conserved but KE is lost due to deformations, sound, etc, AND the objects stick together after collision!

• Example: cars that collide and stick together

fvmmvmvm )( 212211

EXAMPLES:

• https://www.youtube.com/watch?v=AkB81u5IM3I

• https://www.youtube.com/watch?v=6TA1s1oNpbk

• https://www.youtube.com/watch?v=6TA1s1oNpbk

CENTER OF MASS

• The point about which a body moves as if all forces were exerted there.

• The point has an x and y component.

• SI unit is the meter (m)

• Example: A 12 m by 12 m raft has a mass

of 700 kg. Three people sit on the raft. Each

person has a mass of 45 kg and sit at the

following points: (0,6m), (6m,0), and

(2m, 4m). What is the center of mass of the

system? Assume the raft’s center is at (6m, 6m).

M

ymymymy

M

xmxmxmx

cm

cm

...

...

332211

332211