Momentum & Impulse Level 1 Physics

What you need to know Essential Questions Objectives How is impulse and momentum related? How does the law of conservation of momentum apply to objects at rest? In motion? Objectives Define and give examples of impulse and momentum Restate Newton’s Second Law in terms of momentum Calculate the change in momentum from the area under the curve of a force versus time graph Derive a statement of the conservation of momentum between two objects by applying Newton’s Third Law Define and recognize examples of elastic and inelastic collisions Explain which conservation laws apply to each type of collision Demonstrate proficiency in solving problems involving conservation of momentum in collisions

Impulse Equals Change in Momentum Remember the following; N.S.L & definition of acceleration Units of impulse: N*s Units of momentum: kg*m/s

Impulse and Momentum Impulse Change in Momentum Notice the relationship with force and time

Impulse – Momentum Relationships

Impulse – Momentum Relationships Constant Since TIME is directly related to the VELOCITY when the force and mass are constant, the LONGER the cannonball is in the barrel the greater the velocity. Also, you could say that the force acts over a larger displacement, thus there is more WORK. The work done on the cannonball turns into kinetic energy.

Impulse – Momentum Relationships Which would be more damaging: driving into a massive concrete wall, or driving at the same speed into a head-on collision with an identical car traveling toward you at the same speed? Both cases are equivalent, because either way, your car is rapidly decelerating to a dead stop. The dead stop is easy to see when hitting the wall, and a little thought will show the same is true when hitting the car. If the oncoming car were traveling slower, with less momentum, you'd keep going after the collision with more 'give,' and less damage (to you!). But if the oncoming car had more momentum than you, it would keep going and you'd snap into a sudden reverse with greater damage. Identical cars at equal speeds means equal momenta -- zero before, zero after collision.

Collisions Consider 2 objects heading towards one another. Upon colliding… N.T.L. says that the FORCE they exert on each other is EQUAL but in the OPPOSITE direction The time of impact is the SAME for both… Therefore, the IMPULSES of the 2 objects are also EQUAL and OPPOSITE

Collisions If IMPUSES are EQUAL, then the MOMEMTUMS of each object are EQUAL as well The marks are called primes and they indicate the velocity after the collision.

Momentum is CONSERVED In the absence of external forces, the total momentum before a collision is equal to the total momentum after the collision – The Law of Conservation of Momentum

Example

Types of Collisions A situation where the objects DO NOT STICK is one type of collision Notice that in EACH case, you have TWO objects BEFORE and AFTER the collision.

A “no stick” type collision Spbefore = Spafter -10 m/s

A “stick” type of collision Spbefore = Spafter 5 m/s

The “explosion” type This type is often referred to as “backwards inelastic”. Notice you have ONE object ( we treat this as a SYSTEM) before the explosion and TWO objects after the explosion.

Backwards Inelastic - Explosions Suppose we have a 4-kg rifle loaded with a 0.010 kg bullet. When the rifle is fired the bullet exits the barrel with a velocity of 300 m/s. How fast does the gun RECOIL backwards? Spbefore = Spafter -0.75 m/s

Collision Summary Elastic Collision = Kinetic Energy is Conserved Sometimes objects stick together or blow apart. In this case, momentum is ALWAYS conserved. When 2 objects collide and DON’T stick When 2 objects collide and stick together When 1 object breaks into 2 objects Elastic Collision = Kinetic Energy is Conserved Inelastic Collision = Kinetic Energy is NOT Conserved

Elastic Collision Since KINETIC ENERGY is conserved during the collision we call this an ELASTIC COLLISION.

Inelastic Collision Since KINETIC ENERGY was NOT conserved during the collision we call this an INELASTIC COLLISION.

Example Granny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion without "braking." Determine the velocity of Granny and Ambrose. How many objects do I have before the collision? How many objects do I have after the collision? 2 1 4 m/s