Momentum Momentum Can be defined as mass in

Momentum

Momentum Can be defined as mass in motion n Is a product of the mass and velocity. n P = mv n A change in momentum requires and external force. – Changes the velocity of the object in motion. – A force exerted over a longer period of time will create a larger change in momentum. – Impulse § Force exerted over a period of time Force x Time = Impulse

Momentum n Linear momentum is the product of the mass and the velocity (vector) § in direction of velocity § SI unit is N s § p from the term progress: n “the quantity of motion with which a body proceeds in a certain direction”.

Impulses Change Momentum n. A § FT = Δp § FT = mvfinal – mvinitial ball in contact with a bat for a longer period of time will have a greater change in momentum. – Momentums have a direction so they are vectors. – Stopping distances depend on impulse momentum. § Heavier objects need more time to stop

Momentum n Concept Questions: – If a truck and a person on rollerskates have the same speed, which would have greater momentum? – How can the situation change so the person has greater momentum?

Momentum n Problem: – A 2250 kg pickup truck has a velocity of 25 m/s east. What is the momentum of the truck?

Impulse n Newton’s Second Law revisited:

Impulse n Concept questions: – Why do airbags help you in an accident? – Why is it better for an egg to fall on a pillow than a sidewalk?

Impulse n Sample Problem: – 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. § F t = mvf-mvi

Conservation of Momentum n Momentum is conserved. – It is never lost , it is simply transferred from one object to another. – Initial momentum = final momentum § mv. A 1 + mv. B 1 = mv. A 2 + mv. B 2 § If two skaters on ice at rest push off each other, their initial momentum zero but their final momentums are equal in magnitude and opposite in direction. n If the net force is zero then the total change in momentum is zero.

Impulse n Using the Impulse Momentum Theorem to find stopping times/distances: – F t = mvf -mvi to find the time or force – x = ½ (vf+vi) t to find distance

Impulse n Sample Problem: – 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? § F t = mvf -mvi

Systems n Any group of objects interacting are known as a system. n 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.

Sea Horse

Collisions n Elastic Collisions – In perfectly elastic collisions 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 is conserved. § mv. A 1 + mv. B 1 = mv. A 2 + mv. B 2 § ½mv 2 A 1 + ½mv 2 B 1 = ½mv 2 A 2 + ½mv 2 B 2

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

Collisions n Perfectly Inelastic Collisions – Two objects collide and stick together and move as one mass. – The velocity of the two objects after the collision remain the same. – Momentum is conserved but the energy is NOT conserved. § § § Some of the energy is used to deform the object. Some of the energy is converted to sound Some is disapated as heat. – The kinetic energy is reduced in the end.

Special Equations for perfectly Elastic Collisions n Criteria to use these equations. – The collision must be perfectly elastic – Must be head on – One of the objects must be stationary. – § v 1’ = (m 1 -m 2) x v 1 (m 1+m 2 ) – § V 2’ = 2 m 1 x (m 1 +m 2) v 1 – v 1’ Final velocity of moving object – v 1 Initial velocity of moving object – V 2’ Final velocity of object initially at rest.

Collisions n Sample Problem: – A 76 kg boater, initially a rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2. 5 m/s to the right, what is the final velocity of the boat?

Momentum Animation http: //physics. weber. edu/amiri/director/dcrfiles/momentum/collision 1 DS. dcr