Chapter 7 Momentum and Impulse - State …

1 Chapter 7 Chapter 7 Momentum andMomentum andImpulseImpulseCollisions!How can we describe the change in velocitiesof colliding football players, or balls collidingwith bats?!How does a strong force applied for a veryshort time affect the motion?!Can we apply Newton s Laws to collisions?!What exactly is Momentum ? How is itdifferent from force or energy?!What does Conservation of Momentum mean?What happens when a ball bounces?"When it reaches the floor,its velocity quickly changesdirection."There must be a strongforce exerted on the ball bythe floor during the shorttime they are in contact."This force provides theupward accelerationnecessary to change thedirection of the ball happens when a ball bounces?"Forces like this aredifficult to analyze:#Strong forces that actfor a very short time.

2 #Forces that may changerapidly during the collision."It will help to writeNewton s second law in termsof the total change in velocityover time, instead ofacceleration: ! Impulse = change in Momentum = "pMomentum and Impulse "Multiply both sides of Newton s secondlaw by the time interval over which theforce acts:"The left side of the equation is Impulse ,the (average) force acting on an objectmultiplied by the time interval over whichthe force acts."How a force changes the motion of an object depends onboth the size of the force and how long the force acts."The right side of the equation is the change in themomentum of the object."The Momentum of the object is the mass of the object timesits and ImpulseA bowling ball and a tennis ball can have the samemomentum, if the tennis ball with its smaller mass has amuch larger Impulse acting on an object produces a changein Momentum of the object that is equal in bothmagnitude and direction to the a ballbounces back withthe same speed,the momentumchanges from mvto -mv, so thechange inmomentum ofMomentum"Does Newton s third lawstill hold?

3 $For every action, there isan equal but oppositereaction.$The defensive back exertsa force on the fullback,and the fullback exerts anequal but opposite forceon the defensive ofMomentum$The impulses on both areequal and opposite.$The changes inmagnitude for each areequal and opposite.$The total change of themomentum for the twoplayers is ofMomentumIf the netexternal forceacting on a systemof objects is zero,the totalmomentum of thesystem 100-kg fullback moving straight downfieldcollides with a 75-kg defensive back. Thedefensive back hangs on to the fullback, andthe two players move together after thecollision. What is the initial Momentum of eachplayer?What is the initial Momentum of each player?Fullback:p = mv = (100 kg)(5 m/s) = 500 kg m/sDefensive back:p = mv = (75 kg)(-4 m/s) = -300 kg m/sWhat is the total Momentum of the system?

4 Total Momentum : ptotal = pfullback + pdefensive back= 500 kg m/s - 300 kg m/s= 200 kg m/sWhat is the velocity of the two playersimmediately after the collision?Total mass: m = 100 kg + 75 kg= 175 kgVelocity of both: v = ptotal / m= (200 kg m/s) / 175 kg= m/sRecoil!Why does a shotgun slam againstyour shoulder when fired,sometimes painfully?!How can a rocket accelerate inempty space when there is nothingthere to push against except itself?Two skaters of different masses prepare topush off against one another. Which one willgain the larger velocity?a)The more massive oneb)The less massive onec)They will each have equal butopposite velocities.#The net external force acting on thesystem is zero, so conservation ofmomentum applies.

5 #Before the push-off, the total initialmomentum is zero.#The total Momentum after the push-off should also be can the total Momentum be zero when atleast one of the skaters is moving?#Both must move withmomentum values equal inmagnitude but opposite indirection: p2 = !p1#When added together, thetotal final Momentum of thesystem is then zero.#Since Momentum is masstimes velocity p = mv, theskater with the smaller massmust have the largervelocity: m1v1 = m2v2"The lighter objectattains the largervelocity to equalizethe magnitudes ofthe momentums ofthe two objects."The total momentumof the system isconserved and doesnot is what happens when a brief forcebetween two objects causes the objects tomove in opposite Momentum conserved when shooting ashotgun?

6 "The explosion of the powder causes the shot tomove very rapidly forward."If the gun is free to move, it will recoil backward witha Momentum equal in magnitude to the momentumof the shot."Even though the mass of the shot is small, itsmomentum is large due to its large velocity."The shotgun recoils with a Momentum equal inmagnitude to the Momentum of the shot."The recoil velocity of the shotgun will be smallerthan the shot s velocity because the shotgun hasmore mass, but it can still be can you avoid a bruised shoulder?"If the shotgun is held firmly against your shoulder, itdoesn t hurt as "If you think of the system as just the shotgun andthe pellets, then your shoulder applies a strongexternal force to the system."Since conservation of Momentum requires theexternal force to be zero, the Momentum of thissystem is not conserved.

7 "If you think of the system as including yourself withyour shoulder against the shotgun, then momentumis conserved because all the forces involved areinternal to this system (except possibly frictionbetween your feet and the earth)."With your mass added to the system, the recoilvelocity is smaller."If you think of the system as including yourself andthe earth, then Momentum is conserved because allthe forces involved are internal to this system."The large mass of the earth means that the changein Momentum of the earth would be does a rocket accelerate in empty spacewhen there is nothing to push against?"The exhaust gases rushing out of the tail of therocket have both mass and velocity and, therefore, Momentum ."The Momentum gained by the rocket in the forwarddirection is equal to the Momentum of the exhaustgases in the opposite direction.

8 "The rocket and the exhaust gases push againsteach other."Newton s third law and InelasticCollisions"Different kinds of collisionsproduce different results.$Sometimes the objects sticktogether.$Sometimes the objects bounceapart.!What is the differencebetween these types ofcollisions?!Is energy conserved as wellas Momentum ?Elastic and InelasticCollisions"A collision in which the objects stick together aftercollision is called a perfectly inelastic collision.$The objects do not bounce at all.$If we know the total Momentum before the collision, we cancalculate the final Momentum and velocity of the now-joinedobjects."For example:$The football players who stay together after colliding.$Coupling railroad railroad cars, all with the same mass of20,000 kg, sit on a track.

9 A fifth car ofidentical mass approaches them with a velocityof 15 m/s. This car collides and couples withthe other four cars. What is the initialmomentum of the system?a)200,000 kg m/sb)300,000 kg m/sc)600,000 kg m/sd)1,200,000 kg m/sm5 = 20,000 kgv5= 15 m/spinitial = m5v5= (20,000 kg)(15 m/s)= 300,000 kg m/sWhat is the velocity of the five coupled carsafter the collision?a)1 m/sb)3 m/sc)5 m/sd)10 m/smtotal = 100,000 kgpfinal= pinitialvfinal= pfinal / mtotal= (300,000 kg m/s)/(100,000 kg)= 3 m/sIs the kinetic energy after the railroad carscollide equal to the original kinetic energy ofcar 5?a)yesb)noc)It = 1/2 m5 v52 = 1/2 (20,000 kg)(15 m/s)2= 2250 kJKEfinal = 1/2 mtotal vfinal2= 1/2 (100,000 kg)(3 m/s)2= 450 kJKEfinal !

10 KEinitialElastic and InelasticCollisions"Energy is not conserved in a perfectly inelasticcollision."If the objects bounce apart instead of stickingtogether, the collision is either elastic or partiallyinelastic.$An elastic collision is one in which no energy is lost.$A partially inelastic collision is one in which some energyis lost, but the objects do not stick together.$The greatest portion of energy is lost in the perfectlyinelastic collision, when the objects stick."A ball bouncing off a floor or wall with no decrease inthe magnitude of its velocity is an elastic collision.$The kinetic energy does not decrease.$No energy has been lost."A ball sticking to the wall is a perfectly inelasticcollision.$The velocity of the ball after the collision is zero.