MomentumMomentumChapter 6Chapter 6

MomentumMomentum► Related to inertia, not the same.Related to inertia, not the same.► Symbol is pSymbol is p► p=mvp=mv► Units of kgm/sUnits of kgm/s

1.1. What is the momentum of a 75kg What is the momentum of a 75kg rock rolling at 2m/s?rock rolling at 2m/s?

ImpulseImpulsevmpFt

►No symbolNo symbol► Impulse has the same unit as momentum.Impulse has the same unit as momentum.► The relationship between impulse and The relationship between impulse and

momentum is called the Impulse-Momentum momentum is called the Impulse-Momentum theorem.theorem.

► ExamplesExamples AirbagsAirbags Nets / CatchingNets / Catching Follow throughFollow through PaddingPadding

Practice ProblemsPractice Problems2.2. A pro exerts a 150N force on a tennis A pro exerts a 150N force on a tennis

ball with the racquet. If the ball has a ball with the racquet. If the ball has a mass of 0.060kg and is in contact with mass of 0.060kg and is in contact with the strings for 0.030s, what is the the strings for 0.030s, what is the change in kinetic energy of the ball change in kinetic energy of the ball when it leaves the racquet? Assume when it leaves the racquet? Assume the ball starts from rest.the ball starts from rest.

3.3. How much more force is needed to How much more force is needed to make a 0.7kg ball initially going at make a 0.7kg ball initially going at 4.2m/s to bounce back from a wall at 4.2m/s to bounce back from a wall at 2m/s in 0.022s than to make it stop?2m/s in 0.022s than to make it stop?

Conservation of MomentumConservation of Momentum► In a closed system, the total momentum In a closed system, the total momentum

does not change.does not change.►Requires that no outside force is present.Requires that no outside force is present.► In equation form, with two objects:In equation form, with two objects:

mm1 1 vv11+ m+ m2 2 vv22= m= m1 1 vv11’+ m’+ m2 2 vv22’’► If there are more than two objects, If there are more than two objects,

simply add the appropriate number of simply add the appropriate number of terms to each side.terms to each side.

Internal vs External forcesInternal vs External forces► Internal forces are those between Internal forces are those between

objects in a systemobjects in a system►External forces are those coming from External forces are those coming from

outside of the systemoutside of the system►Defining the system appropriately is key Defining the system appropriately is key

to observing conservation of momentumto observing conservation of momentum►ExamplesExamples

Gun / BulletGun / Bullet Stepping off a boatStepping off a boat

PracticePractice4.4. Two ducks on roller skates, one travelling at Two ducks on roller skates, one travelling at

6m/s and the other at 2.5m/s, collide head on. 6m/s and the other at 2.5m/s, collide head on. If the first duck has a mass of 7.8kg and a final If the first duck has a mass of 7.8kg and a final speed of 7.1m/s backwards and the second speed of 7.1m/s backwards and the second duck has a final speed of 1.4m/s backwards, duck has a final speed of 1.4m/s backwards, what is the mass of the second duck?what is the mass of the second duck?

5.5. A kid on a skateboard, initially at rest, throws A kid on a skateboard, initially at rest, throws a 20kg cat he was holding at 4.5m/s. If the kid a 20kg cat he was holding at 4.5m/s. If the kid and the skateboard have a combined mass of and the skateboard have a combined mass of 55kg, what is their final velocity?55kg, what is their final velocity?

#6#6► An 83g Pokey is An 83g Pokey is

thrown at Gumby thrown at Gumby with a speed of with a speed of 16m/s. Gumby has a 16m/s. Gumby has a mass of 370g and is mass of 370g and is initially standing still. initially standing still. After the collision, After the collision, the two stick the two stick together. What is together. What is their final speed?their final speed?

Elastic vs Inelastic CollisionsElastic vs Inelastic Collisions► Elastic collisionsElastic collisions

All energy that starts as kinetic ends as kineticAll energy that starts as kinetic ends as kinetic No permanent deformationNo permanent deformation Things don’t stickThings don’t stick Allows a problem to be solved with fewer givens.Allows a problem to be solved with fewer givens.

► Inelastic collisionsInelastic collisions While total energy is conserved, initial kinetic While total energy is conserved, initial kinetic

may switch to other formsmay switch to other forms Frequently, there is deformationFrequently, there is deformation When the book says perfectly inelastic collision, When the book says perfectly inelastic collision,

they mean that the two objects stick together they mean that the two objects stick together after the collision.after the collision.

#7#7►An 800 g billiard ball traveling at 3 An 800 g billiard ball traveling at 3

m/sec collides head-on with a 900 g m/sec collides head-on with a 900 g billiard ball at rest. What is the billiard ball at rest. What is the velocity of the balls after the collision? velocity of the balls after the collision? Assume that the collision is elastic.Assume that the collision is elastic.

The Elastic Collision EquationThe Elastic Collision Equation

'' 2211 vvvv

► Can only be used if the problem explicitly Can only be used if the problem explicitly states that the collision is elastic.states that the collision is elastic.

For 10 pointsFor 10 points► In an elastic collision, both momentum and In an elastic collision, both momentum and

kinetic energy are conserved, therefore:kinetic energy are conserved, therefore:

2222

12112

12222

12112

1

22112211

''

''

vmvmvmvm

vmvmvmvm

► If you start with those two equations and derive the If you start with those two equations and derive the elastic collision equation, you will earn 10 points.elastic collision equation, you will earn 10 points.

Problems #8 & 9Problems #8 & 9► Two pool balls collide elastically. The first, with a Two pool balls collide elastically. The first, with a

mass of 0.37kg, has an initial velocity of 1.5m/s mass of 0.37kg, has an initial velocity of 1.5m/s and a final velocity of -1.85m/s. The second ball and a final velocity of -1.85m/s. The second ball has a final velocity of 0.8m/s. What is:has a final velocity of 0.8m/s. What is: The initial velocity of the second ball?The initial velocity of the second ball? The mass of the second ball?The mass of the second ball?

► A 1.2kg ball traveling at 2.3m/s collides A 1.2kg ball traveling at 2.3m/s collides elastically with a 4.5kg ball traveling at 1.7m/s in elastically with a 4.5kg ball traveling at 1.7m/s in the opposite direction. What are the final the opposite direction. What are the final velocities of the two balls?velocities of the two balls?

#10#10►Two blocks collide elastically. The first Two blocks collide elastically. The first

has a mass of 0.77kg and an initial has a mass of 0.77kg and an initial velocity of 12m/s. The second has a velocity of 12m/s. The second has a mass of 1.2kg and an initial velocity of mass of 1.2kg and an initial velocity of 3m/s in opposite direction. What are 3m/s in opposite direction. What are their final velocities?their final velocities?

Conservation of Both Conservation of Both Momentum and Energy - #11Momentum and Energy - #11

►mm11=2kg=2kg►mm22=3kg=3kg► Both start from restBoth start from rest► v’v’11=1.3m/s=1.3m/s► Initial height of box Initial height of box

1 is 3.1m1 is 3.1m► v’v’22=?=?

►A 200g bullet fired at 350m/s is fired A 200g bullet fired at 350m/s is fired into a block which then slides across into a block which then slides across the floor. If the block and the floor the floor. If the block and the floor have a coefficient of friction equal to have a coefficient of friction equal to 0.57, how far will the block travel 0.57, how far will the block travel before coming to a stop? Assume that before coming to a stop? Assume that the block has a mass of 4kg.the block has a mass of 4kg.

#12#12