momentum linear momentum linear momentum impulse impulse conservation of momentum conservation of...

MOMENTUMMOMENTUM Linear MomentumLinear Momentum ImpulseImpulse Conservation of MomentumConservation of Momentum Types of CollisionTypes of Collision 2-D Momentum2-D Momentum

MOMENTUMMOMENTUM How do you chop through cement How do you chop through cement blocks with a bare hand?blocks with a bare hand?Why does falling on a wooden floor Why does falling on a wooden floor hurt less than onto a cement floor?hurt less than onto a cement floor?Why do people in larger vehicles Why do people in larger vehicles end up with fewer injuries in end up with fewer injuries in accidents?accidents?

Linear MomentumLinear Momentum

Measure of how hard it is to stop a Measure of how hard it is to stop a moving object or change the moving object or change the motionmotion’’s directions direction

How a mass moves in a straight pathHow a mass moves in a straight path Momentum = mass times velocityMomentum = mass times velocity p = m vp = m v Units: kg m/s (SI) Units: kg m/s (SI) Vector; same Vector; same direction as velocitydirection as velocity

IMPULSEIMPULSE Directly proportional to force and Directly proportional to force and

timetime Force exerted over timeForce exerted over time Derived from NewtonDerived from Newton’’s 2s 2ndnd Law of Law of

motionmotion F = ma = mF = ma = mv/t = v/t = p/tp/t I = F tI = F t Units: Ns (SI)Units: Ns (SI)

IMPULSEIMPULSE

Area under the curve of the F vs tArea under the curve of the F vs t

IMPULSE-MOMENTUM IMPULSE-MOMENTUM THEOREMTHEOREM

Impulse is the change in momentumImpulse is the change in momentum I = I = ΔΔp = pp = pff - p - p°°

Ft = mvFt = mvff – mv – mv° ° = m (v= m (vf f - v- v°°)) Units : Ns = kg m/sUnits : Ns = kg m/s Momentum is in the same direction Momentum is in the same direction

as Forceas Force

IMPULSE MOMENTUM THEOREMIMPULSE MOMENTUM THEOREM

Bouncing causes a greater change in Bouncing causes a greater change in momentum and impulse.momentum and impulse.

EFFECT OF COLLISION TIME EFFECT OF COLLISION TIME UPON FORCEUPON FORCE

Air bagsAir bags Seat BeltsSeat Belts BoxingBoxing PaddingPadding BaseballBaseball Throwing an egg on the bed sheetThrowing an egg on the bed sheet Car collisions…crumple zonesCar collisions…crumple zones

IMPULSE-MOMENTUM THEOREMIMPULSE-MOMENTUM THEOREM

CONSERVATION OF CONSERVATION OF MOMENTUMMOMENTUM

For a collision in an isolated system, the For a collision in an isolated system, the total momentum before the collision = total momentum before the collision = the total momentum after collision.the total momentum after collision.

If one object gains momentum then the If one object gains momentum then the second object has lost the same amount. second object has lost the same amount.

Momentum is Momentum is ALWAYSALWAYS conserved so conserved so constantconstant

ppbeforebefore = p = pafterafter

Number of momentum equations = Number of momentum equations = number of drawingsnumber of drawings


• p° = pf

• ptruck + pcar = ptruck’ + pcar’

• mtruckvtruck + mcarvcar = mtruckvtruck’ + mcarvcar’


• p° = pf

• pbigfish + plittlefish = ptotal

• mbigfishvbigfish + mlittlefishvlittlefish= mbigfish+littlefishvt

TYPES OF COLLISIONTYPES OF COLLISION

Types of collisionTypes of collision Elastic collisionElastic collision

• Momentum is conservedMomentum is conserved• KE is conservedKE is conserved• Bounce off of each otherBounce off of each other

Inelastic collisionInelastic collision• Momentum is conservedMomentum is conserved• KE is KE is NOTNOT conserved conserved• Damaged or stick togetherDamaged or stick together

TYPES OF COLLISIONTYPES OF COLLISION

Two types of inelastic collisionTwo types of inelastic collision Perfectly inelastic collisionPerfectly inelastic collision

• Objects collide and stick togetherObjects collide and stick together Inelastic collisionInelastic collision

• Objects collide and damage is presentObjects collide and damage is present

LINEAR MOMENTUMLINEAR MOMENTUM Jocko, who has a mass of 60 kg and stands at rest Jocko, who has a mass of 60 kg and stands at rest

on ice, catches a 20 kg ball that is thrown to him on ice, catches a 20 kg ball that is thrown to him at 10 km/h. How fast does Jocko and the ball at 10 km/h. How fast does Jocko and the ball move across the ice? move across the ice?

The momentum before the catch is all in the ball, The momentum before the catch is all in the ball, 20 kg x 10 km/h = 200 kg km/h20 kg x 10 km/h = 200 kg km/h

This is also the momentum after the catch, This is also the momentum after the catch, where the moving mass is 80 kgwhere the moving mass is 80 kg

60 kg for Jocko and 20 kg for the caught ball.60 kg for Jocko and 20 kg for the caught ball.

LINEAR MOMENTUMLINEAR MOMENTUM The roads in Dr. J's neighborhood are slightly more crowded The roads in Dr. J's neighborhood are slightly more crowded

in the mornings these days since he has taken up jogging. in the mornings these days since he has taken up jogging. The crowding comes from the crew that helps Dr. J get The crowding comes from the crew that helps Dr. J get through this physical fit that is overrunning the country. J. through this physical fit that is overrunning the country. J. Jr. marks off a new course each day while Timex mans the Jr. marks off a new course each day while Timex mans the stopwatch. Tripod is there at the end supporting a tray of stopwatch. Tripod is there at the end supporting a tray of cereal, fruit, and bacon on his nose (his idea of a balanced cereal, fruit, and bacon on his nose (his idea of a balanced breakfast). Dr. J does have one quirk - he doesn't use breakfast). Dr. J does have one quirk - he doesn't use shoelaces. As a result, his shoes always look like they are shoelaces. As a result, his shoes always look like they are ready to come apart when he finishes. (Don't most joggers ready to come apart when he finishes. (Don't most joggers finish with their tongues hanging out?) But alas, this is the finish with their tongues hanging out?) But alas, this is the day that Dr. J finally gets tired of it all. His course takes him day that Dr. J finally gets tired of it all. His course takes him through the local park, but a thick fog has decreased through the local park, but a thick fog has decreased visibility. As a result, he runs into a swing made from an old visibility. As a result, he runs into a swing made from an old tire suspended by a long rope. Dr. J experiences a new high tire suspended by a long rope. Dr. J experiences a new high as he and the tire rise 0.3 m above their initial level. If Dr. J as he and the tire rise 0.3 m above their initial level. If Dr. J weighs 750 N and the mass of the tire is 10 kg, how fast weighs 750 N and the mass of the tire is 10 kg, how fast was Dr. J running? was Dr. J running?

Chapter 9: R pg 178Chapter 9: R pg 178

1) A compact car, mass 725 kg, 1) A compact car, mass 725 kg, is moving at +100 km/h.is moving at +100 km/h.a) Find its momentum.a) Find its momentum.b) At what velocity is the b) At what velocity is the momentum of a larger car, mass momentum of a larger car, mass 2175 kg , equal to that of the 2175 kg , equal to that of the smaller car?smaller car?

2.02 x 10 2.02 x 10 44 kgm/s; 33.4 km/h kgm/s; 33.4 km/h


2) A snowmobile has a mass of 2.50 2) A snowmobile has a mass of 2.50 x 10x 1022 kg. A constant force is exerted kg. A constant force is exerted on it for 60.0 s. The snowmobileon it for 60.0 s. The snowmobile’’s s initial velocity is 6.00 m/s and its initial velocity is 6.00 m/s and its final velocity 28.0 m/s. final velocity 28.0 m/s.

a) What is its change in momentum?a) What is its change in momentum? b) What is the magnitude of the b) What is the magnitude of the

force exerted on it?force exerted on it? 5.5 x 10 5.5 x 10 33 kgm/s; 91.7 N kgm/s; 91.7 N


3) The brakes exert a 6.40 x 103) The brakes exert a 6.40 x 1022 N force on N force on a car weighing 15680 N and moving at 20.0 a car weighing 15680 N and moving at 20.0 m/s. The car finally stops. m/s. The car finally stops.

a) What is the cara) What is the car’’s mass?s mass? b) What is the initial momentum?b) What is the initial momentum? c) What is the change in the carc) What is the change in the car’’s s

momentum?momentum? d) How long does the braking force act on d) How long does the braking force act on

the car to bring it to a halt?the car to bring it to a halt? 1.60 x 10 1.60 x 10 33 kg; 3.20 x 10 kg; 3.20 x 10 44 kgm/s; - 3.20 x kgm/s; - 3.20 x

10 10 44 kgm/s; 50.0 s kgm/s; 50.0 s


4) Figure 9-1 shows, as a function of time, 4) Figure 9-1 shows, as a function of time, the force exerted by a ball that collided the force exerted by a ball that collided with a box at rest. The impulse, Fwith a box at rest. The impulse, Ft, is the t, is the area under the curve. area under the curve.

a) Find the impulse given to the box by the a) Find the impulse given to the box by the ball.ball.

b) If the box has a mass of 2.4 kg, what b) If the box has a mass of 2.4 kg, what velocity did it have after the collision.velocity did it have after the collision.

5.25 Ns; 2.2 m/s5.25 Ns; 2.2 m/s

Answers: R pg 193Answers: R pg 193

1)1) 351 kgm/s351 kgm/s2)2) 4.8 kgm/s4.8 kgm/s3)3) 42 m/s42 m/s4)4) 60 Ns; 20.0 m/s60 Ns; 20.0 m/s5)5) 2.04 x 102.04 x 1044 Ns; 300 N Ns; 300 N6)6) 2.35 x 102.35 x 1044 kgm/s; 2.6 x 10 kgm/s; 2.6 x 1044 N N7)7) 260 N260 N8)8) -250 N-250 N9)9) 1100 kg1100 kg10)10) 1300 s1300 s

Momentum in 1-DMomentum in 1-DObjects bounce apartObjects bounce apart

A 0.15 kg blue billiard ball moving at 8.0 m/s A 0.15 kg blue billiard ball moving at 8.0 m/s to the right hits a similar red billiard ball to the right hits a similar red billiard ball at rest. If the blue ball continues to move at rest. If the blue ball continues to move to the right at 2.5 m/s, what is the to the right at 2.5 m/s, what is the velocity of the red ball.velocity of the red ball.

ptotal = ptotalptotal = ptotal’’

ppbb + + pprr = = ppbb ’’ + + pprr ’’

mmbbvvbb + + mmrrvvrr = = mmbbvvbb ’’ + + mmrrvvrr ’’ 0.15 kg(8.0 m/s)0.15 kg(8.0 m/s) + + 0.15 kg(0m/s)0.15 kg(0m/s) = = 0.15 kg(2.5 m/s)0.15 kg(2.5 m/s) + +

0.15kg(v0.15kg(vrr ’’))

vvrr ’’ = 5.5 m/s right = 5.5 m/s right

Momentum in 1-DMomentum in 1-DObjects stick togetherObjects stick togetherTwo balls of clay, a blue one being 2.3 kg Two balls of clay, a blue one being 2.3 kg

and the second red one being 5.6 kg, hit and the second red one being 5.6 kg, hit each other and stick together. If the blue each other and stick together. If the blue one was moving to the right at 12 m/s, one was moving to the right at 12 m/s, and the red was moving at 8.1 m/s to the and the red was moving at 8.1 m/s to the left, what is their final velocity?left, what is their final velocity?

ptotal = ptotalptotal = ptotal’’

ppbb + + pprr = = pptotaltotal

mmbbvvbb + + mmrrvvrr = v = v’’ ( (mmbb + + mmrr)) 2.3 kg(12.0 m/s)2.3 kg(12.0 m/s) + + 5.6 kg(-8.1m/s)5.6 kg(-8.1m/s) = = vv ’’((2.3 kg2.3 kg + + 5.6 kg5.6 kg)) vv ’’ = -2.2 m/s left = -2.2 m/s left

Chapter 9: R pg 185Chapter 9: R pg 185 5) A 0.105 kg hockey puck moving at 48 5) A 0.105 kg hockey puck moving at 48

m/s is caught by a 75 kg goalie at rest. m/s is caught by a 75 kg goalie at rest. With what speed does the goalie slide on With what speed does the goalie slide on the ice?the ice?

0.067 m/s0.067 m/s 6) A 35.0 g bullet strikes a 5.0 kg 6) A 35.0 g bullet strikes a 5.0 kg

stationary wooden block and embeds stationary wooden block and embeds itself in the block. The block and bullet itself in the block. The block and bullet fly off together at 8.6 m/s. What was the fly off together at 8.6 m/s. What was the original velocity of the bullet?original velocity of the bullet?

1200 m/s1200 m/s


7) A 35.0 g bullet moving at 475 m/s strikes a 7) A 35.0 g bullet moving at 475 m/s strikes a 2.5 kg wooden block. The bullet passes through 2.5 kg wooden block. The bullet passes through the block, leaving at 275 m/s. The block was at the block, leaving at 275 m/s. The block was at rest when it was hit. How fast is it moving when rest when it was hit. How fast is it moving when the bullet leaves?the bullet leaves?

2.8 m/s2.8 m/s 8) A 0.50 kg ball traveling at 6.0 m/s collides 8) A 0.50 kg ball traveling at 6.0 m/s collides

head-on with a 1.00 kg ball moving in the head-on with a 1.00 kg ball moving in the opposite direction at a velocity of –12.0 m/s. opposite direction at a velocity of –12.0 m/s. The 0.50 kg ball moves away at –14 m/s after The 0.50 kg ball moves away at –14 m/s after the collision. Find the velocity of the second the collision. Find the velocity of the second ball. ball.

- 2.0 m/s- 2.0 m/s


9) A 4.00 kg model rocket is launched, 9) A 4.00 kg model rocket is launched, shooting 50.0 g of burned fuel from its shooting 50.0 g of burned fuel from its exhaust at an average velocity of 625 m/s. exhaust at an average velocity of 625 m/s. What is the velocity of the rocket after the What is the velocity of the rocket after the fuel has burned?fuel has burned?

7.91 m/s7.91 m/s 10) A thread holds two carts together on a 10) A thread holds two carts together on a

frictionless surface as in the figure. A frictionless surface as in the figure. A compressed spring acts upon the carts. compressed spring acts upon the carts. After the thread is burned, the 1.5 kg cart After the thread is burned, the 1.5 kg cart moves with a velocity of 27 cm/s to the moves with a velocity of 27 cm/s to the left. What is the velocity of the 4.5 kg left. What is the velocity of the 4.5 kg cart? cart?

9.0 cm/s to the right9.0 cm/s to the right


11) Two campers dock a canoe. 11) Two campers dock a canoe. One camper steps onto the dock. One camper steps onto the dock. This camper has a mass of 80.0 kg This camper has a mass of 80.0 kg and moves forward at 4.0 m/s. With and moves forward at 4.0 m/s. With what speed and direction do the what speed and direction do the canoe and the other camper move if canoe and the other camper move if their combined mass is 110 kg?their combined mass is 110 kg?

2.9 m/s in the opposite direction2.9 m/s in the opposite direction


12) A colonial gunner sets up his 225 kg 12) A colonial gunner sets up his 225 kg cannon at the edge of the flat top of a high cannon at the edge of the flat top of a high tower. It shoots a 4.5 kg cannon ball tower. It shoots a 4.5 kg cannon ball horizontally. The ball hits the ground 215 horizontally. The ball hits the ground 215 m from the base of the tower. The cannon m from the base of the tower. The cannon also moves, on frictionless wheels, and also moves, on frictionless wheels, and falls off the back of the tower, landing on falls off the back of the tower, landing on the ground. the ground. a) What is the horizontal distance of the a) What is the horizontal distance of the cannoncannon’’s landing, measured from the base s landing, measured from the base of the back of the tower?of the back of the tower?

b) Why do you not need to know the width b) Why do you not need to know the width of the tower?of the tower?

4.3 m/s; speed remains constant4.3 m/s; speed remains constant

Answer: R pg 193Answer: R pg 193

11)11) 30.0 s30.0 s12) 0.05 s; -4000 N; 410 kg: no; holding a child is 12) 0.05 s; -4000 N; 410 kg: no; holding a child is

dangerous to the childdangerous to the child13) 888 kgm/s; 43.613) 888 kgm/s; 43.6°° SE SE14) 63 kgm/s; 63 Ns; 20000 N; 4000 N14) 63 kgm/s; 63 Ns; 20000 N; 4000 N15) 150 kgm/s; 150 Ns; 3000 N; 5W15) 150 kgm/s; 150 Ns; 3000 N; 5W16) 780 kgm/s; -780 kgm/s; 780 kgm/s; 6.1 m/s16) 780 kgm/s; -780 kgm/s; 780 kgm/s; 6.1 m/s17) 1.0 x 1017) 1.0 x 10-3-3 kgm/s; -6.0 x 10 kgm/s; -6.0 x 10-4-4 kgm/s; 6.0 x 10 kgm/s; 6.0 x 10-4-4

kgm/s; 1.6 x 10kgm/s; 1.6 x 10-3-3 kgm/s; 16 cm/s kgm/s; 16 cm/s18) –100 kgm/s; - 500 kgm/s18) –100 kgm/s; - 500 kgm/s19) 11m/s19) 11m/s20) 340 m/s20) 340 m/s21) 10.6 m/s21) 10.6 m/s

Momentum in 2-DMomentum in 2-D

A 1.20 kg red ball moving to the right at A 1.20 kg red ball moving to the right at 17.1 m/s strikes a stationary 2.31 kg blue 17.1 m/s strikes a stationary 2.31 kg blue ball. If the final velocity of the red ball is ball. If the final velocity of the red ball is 13.5 m/s at 23.013.5 m/s at 23.0°° above the horizontal, above the horizontal, determine the final velocity of the blue determine the final velocity of the blue ball.ball.


Momentum is conservedMomentum is conserved Write a x and y equation.Write a x and y equation. For x:For x:

pprxrx + + ppbxbx = = pprxrx’’ + + ppbxbx’’ For y:For y:

ppryry + + ppbyby = = ppryry’’ + + ppbyby’’ Resolve v in vResolve v in vxx and v and vy y or determine the or determine the

resultantresultant Find angleFind angle Blue ball is traveling at 3.66 m/s at an Blue ball is traveling at 3.66 m/s at an

angle of 48.4angle of 48.4°° below the horizontal below the horizontal


A 1.20 kg red ball moving at 10.0 A 1.20 kg red ball moving at 10.0 m/s strikes a 2.31 kg blue ball m/s strikes a 2.31 kg blue ball moving at 15.0 m/s. If the final moving at 15.0 m/s. If the final velocity of the red ball is 13.5 m/s, velocity of the red ball is 13.5 m/s, determine the final velocity of the determine the final velocity of the blue ball. Make use of the angles blue ball. Make use of the angles drawn in the following diagram.drawn in the following diagram.


Blue ball is moving at 10.5 m/s at an Blue ball is moving at 10.5 m/s at an angle of 23 degree above the angle of 23 degree above the horizonhorizon


13) A 1325 kg car moving north at 13) A 1325 kg car moving north at 27.0 m/s collides with a 2165 kg car 27.0 m/s collides with a 2165 kg car moving east at 17.0 m/s. They stick moving east at 17.0 m/s. They stick together. Draw vector diagram of together. Draw vector diagram of the collision. In what direction and the collision. In what direction and with what speed do they move after with what speed do they move after the collision? the collision?

44.2 44.2 ° NE, 14.7 m/s° NE, 14.7 m/s


14) A 6.0 kg object, A, moving at velocity 3.0 14) A 6.0 kg object, A, moving at velocity 3.0 m/s, collides with 6.0 kg object, B, at rest. After m/s, collides with 6.0 kg object, B, at rest. After the collision, A moves off in a direction 40.0the collision, A moves off in a direction 40.0°° to to the left of its original direction. B moves off in a the left of its original direction. B moves off in a direction 50.0direction 50.0°° to the right of A to the right of A’’s original s original direction? direction?

a) Draw a vector diagram and determine the a) Draw a vector diagram and determine the momenta of object A and object B after the momenta of object A and object B after the collision.collision.

b) What is the velocity of each object after the b) What is the velocity of each object after the collision?collision?

ppaa ’’ = 14 kg m/s; p = 14 kg m/s; pbb ’’ = 12 kgm/s; v = 12 kgm/s; vaa ’’ = 2.3 m/s = 2.3 m/s 4040° to left; ° to left; vvbb ’’ = 2.0 m/s 60 = 2.0 m/s 60° to left ° to left


15) A stationary billiard ball, mass 0.17 15) A stationary billiard ball, mass 0.17 kg, is struck by an identical ball moving kg, is struck by an identical ball moving at 4.0 m/s. After the collision, the second at 4.0 m/s. After the collision, the second ball moves off at 60ball moves off at 60°° to the left of its to the left of its original direction. The stationary ball original direction. The stationary ball moves off at 30moves off at 30°° to the right of the to the right of the second ballsecond ball’’s original direction. What is s original direction. What is the velocity of each ball after the the velocity of each ball after the collision?collision?

vvaa ’’ = 3.5 m/s 30 = 3.5 m/s 30° to right; ° to right; vvbb ’’ = 2.0 m/s = 2.0 m/s 6060° to left ° to left

Answers: R pg 194Answers: R pg 194

22) 5.0 m/s west22) 5.0 m/s west23) 1: -1.5 23) 1: -1.5 24) 10 m/s24) 10 m/s25) 0.041 m/s, yes25) 0.041 m/s, yes26) –0.500 kgm/s; -0.995 kgm/s26) –0.500 kgm/s; -0.995 kgm/s27) 0.22 m/s27) 0.22 m/s28) 3.1 m/s; 1.24 m/s; 1.6 s; 0.99 m28) 3.1 m/s; 1.24 m/s; 1.6 s; 0.99 m29) 3.6 kgm/s 3429) 3.6 kgm/s 34°° NW; 1.8 m/s 34 NW; 1.8 m/s 34°° NW NW30) 5.4 Ns 2230) 5.4 Ns 22°° from original direction from original direction31) 170 kg31) 170 kg34) 1800 N; 3600 N34) 1800 N; 3600 N

LAB WRITE UPLAB WRITE UP Introduction (background, objective, theories Introduction (background, objective, theories

etc.)etc.) MaterialsMaterials Procedure (You must include step by step Procedure (You must include step by step

directions including diagrams. Directions directions including diagrams. Directions should be written so that anyone can follow the should be written so that anyone can follow the steps to rebuild your bridge.)steps to rebuild your bridge.)

Data/CalculationsData/CalculationsMass of the bridge, Mass of the load, Mass ratio Mass of the bridge, Mass of the load, Mass ratio of bridge/loadof bridge/load

Conclusion (errors, theories summarize what Conclusion (errors, theories summarize what happened, what can you do better, etc)happened, what can you do better, etc)

GRADINGGRADING

1.1. Construction: (50 pts)Construction: (50 pts) A) 30 pts: building the bridge without any A) 30 pts: building the bridge without any

violation of the rules and materials above. violation of the rules and materials above. B) 3 pts: lightest bridgeB) 3 pts: lightest bridge

C) 3 pts: holds the heaviest load C) 3 pts: holds the heaviest load D) 5 pts: lowest bridge to mass ratio in D) 5 pts: lowest bridge to mass ratio in

each respective class, the remaining 9 each respective class, the remaining 9 points will be distributed among the other points will be distributed among the other teams in the class based on their ratios.teams in the class based on their ratios.

2.2. Lab Report: (50 pts)Lab Report: (50 pts)

DUE DATESDUE DATES

DUE DATE for the BRIDGE: DUE DATE for the BRIDGE: Friday, Friday, January 12, 2007January 12, 2007

DUE DATE for the LAB REPORTS: DUE DATE for the LAB REPORTS: The The day after you test your bridge!day after you test your bridge!

ALL LONG TERM PROJECTS ARE DUE ON ALL LONG TERM PROJECTS ARE DUE ON THEIR DUE DATES!! A 10 % DEDUCTION THEIR DUE DATES!! A 10 % DEDUCTION FOR EACH DAY WILL BE ASSESSED ON FOR EACH DAY WILL BE ASSESSED ON LATE PROJECTS! THIS INCLUDES THE LATE PROJECTS! THIS INCLUDES THE WEEKENDS! IF YOU PLAN TO BE WEEKENDS! IF YOU PLAN TO BE ABSENT ON THAT DATE, YOU NEED TO ABSENT ON THAT DATE, YOU NEED TO TURN IT IN EARLIER OR HAVE SOMEONE TURN IT IN EARLIER OR HAVE SOMEONE BRING IT INBRING IT IN

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