Momentum And Collision - MR. D PHYSICS
Momentum andCollisionChapter 6
Momentum andImpulse
Linear Momentum Momentum is defined as mass timesvelocity. Momentum is represented by thesymbol p, and is a vector quantity.p mvmomentum mass velocity
Momentum Momentum has the dimensions of massx length/time (kg x m/s) When do you use the word momentum? “gaining momentum” or “picking upspeed” Coasting on a bike going down a hill You accelerate and velocity increaseswith time.
Bowling ball or basketball? Picture two lanes at a bowling alley. One with a bowling ball the other with abasketball going at the same speed. Which will exert more force on the pins? Why? More momentum
Example A 2250 kg pickup truck has a velocity of25 m/s to the east. What is themomentum of the truck?
Solution p mv (2250 kg)(25 m/s east) 5.6 x 104 kg x m/s to the east
Your Turn A deer with a mass of 146 kg is runninghead-on toward you at a speed of 17m/s. You are going north find themomentum of the deer. A 21 kg child on a 5.9 kg bike is ridingwith a velocity of 4.5 m/s to thenorthwest. What is the total momentum of the childand the bike together?What is the momentum of the child?What is the momentum of the bike?
Linear Momentum Impulse The product of the force and the time over whichthe force acts on an object is called impulse. The impulse-momentum theorem states thatwhen a net force is applied to an object over acertain time interval, the force will cause a changein the object’s momentum.F t p mvf – mviforce time interval change in momentum
Linear Momentum Stopping times and distances depend onthe impulse-momentum theorem. Force is reduced when the time intervalof an impact is increased.
Example A 1400 kg car moving westward with avelocity of 15 m/s collides with a utilitypole and is brought to rest in 0.30 s.Find the force exerted on the car duringthe collision.
Solution F t p mvf – mvi F mvf – mvi t F (1400kg)(0 m/s) – (1400 kg)(-15 m/s)0.30 s F 7.0 x 104 N to the east
Your Turn II A 0.50 kg football is thrown with a velocity of 15m/s to the right. A stationary receiver catchesthe ball and brings it to rest in 0.020 s. What isthe force exerted on the ball by the receiver? An 82 kg man drops from rest on a diving board3.0 m above the surface of the water andcomes to rest 0.55 s after reacing the water.What is the net force on the diver as he isbrought to rest? A 0.40 kg soccer ball approaches a playerhorizontally with a velocity of 18 m/s to thenorth. The player strikes the ball and cause itto move in the opposite direction with a velocityof 22 m/s. What is the impulse delivered to theball by the player?
Impulse-Momentum Theorem Stopping times and distances depend onthe impulse-momentum theorem. Highway safety engineers use theimpulse-momentum theorem todetermine stopping distances and safefollowing distances for cars and trucks.
Example A 2240 kg car traveling to the west slowsdown uniformly from 20.0 m/s to 5.00m/s. How long does it take the car todecelerate if the force on the car is 8410N to the east? How far does the cartravel during deceleration?
Solution Givens: Mass 2240 kg vi 20.0 m/s to the west - 20.0 m/s vf 5.00 m/s to the west - 5.00 m/s F 8410 N to the east Equation to use: F t p t p / F t mvf – mvi / F
Plug and Chug t mvf – mvi / F t (2240 kg)(-5.00 m/s)-(2240 kg)(-20.0 m/s)8410 kg x m/s2 t 4.00 s x ½ (vi vf) t x ½ (-20.0 m/s – 5.00 m/s)(4.00 s) x - 50.0 m 50.0 m to the west
Your Turn III A 2500 kg car traveling to the north isslowed down uniformly from an initialvelocity of 20.0 m/s by a 6250 N brakingforce acting opposite the car’s motion.Use the impulse-momentum theorem toanswer the following questions: What is the car’s velocity after 2.50 s?How far does the car move during 2.50 s?How long does it take the car to come to acomplete stop?
Impulse-Momentum Theorem Force is reduced when the time interval of animpact is increased. Examples Nets or giant air mattresses used to catch people. Page 203 in your book shows an image of a girlbeing tossed in the ir and caught in a blanket. The blanket “gives way” and extends the time ofcollision to change the momentum over alonger period of time. Consider the egg on the next slide and explaingwhat is happening
Impulse-Momentum Theorem
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Conservation ofMomentum
Momentum is Conserved So far we only have considered the momentum of only one object at a time.Now we will look at two or more objectsinteracting with each other.Picture this. . .You are playing pool. You strike the cue ball ithits the 8 ball. The 8 ball had no momentumbefore they collided.During the collision the cue ball losesmomentum and the 8 ball gains momentum.The momentum the cue ball loses is the sameamount that the 8 ball gained.
Momentum is Conserved The Law of Conservation ofMomentum:The total momentum of all objectsinteracting with one another remainsconstant regardless of the nature of theforces between the objects.m1v1,i m2v2,i m1v1,f m2v2,ftotal initial momentum total finalmomentum
Momentum is Conserved The total momentum of all objectsinteracting with one another remainsconstant regardless of the nature of theforces between the objects. Go back to the pool table example. Thecue ball and the 8 ball do not have aconstant momentum, but the totalmomentum is constant.
Momentum is Conserved Consider objects pushing away fromeach other. You jump up. You push of the Earth.Take you mv. Let’s say 60 kg m/s upward. Thatmeans that the Earth must have acorresponding momentum of 60 kg m/sdownward. However, the has anenormous mass which means its velocityis very small.
Momentum is Conserved Picture this . . . Two people on skates facing oneanother. They push away from oneanother. Initially, they are both at restwith a momentum of 0. When the pushaway, they move in opposite directionswith equal but opposite momentum, sothat the total momentum is 0.
Example A 76 kg boater, initially at rest in astationary 45 kg boat, steps out of theboat and onto the dock. If the boatermoves out of the boat with a velocity of2.5 m/s to the right, what is the finalvelocity of the boat?
Solution Given:m1 76 kg m2 45 kgv1,i 0v2,i 0v1,f 2.5 m/s to the rightUnknown:v2,f ?
Solution Choose an equation or situation:Because the total momentum of anisolated system remains constant, thetotal initial momentum of the boater andthe boat will be equal to the total finalmomentum of the boater and the boat.m1v1,i m2v2,i m1v1,f m2v2,f
Solution Because the boater and the boat are initially atrest, the total initial momentum of the system isequal to zero. Therefore, the final momentum ofthe system must also be equal to zero.m1v1,f m2v2,f 0Rearrange the equation to solve for the final velocityof the boat.m2 v 2,f – m1v1,fv 2,f m1 – v1,f m2
Solution Substitute the values into theequation and solve:v 2,fv 2,f 76 kg – 2.5 m/s to the right 45 kg –4.2 m/s to the right
Solution The negative sign for v2,f indicates thatthe boat is moving to the left, in thedirection opposite the motion of theboater. Therefore,v2,f 4.2 m/s to the left
Your Turn IV A 63.0 kg astronaut is on a space walk whenthe tether line to the shuttle breaks. Theastronaut is able to throw a spare 10.0 kgoxygen tank in a direction away from the shuttlewith a speed of 12.0 m/s, propelling theastronaut back to the shuttle. Assuming that theastronaut starts from rest with respect to theshuttle, find the astronaut’s final speed withrespect to the shuttle after the tank is thrown. An 85.0 kg fisherman jumps from a dock into a135.0 kg rowboat at rest on the west side of thedock. If the velocity of the fisherman is 4.30m/s to the west as he leaves the dock, what isthe final velocity of the fisherman and the boat?
Your Turn IV Each croquet ball in a set has a mass of 0.50kg. The green ball, traveling at 12.0 m/s,strikes the red ball, which is at rest. Assumingthat the croquet ball slide on a frictionlesssurface and all collisions are head-on, find thefinal speed of the red ball in each of thefollowing situations: The green ball stops moving after it strikes the redball.The green ball continues moving after the collisionat 2.4 m/s in the same direction.
Momentum is Conserved Newton’s third law leadsto conservation ofmomentum During the collision, theforce exerted on eachbumper car causes achange in momentum foreach car. The total momentum isthe same before and afterthe collision.
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Elastic and InelasticCollisions
Collisions Perfectly inelastic collision A collision in which two objects stick together aftercolliding and move together as one mass is calleda perfectly inelastic collision. Example: The collision between two footballplayers during a tackle. Conservation of momentum for a perfectlyinelastic collision:m1v1,i m2v2,i (m1 m2)vftotal initial momentum total final momentum
Example A 1850 kg luxury sedan stopped at a traffic lightis struck from behind by a compact car with amass of 975 kg. The two cars becomeentangled as a result of the collision. If thecompact car was moving with a velocity of 22.0m/s to the north before the collision, what is thevelocity of the entangled mass after thecollision?Given: m1 1850 kgv1,i 0 m/sUnknown: vfm2 975 kgv2,i 22.0 m/s north
Solution Choose your equation:m1v1,i m2v2,i (m1 m2)vfvf m1v1,i m2v2,i(m1 m2)vf (1850 kg)(0 m/s) (975 kg)(22.0 m/s)(1850 kg 975 kg)vf 7.59 m/s north
Your Turn V A 1500 kg car traveling at 15.0 m/s to the south collideswith a 4500 kg truck that is initially at rest at a stoplight.The car and truck stick together and move together afterthe collision. What is the final velocity of the two-vehiclemass? You are shopping at Publix and toss a 9.0 kg bag of riceinto a stationary 18.0 kg shopping cart. The bag hits thecart with a horizontal speed of 5.5 m/s toward the front ofthe cart. What is the final speed of the cart and the bag? A 47.4 kg student runs down the sidewalk and jumps witha horizontal velocity of of 4.20 m/s onto a stationaryskateboard. The student and the skateboard move downthe sidewalk with a speed of 3.95 m/s. Find the following: The mass of the skatboardHow fast the student would have to jump to have afinal speed of 5.00 m/s
Kinetic Energy in InelasticCollisions In an inelastic collision the total kinetic energydoes not remain constant when the objectscollide and stick together. Some energy is converted into sound energyand internal energy as the objects deformduring the collision. Elastic in physics refers to a material that whenwork is done to deform the material during acollision the same amount of work is done toreturn the material to its original shape. Inelastic material does not return to its originalshape and therefore some energy is convertedto sound or heat.
Example Two clay balls collide head-on in aperfectly inelastic collision. The first ballhas a mass of 0.500 kg and an initialvelocity of 4.00 m/s to the right. Thesecond ball has a mass of 0.250 kg andan initial velocity of 3.00 m/s to the left.What is the decrease in kinetic energyduring the collision?
Solution Given:m1 0.500 kgv1,i 4.00 m/s to the rightv1,i 4.00 m/sv2,i 3.00 m/s to the leftv2,i –3.00 m/sUnknown: KE ?m2 0.250 kg
Solution The change in kinetic energy is simplythe initial kinetic energy subtracted fromthe final kinetic energy. KE KEi – KEfDetermine both the initial and final kineticenergy.1122Initial: KEi KE1,i KE2,i m1v1,i m2v 2,i2212Final: KEf KE1,f KE2,f m1 m2 v f2
Solution Use the equation for a perfectly inelasticcollision to calculate the final velocity.vf m1v1,i m2v 2,im1 m2(0.500 kg)(4.00 m/s) (0.250 kg)(–3.00 m/s)vf 0.500 kg 0.250 kgv f 1.67 m/s to the right
Solution Next calculate the initial and final kineticenergy.11220.500kg4.00m/s 0.250kg–3.00m/s 5.12 J2212KEf 0.500 kg 0.250 kg 1.67 m/s 1.05 J2KEi
Solution Finally, calculate the change in kineticenergy. KE KEf – KEi 1.05 J – 5.12 J KE –4.07 J
Your Turn VI A 0.25 kg arrow with a velocity of 12 m/s to the weststrikes and pierces the center of a 6.8 kg target. What isthe final velocity of the combined mass? What is thedecrease in kinetic energy during the collision? A clay ball with a mass of 0.35 kg hits another 0.35 kg ballat rest, and the two stick together. The first ball has aninitial speed of 4.2 m/s. What is the final speed of bothballs? Calculate the decrease in kinetic energy thatoccurs during the collision. A 56 kg ice skater traveling at 4.0 m/s to the north meetsand joins hands with a 65 kg skater traveling at 12.0 m/sin the opposite direction. Without rotating the two skaterscontinue skating together. What is the final velocity of thetwo skaters and what is the decrease in kinetic energydurning the collision?
Elastic Collisions A collision in which the total momentum andthe total kinetic energy are conserved iscalled an elastic collision. Elastic means that after a collision the objectsremain separated. Two objects collide and return to their originalshapes with no loss of total kinetic energy.After the collision the two objects moveseparately. Both the total momentum and total kineticenergy are conserved.
Real Collisions Most collisions are not perfectly inelastic(they don’t stick together and move asone) Most collisions are not elastic. Even nearly elastic collisions result insome decrease of kinetic energy. A football deforms when kickedA sound is produced (sound signifies adecrease in kinetic energy)
For all intensive purposes We will consider all collisions in whichobjects do not stick together to be elasticcollisions. Therefore, total momentum and totalkinetic energy will stay the same beforeand after the collision.
Kinetic Energy is Conserved inElastic CollisionsPAPBAB PA F tA PB -F tBPAPBAB
Elastic Collisions The total momentum is alwaysconstant throughout the collision. Inaddition, if the collision is perfectlyelastic, the value of the total kineticenergy after the collision is equal tothe value before the collision.m1v1,i m2v 2,i m1v1,f m2v 2,f11112222m1v1,i m2v 2,i m1v1,f m2v 2,f2222
Example A 0.015 kg marble moving to the right at 0.225m/s makes an elastic head-on collision with a0.030 kg shooter marble moving to the left at0.180 m/s. After the collision, the smallermarble moves to the left at 0.315 m/s. Assumethat neither marble rotates before or after thecollision and that both marbles are moving on africtionless surface. What is the velocity of the0.030 kg marble after the collision?
SolutionGiven: m1 0.015 kg m2 0.030 kgv1,i 0.225 m/s to the right, v1,i 0.225m/sv2,i 0.180 m/s to the left, v2,i –0.180m/sv1,f 0.315 m/s to the left, v1,i –0.315m/sUnknown:v2,f ?
Solutionm2 v2,f m1v1i, m2 v2,i – m1v1,fv2,f m1v1,i m2 v2,i – m1v1,fm2v 2,f0.015 kg 0.225 m/s 0.030 kg –0.180 m/s – 0.015 kg –0.315 m/s v 2,f3.4 10 v 2,f0.030 kg–3 kg m/s –5.4 10 –3 kg m/s – –4.7 10 –3 kg m/s2.7 10 –3 kg m/s 3.0 10 –2 kgv2,f 9.0 10 –2 m/s to the right0.030 kg
Solution1111222m1v1,i m2v 2,i m1v1,f m2v 2,2 f22221122KEi 0.015 kg 0.225 m/s 0.030 kg –0.180 m/s 22 8.7 10 –4 kg m2 /s2 8.7 10 –4 J1122KEf 0.015 kg 0.315 m/s 0.030 kg 0.090 m/s 22 8.7 10 –4 kg m2 /s2 8.7 10 –4 J
Your Turn VII Two billiard balls, each with a mass of 0.35 kg, strike eachother head-on. One ball is initially moving left at 4.1 m/sand ends up moving right at 3.5 m/s. The second ball isinitially moving to the right at 3.5 m/s. Assume thatneither ball rotates before or after the collision and thatboth balls are moving on a frictionless surface. Predictthe final velocity of the second ball. A 0.015 kg marble sliding to the right at 12.5 m/s on africtionless surface makes an elastic head-on collisionwith a 0.015 kg marble moving to the left at 18.0 m/s.After the collision, the first marble moves to the left at 18.0m/s. Find the velocity of the second marble after thecollision. Verify your answer by calculating the totalkinetic energy before and after the collision.
Your Turn VII (continued) A 16.0 kg canoe moving to the left at 12.5m/s makes an elastic head-on collision witha 14.0 kg raft moving to the right at 16.0m/s. After the collision, the raft moves tothe left at 14.4 m/s. Disregard and effects ofthe water. Find the velocity of the canoeafter the collision. Calculate the total kineticenergy before and after the collision.
Types of Collisions
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Linear Momentum Impulse The product of the force and the time over which the force acts on an object is called impulse. The impulse-momentum theorem states that when a net force is applied to an object over a certain time interval, the force will cause a change in the object's momentum. F t p mv f - mv i
CHAPTER 3 MOMENTUM AND IMPULSE prepared by Yew Sze Ling@Fiona, KML 2 3.1 Momentum and Impulse Momentum The linear momentum (or "momentum" for short) of an object is defined as the product of its mass and its velocity. p mv & & SI unit of momentum: kgms-1 or Ns Momentum is vector quantity that has the same direction as the velocity.
4. Impulse - Momentum 3. This area is called Impulse F.dt r. 5/14/2008 Momentum - 1 25 Force, Time and Momentum The area under the force-time graph equals the change in linear momentum. If the LHS of this . Collisions - Linear Momentum is always conserved Is the collision force gravity or springs? - If YES, then Kinetic .
1. Impulse and Momentum: You should understand impulse and linear momentum so you can: a. Relate mass, velocity, and linear momentum for a moving body, and calculate the total linear momentum of a system of bodies. Just use the good old momentum equation. b. Relate impulse to the change in linear momentum and the average force acting on a body.
momentum is kg·m/s. Linear Momentum Linear momentum is defined as the product of a system's mass multiplied by its velocity: p mv. (8.2) Example 8.1Calculating Momentum: A Football Player and a Football (a) Calculate the momentum of a 110-kg football player running at 8.00 m/s. (b) Compare the player's momentum with the
Momentum (p mv)is a vector, so it always depends on direction. Sometimes momentum is if velocity is in the direction and sometimes momentum is if the velocity is in the direction. Two balls with the same mass and speed have the same kinetic energy but opposite momentum. Momentum vs. Kinetic Energy A B Kinetic Energy Momentum
Momentum ANSWER KEY AP Review 1/29/2018 Momentum-1 Bertrand Momentum How hard it is to stop a moving object. Related to both mass and velocity. For one particle p mv For a system of multiple particles P p i m i v Units: N s or kg m/s Momentum is a vector! Problem: Momentum (1998) 43. The magnitude of the momentum of the
momentum), it is optimal for investors to hold less or may short the momentum asset and hence sufier less or even beneflt from momentum crashes. Key words: Portfolio selection, momentum crashes, dynamic optimal momentum strategy. JEL Classiflcation: C32, G11 Date: March 11, 2016. 1
Momentum: Unit 1 Notes Level 1: Introduction to Momentum The Definition Momentum is a word we sometime use in everyday language. When we say someone has a lot of momentum, it means they are on a roll, difficult to stop, really moving forward. In physics, momentum means "mass in motion". The more mass an object has, the more momentum it has.
