MOMENTUM AND IMPULSE Chapter 8

Linear Momentum, p Momentum is a measure of how hard it is to stop or turn a moving object. It is moving inertia. (single particle) (system of particles) Units of momentum: kg(m/s) or (N)(S) Since velocity, v, is a vector, momentum, p, is a vector. p is in the same direction as v

A B Linear Momentum, p Which car has more momentum? A or B The faster car, A.

A B Linear Momentum, p Which car has more momentum? A or B The more massive vehicle, B.

Newton’s 2nd Law The rate of change of momentum of a body is equal to the net force applied to it.

Example - Washing a car: momentum change and force Example - Washing a car: momentum change and force. Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s and is aimed at the side of a car, which stops it (that is we ignore any splashing back). What is the force exerted by the water on the car? In each second, 1.5 kg of water leaves hose and has v=20 m/s. By Newton’s 3rd law, force exerted by water on the car is +30 N

Example - Washing a car: momentum change and force Example - Washing a car: momentum change and force. What if the water splashes back from the car? Would the force on the car be more or less? In each second, 1.5 kg of water leaves hose and has v=20 m/s. If the water splashes back Change in momentum would be greater and so the force should be greater. The car exerts a force on the water not only to stop it, but an extra force to give it momentum in the opposite direction

vi vf v Fnet Newtons 2nd Law Slope ~ Fnet Impulse, I area = I=Dp Contact begins Contact ends area = I=Dp

Impulse-Momentum Theorem Impulse is the product of a net external force and time which results in a change in momentum Units are N s or kg m/s Impulsive forces are generally of high magnitude and short duration.

Impulse-Momentum Theorem “riding the punch” Impulse on a graph: area under the curve

DO NOW – Force to stop a car: momentum change, force and impulse DO NOW – Force to stop a car: momentum change, force and impulse. A 2200 kg vehicle traveling at 26 m/s can be stopped in 21 s by gently applying the brakes. It can be stopped in 3.8 s if the driver slams on the brakes, or in 0.22s if it hits a concrete wall. What impulse is exerted on the vehicle in eachof these stops? What net force is exerted in each case? For all three

DO NOW – Force to stop a car: momentum change, force and impulse DO NOW – Force to stop a car: momentum change, force and impulse. What net force is exerted on the vehicle in each of these stops? STOP BY: Gentle brake 0.12 Gs Slam brake 0.68 Gs Concrete wall 11.8 Gs 12

“Newtons 2nd law of motion”: Football kick, Newtons laws and Impulse Collision simulation http://www.walter-fendt.de/ph14e/collision.htm “Newtons 2nd law of motion”: Football kick, Newtons laws and Impulse http://www.nbclearn.com/portal/site/learn/nfl/cuecard/50974/ http://www.youtube.com/watch?v=yUpiV2I_IRI&feature=related car crash 22 min 13

Problem: This force acts on a 1. 2kg object moving at 120. 0m/s Problem: This force acts on a 1.2kg object moving at 120.0m/s. The direction of force is aligned with velocity. What is the new velocity of the object? vf = 328 m/s 14

Problem: This force acts on a 1. 2kg object moving at 120. 0m/s Problem: This force acts on a 1.2kg object moving at 120.0m/s. The direction of force is aligned with velocity. What is the new velocity of the object? vf = -88.3 m/s 15

Impulse Impulse

Problem: A 150-g baseball moving at 40 m/s 15o below the horizontal is struck by a bat. It leaves the bat at 55 m/s 35o above the horizontal. What is the impulse exerted by the bat on the ball? If the collision took 2.3 ms, what was the average force of the bat on the ball? vf = 55 35o 15o vi = 40

Impulse-Momentum Theorem Work-Energy Theorem Impulse on a graph: area under the F-t curve Work on a graph: area under the F-x curve VECTOR SCALAR

Problem: a tennis player receives a shot with the ball (0 Problem: a tennis player receives a shot with the ball (0.6 kg) travelling horizontally at 50.0 m/s and returns the shot with the ball travelling horizontally at 40.0m/s in the opposite direction. A) what is the impulse delivered to the ball by the racket? B) what work does the racquet do on the ball? vi=50 vf=40

A ball is dropped to the ground DEMO 1: A ball is dropped to the ground Forces acting on the ball as it is falling Is there a net force? mv1 Is the momentum of the ball conserved (constant) as it falls? FG Dp ≠ 0 mv2 Describe a system in which the total momentum is conserved.

A ball is dropped to the ground DEMO 1: A ball is dropped to the ground A system in which the total momentum is conserved – BALL + EARTH FG,ball,earth FG,earth,ball Dp = 0 In this system of the Ball + Earth, there are NO EXTERNAL FORCES. Only forces are those between the objects in the system

Conservation of Momentum 2 m2v2 1 m1v1 F12 F21 1 2 1 m1v’1 2 m2v’2 momentum before = momentum after as long as NO EXTERNAL FORCE ACTS

Newtons 2nd Law 1 m1v1 2 m2v2 m2v’2 m1v’1 F21 F12 BALL 1 BALL 2 Newtons 3rd Law Conservation of Momentum

Conservation of Momentum can be extended to include any number of interacting bodies Total momentum of system (vector sum of momenta of all objects) If there are NO external forces LAW OF CONSERVATION OF MOMENTUM – The total momentum of an isolated system of bodies remains constant

LAW OF CONSERVATION OF MOMENTUM The total momentum of an isolated system of bodies remains constant. A system is a set of objects that interacts with each other. An isolated system in one in which the only forces present are those between the objects of the system and those will be zero because of Newtons 3rd law. ( ) Momentum in space

Example. Railroad cars collide: momentum conserved Example. Railroad cars collide: momentum conserved. A 10,000 kg railroad car traveling at a speed of 24 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward? v1 = 24 v2= 0 v’

DO NOW Rifle recoil. Calculate the recoil velocity of a 5 DO NOW Rifle recoil. Calculate the recoil velocity of a 5.0 kg rifle that shoots a 0.050 kg bullet at a speed of 120 m/s. before shooting v’R after shooting v’B

Collisions In all collisions where ΣFext = 0, momentum is conserved Elastic Collisions No deformation occurs. Kinetic energy is also conserved. Inelastic Collisions: Deformation occurs. Kinetic energy is lost. Perfectly Inelastic Collisions Objects stick together, kinetic energy is lost. Explosions Reverse of perfectly inelastic collision, kinetic energy is gained.

Inelastic Collisions: http://www.science-animations.com/support-files/collisions.swf

Example. Railroad cars, inelastic collision Example. Railroad cars, inelastic collision. A railroad car of mass 3000 kg, moving at 20 m/s eastward, strikes head-on a railroad car of mass 1000 kg that is moving at 20 m/s westward. The railroad cars stick together after the impact. What is the magnitude and direction of the velocity of the combined mass after the collision? Prove that the collision is inelastic by KE analysis. v1 = 20 v2 = 20 v’

v1 = 20 v2 = 20 v’ Example. Railroad cars, inelastic collision. KE is reduced so collision is inelastic

Bouncing ball

Example. Old cannons were built on wheeled carts, both to facilitate moving the cannon and to allow the cannon to recoil when fired. When a 150 kg cannon and cart recoils at 1.5 m/s, at what velocity would a 10 kg cannonball leave the cannon? v’c = 1.5 v’B = ?

Example. Pool or billiards. A billiard ball of mass 0 Example. Pool or billiards. A billiard ball of mass 0.5 kg moving with a velocity of 3 m/s collides head on in an elastic collision with a second ball of equal mass at rest (v2 = 0). What are the speeds of the 2 balls after the collision? v2= 0 v1 = 3

v2= 0 v1 = 3 Example. Pool or billiards. from conservation of momentum: Since collision is elastic, kinetic energy is also conserved:

Truck Collision In a head-on collision: Which truck will experience the greatest force? Which truck will experience the greatest impulse? Which truck will experience the greatest change in momentum? Which truck will experience the greatest change in velocity? Which truck will experience the greatest acceleration? Which truck would you rather be in during the collision?

Truck Collision same same same In a head-on collision: Which truck would you rather be in during the collision?

Example. A nuclear collision. A proton of mass 1 Example. A nuclear collision. A proton of mass 1.01 u (unified atomic mass units) traveling with a speed of 3.60 x 104 m/s has an elastic, head-on collision with a Helium (He) nucleus (mHe = 4.00 u) at initially rest. What are the velocities of the proton and Helium nucleus after the collision? vP = 3.6 x 104 vHe= 0

vP = 3.6 x 104 vHe= 0 Example. A nuclear collision. from conservation of momentum: Since collision is elastic, kinetic energy is also conserved:

Example. A nuclear collision. A proton of mass 1 Example. A nuclear collision. A proton of mass 1.01 u (unified atomic mass units) traveling with a speed of 3.60 x 104 m/s has an elastic, head-on collision with a Helium (He) nucleus (mHe = 4.00 u) at initially rest. What are the velocities of the proton and Helium nucleus after the collision? vP = 3.6 x 104 vHe= 0

Example. Propulsion in space: explosion.

Example. Propulsion in space: explosion Example. Propulsion in space: explosion. An astronaut at rest in space fires a thruster pistol that expels 35 g of hot gas at 875 m/s. The combined mass of astronaut and pistol is 84 kg. How fast and in what direction is the astronaut moving after firing the pistol? v’A = ? v’G = 875

For 2-dimensional collisions Conservation of Momentum can also be applied in 2 or 3 dimensions For 2-dimensional collisions Use conservation of momentum independently for x and y dimensions. You must resolve your momentum vectors into x and y components when working the problem

2 Dimensional Problem: A pool player hits the 14- ball in the x-direction at 0.80 m/s. The 14-ball knocks strikes the 8-ball, initially at rest, which moves at a speed of 0.30 m/s at an angle of 35o angle below the x-axis. Determine the angle of deflection of the 14-ball. v’1 v1=0.8 q1 q2=350 q1= 17.20 v’2=0.3 v’1= 0.58 m/s

The diagram depicts the before- and after-collision speeds of a car that undergoes a head-on-collision with a wall. In Case A, the car bounces off the wall. In Case B, the car crumples up and sticks to the wall. a. In which case is the change in velocity the greatest? b. In which case is the change in momentum the greatest? c. In which case is the impulse the greatest? d. In which case is the force that acts upon the car the greatest (assume same contact times)?

Mythbusters giant Newtons cradle http://www.youtube.com/watch?feature=endscreen&v=OuA-znVMY3I&NR=1 Collision simulation http://www.walter-fendt.de/ph14e/collision.htm “Newtons 2nd law of motion”: Football kick, Newtons laws and Impulse “Newtons 3rd law of motion”: Football kick, conservation of momentum and collisions http://www.nbclearn.com/portal/site/learn/nfl/cuecard/50974/ http://www.youtube.com/watch?v=yUpiV2I_IRI&feature=related car crash 22 min interactive quiz