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Get the books off the cart and silently read pp 8692. Momentum • All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. • The amount of momentum which an object has is dependent upon two variables: – how much matter is moving? – how fast the matter is moving? • Momentum: "mass in motion” • Equation: p = m x v • Unit: kg*m/s Momentum • Momentum is a vector quantity. Momentum Consider a Mack truck and a roller skate moving down the street at the same speed. The considerably greater mass of the Mack truck gives it a considerably greater momentum. If the Mack truck were at rest, which would have the greater momentum? If an object is at rest, the momentum of that object is “0” because there is no mass in motion. Momentum Questions 1. Determine the momentum of a ... a.) 60 kg halfback moving eastward at 9 m/s. p = 540 kg*m/s, east b.) 1000 kg car moving northward at 20 m/s. p = 20,000 kg*m/s, north c.) 40 kg man moving southward at 2 m/s. p = 80 kg*m/s, south Momentum Questions 2. A car possesses 20,000 units of momentum. What would be the car's new momentum if ... a.) its velocity were doubled p = 40,000 units b.) its mass were doubled p = 40,000 units c.) both its velocity and mass were doubled p = 80,000 units If the boulder and the boy have the same momentum, will the boulder crush the boy? Hint: think about the momentum formula! p = mv DEMONSTRATIONS • Egg and the Blanket • Bowling Ball IMPULSE – A force applied for a period of time which results in a change of momentum. Impulse = change in momentum F∆t = ∆p = ∆(mv) F∆t = mvf - mvi F∆t = m (vf – vi) To change the momentum of a body, a force must be applied to the mass. The longer this force is applied to the mass, the greater effect it will have on changing the momentum. The Wall The Haystack Impulse • A change in momentum in a short time requires a large force. • A change in momentum in a long time requires a small force. Greatest velocity change? Greatest acceleration? Greatest momentum change? Greatest Impulse? Therefore, a larger Force and impulse occurs! Before the space shuttle lands, why does it take giant S curves? To increase landing time and decrease the force of the landing 1. An 80 kg skier loses control and demolishes a snow bank. If it takes the skier 3 seconds to come to rest from an impact speed of 9 m/s, find: (a) the impulse on the man -720 kg*m/s (b) the average force exerted on him by the -240 N snow bank Lab Activity Materials Plot and calculate Impulse dynamic cart Plot Fvs t graph force sensor plot v vs t graph motion sensor Area is equal to impulse change in momentum is equal to impulse F vs t graph • Area under the curve • Constant F 7500 F (N) 10 t (s) 20 • Find Area: =L x W =F x t = 7500 x 20 = 150,000 Ns Impulse from an F vs t graph • Area under the curve • Impulse = ∆F * t 7500 F (N) 10 t (s) 20 • Find Area: = 2(1/2 *b*h) = 2(1/2*10*7500) = 75,000 Ns Lab Activity-Demonstration Collision Lab • Conservation of Momentum • i = f • Purpose: Find relationship of cars before, and after collision • Bouncy a) same mass, one not moving • • b) same mass, both moving c) different. mass one not moving Sticky a) same mass, one not moving b) same mass, both moving c) different. mass one not moving Explosion a) same mass b) different mass Find: m, t1, vi, tf, vf, mvi, mvf for both cars Conclusion: summarize what you have learnt from the lab Plot: i vs. f To change momentum, exert an impulse on it. An outside push or pull is required to change momentum. Hey! It’s the Law! The momentum of a system remains the same unless acted upon by an external force. Can you think of any examples where you think momentum is conserved? Shooting Pool Newton’s Balls Firecracker both sides gain momentum net momenta = zero momentum is conserved Conservation of Momentum What happens to the speed of a fighter aircraft chasing another when it opens fire? What happens to the speed of the pursued aircraft when it returns the fire (from the rear guns)? Bored Astronauts Suppose there are 3 astronauts outside a spaceship. Two of them decide to play catch. All the astronauts weigh the same and are equally strong. The game begins with the first astronaut throwing the second astronaut to the third. How long will the game last? Σ(m1v1) i= Σ(m2v2)f m1v1i + m2v2i = m1v1f + m2v2f Watch out for negatives!!! Tennis and Cannon Activity • Conservation of Momentumexplosion interaction • pi = pf • m1v1i + m2v2i = m1v1f + m2v2f Find the velocity of the rifle. -0.75 m/s Follow-up Question: Would you want to fire a rifle that has a bullet ten times as massive as the rifle? Explain. Three Types of Interactions 1. Bouncy Interaction – two objects collide and bounce off each other. No permanent deforming damage. m1v1i + m2v2i = m1v1f + m2v2f 2. Sticky Interaction – two objects collide and stick together. Final velocities are the same. m1v1i + m2v2i = (m1 + m2)vf 2. Explosion Interaction – two objects explode and move apart from each other. m1v1i + m2v2i = m1v1f + m2v2f The Next Michelle Kwan…? A softball player wishes to determine her mass. She glides without friction along on some ice skates at 1.5 m/s, and throws a ball of 0.8 kg mass at 27 m/s. She then determines that she has slowed to 1.2 m/s. What is her mass? Ans: m = 68 kg Momentum Railroad Problem of Doom A 500 kg railroad car moving at a speed of 30 m/s collides and sticks together with a 1000 kg railroad car initially at rest. What will be the resulting speed of the cars after the collision? Sample Problem A truck and a car collide head on. The speed of the truck was 20 m/s, and that of the car was 30 m/s. The truck has a mass of 5 times that of the car. If they stick together after the collision, how fast are they moving, as a unit, just after the collision? The Power of Cheese Salami! A 30 g bullet traveling at 300 m/s rips through a 0.65 kg salami and exits at 236 m/s. How fast does the salami move after the bullet leaves? More Momentum If a Mack truck and a Volkswagen have a head-on collision, which vehicle will experience the greatest force of impact? The greatest impulse? The greatest change in momentum? The greatest acceleration? Find the impulse for the following graph. 60 50 40 F (N) 30 20 10 2 4 6 8 10 12 14 16 18 20 22 t (s) Conservation of Momentum A golf ball is moving with 1 kgm/s and bounces of a bowling ball initially at rest; after the collision, what is the momentum of the bowling ball? Conservation of Momentum Farmer Joe shoots a bullet of mass 4 g from a gun of mass 7 kg with a speed of 1420 m/s at his collection of coke cans. What is the speed with which the gun recoils? Answer: V = -0.811 m/s Net ∆mv (before collision) = Net ∆mv (after collision) The total momentum before a collision is equal to the total momentum after a collision – Conservation of Momentum Inelastic Collision: If the mass of each railroad car is the same, determine the velocity after the collision. m/s m/s 5 m/s You guessed it… MOMENTUM Would a head-on collision between two cars be more damaging to the occupants if the cars stick together or if the cars rebound upon impact? inelastic elastic Sailing, Sailing.. Gilligan’s super escape ice sail craft is stalled on a frozen lake on a windless day. His only piece of auxiliary equipment is a large fan that blows air into the sail. If all the wind produced by the fan strikes and bounces backward from the sail, the craft will move: • • • Backward Forward Not at all Review You jump off a table. When you land on the floor you bend your knees in order to… a.) Decrease the impulse on you by the floor b.) Decrease the force applied to you by the floor c.) Increase the time it takes to stop d.) Both a and b e.) Both b and c f. ) All of the above Review A Mack truck and a Volkswagen have a head-on collision. Which vehicle will experience the greatest force of impact? a.) Mack truck b.) Volkswagon c.) impossible to figure out d.) same Find the impulse for the following graph. 60 50 40 F (N) 30 20 10 2 4 6 8 10 12 14 16 18 20 22 t (s)