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Impulse; Conservation of Momentum Intro: Which Train has more momentum? a) While stopped? b) When moving at the same velocity? • Momentum (ρ)- (inertia in motion) the product of mass and velocity of an object • Momentum equation ρ = mv Momentum = mass x velocity • The SI unit for momentum is kg·m/s • Change in momentum equation Δρ = mΔv or Δρ = m(vf – vo) • Ex A: An airplane is launched from an aircraft carrier. The plane is going from south to north. If the airplanes launch velocity is 7.0 x 101 m/s in the direction the ship was sailing and its mass is 2.5 x 104 kg, what is its momentum immediately after the launch (include direction since momentum is a vector). • Ex A: An airplane is launched from an aircraft carrier. The plane is going from south to north. If the airplanes launch velocity is 7.0 x 101 m/s in the direction the ship was sailing and its mass is 2.5 x 104 kg, what is its momentum immediately after the launch (include direction since momentum is a vector). Ex. B: A 0.060kg tennis ball traveling at 10.0 m/s is returned in the opposite direction with a speed of 36.0 m/s. What is the change in momentum of the ball? Ex. B: A 0.060kg tennis ball traveling at 10.0 m/s is returned in the opposite direction with a speed of 36.0 m/s. What is the change in momentum of the ball? • A moving object can have a large momentum if it has a large mass, a lot of speed, or both. A truck traveling the same velocity of a truck would have less velocity • Impulse (J) is a force applied over a period of time • The SI unit for impulse is N·s Impulse = FΔt The man is applying an impulse to the car Ex. C: What is the impulse when a force of 35N is applied for 1.2 seconds? Ex. C: What is the impulse when a force of 35N is applied for 1.2 seconds? • An impulse causes a change in momentum FΔt = mΔv Impulse = change in momentum • The unit for impulse and momentum are equivalent • N·s = kg·m/s The man in the picture is causing an impulse and changing the cars momentum • To increase the momentum of an object the most you want the greatest force possible over the longest time possible FΔt = mΔv • Two cars of equal mass are traveling the same speed. What do we know about their momentum? 10 m/s A B 500kg 500kg 10 m/s • Which car is going to take less time to stop 10 m/s A B 500kg 500kg 10 m/s • Which car is going to take less time to stop • Look at the equation and determine what this means: FΔt = mΔv A B • Which car is going to take less time to stop FΔt = mΔv F Δt = mΔv A B F Δt = mΔv Back to Newtons 2nd Law F=ma • If there is a greater force on the same object you will get a greater acceleration, or deceleration. • Force causes acceleration Ex. D: A 0.060kg tennis ball traveling at 10.0 m/s is returned in the opposite direction with a speed of 36.0 m/s. If the ball is in contact with the racket for 0.020s, with what average force is the ball hit? Ex. D: A 0.060kg tennis ball traveling at 10.0 m/s is returned in the opposite direction with a speed of 36.0 m/s. If the ball is in contact with the racket for 0.020s, with what average force is the ball hit? Ex. E: Two identical cars, each traveling 20 m/s, are brought to a stop. Car a stops by applying its breaks the normal way. Car B stops as a result of running into an unmovable concrete wall. Which of the following statements is TRUE? (explain why the incorrect statements are false) a. b. c. d. Car A has the greatest change in momentum. Car B experiences the greatest impulse. Car B has the greatest change in momentum. Car B has the greatest force applied to it. Ex. E: Two identical cars, each traveling 20 m/s, are brought to a stop. Car a stops by applying its breaks the normal way. Car B stops as a result of running into an unmovable concrete wall. Which of the following statements is TRUE? (explain why the incorrect statements are false) a. Car A has the greatest change in momentum. b. Car B experiences the greatest impulse. c. Car B has the greatest change in momentum. d. Car B has the greatest force applied to it. Bouncing • The impulse needed to bring an object to a stop and “throw it back again” is greater than the impulse required to just bring an object to a stop. • To produce a stop you reduce momentum to 0 since v=0 • To bounce you need a negative momentum since the direction of velocity changed Problem Set #1 ρ=mv J= FΔt FΔt = mΔv 1. Bernie, whose mass is 70.0 kg, leaves a ski jump with the velocity of 21.0 m/s. What is Bernie’s momentum as he leaves the ski jump? 2. Mark squishes a spider by applying a 20N force for 0.1s. What is the impulse of this action? 3. Ethel hits a 0.20 kg ball at rest causing it to go 20 m/s. What average force is applied if the ball is in contact for 0.4s? Problem Set #1 ρ=mv J= FΔt FΔt = mΔv 1. Bernie, whose mass is 70.0 kg, leaves a ski jump with the velocity of 21.0 m/s. What is Bernie’s momentum as he leaves the ski jump? Problem Set #1 ρ=mv J= FΔt FΔt = mΔv 2. Mark squishes a spider by applying a 20N force for 0.1s. What is the impulse of this action? Problem Set #1 ρ=mv J= FΔt FΔt = mΔv 3. Ethel hits a 0.20 kg ball at rest causing it to go 20 m/s. What average force is applied if the ball is in contact for 0.4s? 0.2 (0.2 Law of Conservation of Momentum • Momentum is neither gained nor lost in the absence of an external force • All momentum before = all momentum after • p1before + p2before = p1after + p2after expanded as • m1v1o + m2v2o = m1v1f + m2v2f • Net momentum before firing is 0 and net momentum after is still 0 • The cannon and the cannonball cancel each other out pcannon before + pcannonball before = 0 before after pcannon after + pcannonball after = 0 Collisions • Collisions follow the conservation of momentum – When two objects collide the net momentum before the collision equals the net momentum of both objects after the collision Net momentumbefore collision = Net momentumafter collision Elastic Collisions • Elastic collision- When objects collide without being permanently deformed and without generating heat. • Net momentumbefore collision = Net momentumafter collision Elastic Collision Equation m1v1o + m2v2o = m1v1f + m2v2f Elastic Collision Example • Objects do not stick together Inelastic Collisions • Inelastic collision- collision where the objects become distorted or generate heat. m1v1o + m2v2o = (m1+m2)(vf) • If the two objects stick together there is one final velocity: Inelastic collision equation m1v1o + m2v2o = (m1+m2)(vf) If the objects sticking together after the collision will have the same combined velocity. Inelastic Collision • Both have the same final velocity since they stick together Types of collisions/conservation of momentum problems 1. Both objects start at rest (conservation of momentum) 2. One object moving other at rest (elastic collision) 3. Both objects moving same direction (elastic collision) 4. Both objects moving opposite directions (elastic collision) 5. One object moving other at rest (inelastic collision) 6. Both objects moving same direction (inelastic collision) 7. Both objects moving opposite directions (inelastic collision) Conservation of momentum 1. Both objects start at rest (conservation of momentum) Vo = 0 for both objects Ex. F: A baseball player standing on a frictionless surface with a mass of 50 kg throws a 0.25 kg ball forward at a velocity of 25 m/s. What is his final velocity and in what direction? Conservation of momentum Ex. F: A baseball player standing on a frictionless surface with a mass of 50 kg throws a 0.25 kg ball forward at a velocity of 25 m/s. What is his final velocity and in what direction? Types of collisions 2. One object moving other at rest (elastic collision) Ex. G: A 1000 kg car traveling at 20.0 m/s hits a 3000 kg truck at rest. If the truck is traveling 10 m/s forward after the elastic collision, what is the cars final velocity? Ex. G: A 1000 kg car traveling at 20.0 m/s hits a 3000 kg truck at rest. If the truck is traveling 10 m/s forward after the elastic collision, what is the cars final velocity? Types of collisions 3. Both objects moving same direction (elastic collision) Ex. H: A 1000 kg car traveling at 20.0 m/s forward hits a 3000 kg truck at 10 m/s in the same direction. If the truck is traveling 15 m/s forward after the elastic collision, what Is the cars final velocity? Ex. H: A 1000 kg car traveling at 20.0 m/s forward hits a 3000 kg truck at 10 m/s in the same direction. If the truck is traveling 15 m/s forward after the elastic collision, what Is the cars final velocity? Types of collisions 4. Both objects moving opposite directions (elastic collision) Ex. I: What is the initial velocity of a 1000 kg car traveling to the right that hits a 3000 kg truck traveling at 20 m/s to the left. After the elastic collision, the truck is traveling 10 m/s and the car is traveling 15 m/s both to the left? Ex. I: What is the initial velocity of a 1000 kg car traveling to the right that hits a 3000 kg truck traveling at 20 m/s to the left. After the elastic collision, the truck is traveling 10 m/s and the car is traveling 15 m/s both to the left? Types of collisions 5. One object moving other at rest (inelastic collision) Ex. J: In an experiment, a toy wooden car with a mass of 300g, initially at rest, is struck in the rear by a 30g dart traveling at 15 m/s as shown. With what speed does the car with the dart stuck in it move after the collision? V= 15 m/s 30g V= 0 m/s 300g V= ? 30g 300g Ex. J: In an experiment, a toy wooden car with a mass of 300g, initially at rest, is struck in the rear by a 30g dart traveling at 15 m/s as shown. With what speed does the car with the dart stuck in it move after the collision? V= 15 m/s 30g V= 0 m/s 300g V= ? 30g 300g Types of collisions 6. Both objects moving same direction (inelastic collision) Ex. K: A 50 kg astronaut traveling at 8 m/s to the left catches a 10 kg meteor traveling at 20 m/s to the left. What is the final velocity of the astronaut holding the meteor? Ex. K: A 50 kg astronaut traveling at 8 m/s to the left catches a 10 kg meteor traveling at 20 m/s to the left. What is the final velocity of the astronaut holding the meteor? Types of collisions 7. Both objects moving opposite directions (inelastic collision) Ex. L: A 50 kg astronaut traveling at 8 m/s to the right catches a 10 kg meteor traveling at 20 m/s to the left. What is the final velocity of the astronaut holding the meteor? Ex. L: A 50 kg astronaut traveling at 8 m/s to the right catches a 10 kg meteor traveling at 20 m/s to the left. What is the final velocity of the astronaut holding the meteor? Problem Set #2 1. A 35 kg child runs across a store at 4.0 m/s and jumps onto a 35 kg shopping cart initially at rest. At what speed will the shopping cart and the child move together across the store assuming negligible friction? 2. Bruno throws a 0.20kg football and knocks over a 0.88kg vase at rest. After the collision the football bounces straight back with a speed of 3.9 m/s while the vase is moving at 2.6 m/s in the opposite direction. How fast did Bruno throw the football? 3. Martha tosses a 1.5kg ball at a 0.8kg milk jug initially at rest. The ball is thrown to the right at 7.8 m/s and continues to move to the right at 3.0 m/s after the collision. What is the velocity of the jug after the collision? 4. Sam, who is 85kg, jumps into a 300 kg rowboat initially at rest. His initial velocity was 5 m/s forward. What is the velocity of Sam in the boat after he lands? Problem Set #2 1. A 35 kg child runs across a store at 4.0 m/s and jumps onto a 35 kg shopping cart initially at rest. At what speed will the shopping cart and the child move together across the store assuming negligible friction? Problem Set #2 2. Bruno throws a 0.20kg football and knocks over a 0.88kg vase at rest. After the collision the football bounces straight back with a speed of 3.9 m/s while the vase is moving at 2.6 m/s in the opposite direction. How fast did Bruno throw the football? Problem Set #2 3. Martha tosses a 1.5kg ball at a 0.8kg milk jug initially at rest. The ball is thrown to the right at 7.8 m/s and continues to move to the right at 3.0 m/s after the collision. What is the velocity of the jug after the collision? Problem Set #2 4. Sam, who is 85kg, jumps into a 300 kg rowboat initially at rest. His initial velocity was 5 m/s forward. What is the velocity of Sam in the boat after he lands?