Impulse; Conservation of Momentum

Impulse; Conservation of Momentum

Intro: Which Train has more momentum? • While stopped? • When moving at the same velocity? Both have no velocity= no momentum The larger has more mass= more momentum

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. 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?

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? They have the same momentum p=mv 10 m/s A 500kg 10 m/s 500kg B

Which car is going to take less time to stop stops in less time 10 m/s A 500kg 10 m/s 500kg B

Which car is going to take less time to stop • Look at the equation and determine what this means: FΔt = mΔv stops in less time A B

with the same momentum • Which car is going to take less time to stop FΔt = mΔv FΔt = mΔv FΔt = mΔv less time= more force A more time= less force B

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. 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) • 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.

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 • 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? • Mark squishes a spider by applying a 20N force for 0.1s. What is the impulse of this action? • 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 • 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 pcannonbefore + pcannonballbefore = 0 before after pcannonafter + pcannonballafter = 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) 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? Vo = 0 for both objects

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 V= 0 m/s V= ? 300g 30g 300g 30g

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 V= 0 m/s V= ? 300g 30g 300g 30g

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?

Impulse; Conservation of Momentum