Homework: WS: momentum & impulse Momentum and Impulse Textbook: 5.1 Homework: WS: momentum & impulse Pg. 238 # 3, 4, 7, 8, 10, 13

Momentum The momentum of an object of mass m in kg and velocity v in m/s is the rate of change of its kinetic energy w.r.t velocity (i.e. taking the derivative of EK) Momentum is a Derive Impulse by taking the time derivative of momentum.

Momentum The momentum of an object of mass m in kg and velocity v in m/s is: Derive Impulse by taking the time derivative of momentum.

Momentum The momentum of an object of mass m in kg and velocity v in m/s is: Derive Impulse by taking the time derivative of momentum.

Ex. Compare the momentum between an average human (80 kg) and a car (1500kg). Both have equal kinetic energy. The car was moving at 5 km/h.

Impulse The change in an object’s momentum is known as the impulse on the object Demo: mini golf, football

A 0.1 kg ball was thrown at a velocity of 10 m/s [E] against a wall and was rebounded at a velocity of 10 m/s [W]. The ball was in contact with the wall for 0.19s. Determine the force that the wall exerted on the ball.

Conservation of Momentum Discuss Conservation of Energy (The importance of conserved quantities, and the idea of isolated systems) Derive Conservation of Momentum Textbook: 5.2 Homework: WS – Conservation of Momentum Read pg 254 - 257

Conservation of Momentum Inelastic Collisions Elastic Collisions

Conservation of Linear Momentum Conservation of Momentum in One Dimension Conservation of Momentum in Two Dimension Pg. 243 #3 - 7 Demo: Momentum of Carts in a Collision Pg. 243 #9

Law of conservation of Momentum It applies to all collisions as long as the net external force acting on the system is zero. - a ball rolling along a frictionless horizontal surface with no external forces acting on the ball is a closed system - a ball thrown upwards is not a closed system because the external force of Earth’s gravity is pulling on it

Conservation of momentum

A competition is held between two teams of physics students, each team made up of two members, and each member having a mass of 70 kg. They want to see whose cart will be moved the fastest by propelling it with a jump. They will start at the west end of a cart of mass 100 kg that is free to roll without friction on a level, east-west track. The plan is to run east along the cart and then jump off with a velocity of 10 m/s, with respect to the cart. The first team decides that its two members will run and jump off together. The second team decides that one member will depart according to the rules, followed by the second. Calculate the final velocity of the cart for each team, and discuss the results.

Elastic and Inelastic Collisions Textbook: 5.3 Homework: WS – Elastic Collisions Discuss: In a collision there are two possible quantities that can be conserved - Momentum and Kinetic Energy Discuss: Why is linear momentum always conserved? Because there is only one kind of linear momentum. Discuss: Kinetic energy is not always conserved because it can change into different forms of energy.

Inelastic Collisions Inelastic Collision: p = 0 Ek  0 Completely Inelastic Collisions: Ek < 0 Pg. 251 #10, 12 Demo: Newton’s Cradle Demo: Elastic Cart Collision

Elastic Collisions Elastic Collisions p = 0 Ek = 0 Determine the velocities after an elastic collision between m1 traveling at v1 and m2 at rest: Pg. 251 #11, 14 Demo: Launching a superball

Ex 0. A 300-g toy train and a 600-g toy train are involved in an elastic collision on a straight section of a model rail. The 300-g train, travelling at 2 m/s, strikes the 600-g train at rest. Determine the velocities of both trains after the collision.

Ex 1. A totally elastic collision occurs between object A, with a mass of 2.0kg, and object B, with a mass of 7.0kg. Object A is moving at 10 m/s [E], while object B is moving at 4.0 m/s [E]. Calculate the velocity of each mass after the collision.

Ex 2. A totally elastic, head-on collision occurs between object A, with a mass of 2.0kg, and object B, with a mass of 7.0kg. Object A is moving at 10 m/s [E], while object B is moving at 4.0 m/s [W]. Calculate the velocity of each mass after the collision.

Conservation of Momentum in 2D Textbook: 5.4 Homework: WS. Momentum 2D

Conservation of Momentum in 2-D In general: Pg. 257 #3, 5, 6

Two identical curling stones of mass 19 Two identical curling stones of mass 19.5 kg collide, as shown on the left. The first stone hits the stationary second stone at the side with a velocity of 5.0 m/s [N]. If the velocity of the first stone is 3.2 m/s [N30°W] after collision, find the velocity of the second stone after collision. Omit any effects due to friction.

A package of mass 4. 7 kg explodes into three pieces A package of mass 4.7 kg explodes into three pieces. One piece, with a mass of 2.0 kg moves with a velocity of 4.0 m/s [N30oW]. Another piece with a mass of 1.5 kg, moves with a velocity of 6.0 m/s [E]. Determine the velocity of the third piece.

Additional Homework Pg. 267, #4-6, 11- 13, 16-18 Pg. 269, # 7-16