Bell Ringer: Define Kinetic Energy, Potential Energy, and Work. What are two forms of Potential Energy that we commonly use? Explain Conservation of Energy and how we utilize it for problem-solving technics. Attempt to define momentum and explain what the conservation of momentum is to the best of your abilities.

Notes 6.3: Conservation of MOMENTUM

Objectives: Apply the definition of momentum. Recognize the conditions under which momentum is conserved. Conduct analyses of the momentum of pairs of objects involved in one-dimensional collisions. Apply the law of conservation of linear momentum to interactions, such as collisions between objects. Relate Newton’s 3rd law to conservation of momentum. Determine the impulse given an object.

Vocabulary: Linear momentum Impulse Collisions Elastic and Inelastic collisions Closed system Isolated systems Law of Conservation of Momentum

Active Physics Book: Chapter 3 – Section 5: p. 306 – 308 (Momentum: Collisions) Chapter 3 – Section 6: p. 312 – 317 (Conservation of Momentum) Chapter 3 – Section 7: p. 324 – 330 (Impulse)

Further Learning: Physics: Principles and Problems (Red Book) Chapter 9 – Section 1 & 2 – p. 228 – 255 (Momentum and Its Conservation) Physics.info: Conservation of Momentum Khan Academy: Conservation of Momentum Physics Classroom: Momentum

Crash Course Physics - Momentum: https://www.youtube.com/watch?v=Y-QOfc2XqOk

Momentum: What is momentum? Momentum – describes the tendency of objects to keep going in the same direction with the same speed. Linear momentum is a vector quantity – it has both a magnitude and a direction. When an object has mass and is moving it is considered to have momentum.

Momentum vs. Inertia: Inertia is another property of mass that resists changes in velocity; however, inertia depends only on mass. Inertia is a scalar quantity. ( 10 kg) Momentum is a property of moving mass that resists changes in a moving object’s velocity. Momentum is a vector quantity. (10 kg x m/s east)

Momentum: The equation for momentum is: 𝑝=𝑚𝑣 p = momentum m = mass v = velocity SI Unit for linear momentum is 𝑘𝑔∙𝑚 𝑠 =𝑁∙𝑠; 𝑁= 𝑘𝑔∙𝑚 𝑠 2

Sample Problem 1: An NFL running back weighing 95 kg can run the 40 meter/yard dash in 4.37 seconds. What is his momentum? Answer: 870 N∙s

Checkpoint1: An automobile with a mass of 1000 kg is moving at 20 m/s. What is the vehicle’s momentum? p = 20,000 N∙s

Impulse: Impulse (J) is essentially the change in momentum. It is a useful concept because it is the amount of force acting within a particular time period. Particularly, it allows us the determine the force (lets say in a crash) just by being able to calculate the change in momentum during a particular time period. Impulse-Momentum Theorem: 𝐹∆𝑡= 𝑝 𝑓 − 𝑝 𝑖

Check Point 2: A batter hits a fastball with a force of 1871 N. The bat and ball are in contact for 7 milliseconds. Before the collision of the ball and bat, the ball with a mass of 0.146 kg has a velocity of -38 m/s. Assume that the positive direction is toward the pitcher. What is the momentum of the ball after the collision? Answer: +7.6 𝑘𝑔∙𝑚 𝑠 What is the baseball’s final velocity? Answer: +52 m/s

(For a Closed-Isolated System) Conservation of Momentum: Linear momentum is a conserved quantity. What does this mean? It means that in a closed and isolated system where there is NO NET FORCE ACTING ON THE SYSTEM, its total linear momentum cannot change. (For a Closed-Isolated System)   𝑃 𝑖 = 𝑃 𝑓

Conservation of Momentum: Under what conditions is the momentum of the system of two balls conserved? The system has to be closed and isolated. So what does that mean? If a closed system than that means that no balls are lost and no balls are gained. If an isolated system, that means the forces involved are internal forces; that is, there are no forces acting on the system by objects outside of the system. Notes: No system on Earth can be absolutely isolated; however, most external interactions are small enough to be ignored.

Conservation of Momentum: Let us assume we have a two particle system. Then we would find that the conservation of momentum equation would look as: p i = p f   (For two bodies that means): p 1i + p 2i = p 1f + p 2f m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f

Collisions: From the Conservation of Momentum we can further analyze collisions. There are three types of collisions that we often talk about: Inelastic Collision – A collision between two objects where conservation of momentum is conserved but the kinetic energy of the system is not conserved. Usually that means that it is lost to thermal energy such as friction amongst other factors. Totally Inelastic Collision – A collision between two objects where the two objects stick together (or one object inside of another). Conservation of momentum is conserved but conservation of kinetic energy is not. - Since stuck together, the objects will have the same final velocity.

Collisions: v 1f = m 1 − m 2 m 1 + m 2 v 1i v 2f = 2m 1 m 1 + m 2 v 1i Elastic collision – when two objects collide and maintains conservation of momentum as well as conservation of kinetic energy. In an elastic collision, the kinetic energy of each colliding body may change, but the total kinetic energy of the system does not change. v 1f = m 1 − m 2 m 1 + m 2 v 1i v 2f = 2m 1 m 1 + m 2 v 1i

Sample Problem 2: A 1875-kg car going 23 m/s rear-ends a 1025-kg compact car going 17 m/s on ice in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision. Answer: +21 m/s

Check Point 3: If two pool balls collide (neglect friction), what type of collision is this? A hockey goalie catches the puck, what type of collision is this? A car crashes against a tree, what type of collision is this? Two ice skaters push off against one another starting from a stationary position. The 45 kg skater acquires a velocity of 0.375 m/s to the right. What velocity does the 60 kg skater acquire? 1. Elastic 2. Perfectly Inelastic 3. Inelastic. 4. 5.0 m/s

Conservation of Momentum Video: https://www.youtube.com/watch?v=2UHS883_P60

Conservation of Momentum Video: https://www.youtube.com/watch?v=ajPqs8NI_eY

Exit Ticket (Higher Order Questions): Which has more momentum: a garbage truck that has stopped to pick up trash or the flies buzzing around the garbage truck? Why? Two objects of identical mass are moving towards each other at the same velocity and crash into each other. Describe the outcome (in terms of motion) for this collision. Two object of identical mass are moving towards each other, one traveling three times faster than the other; they crash into each other. Describe the possible outcomes (in terms of motion) for this collision.

Exit Ticket (Higher Order Questions): What do we mean by conservation of momentum? What is meant by elastic versus inelastic collisions? What factors determine the outcome of an collision? What is the difference between the momentum of a system of objects prior to a collision and after the collision? Why do parents typically want you to drive a large, heavy vehicle rather than a small, lightweight vehicle?