Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Impulse Momentum The impulse-momentum theorem Conservation of momentum Inelastic collisions Chapter 9 Momentum Topics: Sample question: Male rams butt heads at high speeds in a ritual to assert their dominance. How can the force of this collision be minimized so as to avoid damage to their brains? Slide 9-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dot Product Slide 4-19 Dot product or scalar product is a way of multiplying two vectors to get a scalar result Dot products can be calculated either independent of a coordinate system where is the angle between the two vectors Note that in this case the sign of the dot product only depends on the angle Or in component form

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dot Product: Example 1 Dot produce or scalar product is a way of multiplying two vectors to get a scalar result Dot products can be calculated either independent of a coordinate system where is the angle between the two vectors Vector A has a magnitude of 4 units Vector B has a magnitude of 3 units Angle between them = 60 degrees

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dot Product: Example 2 Slide 4-19 Dot product or scalar product is a way of multiplying two vectors to get a scalar result Dot products in component form Let and So

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example 3 Using a dot product to find angle Slide 4-19 We know 2 ways to calculate the dot product Put these two equations for dot product = to each other

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Forces During a Collision Slide 9-20

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Impulse-Momentum Theorem and Conservation of Energy Slide 9-10 System Schema for colliding carts Defining your system (objects of interest) Force diagram on cart Are the gravitational force on the cart from the Earth and The normal force of the track on the cart a Newton 3 pair? A. Yes B. No Deriving Conservation of Momentum from Sum of Forces When to use conservation of Momentum (Sum F ext = 0) and when to use Impulse-Momentum Theorem (Sum F ext = not 0)

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Inelastic Collisions For now, we’ll consider perfectly inelastic collisions: A perfectly inelastic collision results whenever the two objects move off at a common final velocity. Slide 9-21

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Jack stands at rest on a skateboard. The mass of Jack and the skateboard together is 75 kg. Ryan throws a 3.0 kg ball horizontally to the right at 4.0 m/s to Jack, who catches it. What is the final speed of Jack and the skateboard? Slide 9-22

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example A 10 g bullet is fired into a 1.0 kg wood block, where it lodges. Subsequently, the block slides 4.0 m across a floor (µ k = 0.20 for wood on wood). What was the bullet’s speed? Slide 9-23

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Important forms of energy How energy can be transformed and transferred Definition of work Concepts of kinetic, potential, and thermal energy The law of conservation of energy Elastic collisions Chapter 10 Energy Topics: Sample question: When flexible poles became available for pole vaulting, athletes were able to clear much higher bars. How can we explain this using energy concepts? Slide 10-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Forms of Energy Mechanical Energy Thermal Energy Other forms include Slide 10-10

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A “Natural Money” Called Energy Key concepts: Definition of the system. Transformations within the system. Transfers between the system and the environment. Liquid Asset: Cash Saved Asset: Stocks Income Expenses Transformations within system System Transfers into and out of system Slide 10-9

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Basic Energy Model Slide 10-11

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 10-7 Discussion of pendulum and energy conservation Observation: where does the energy go => E k => E g And then E g => E k

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Observation: where does the energy go => E k => E g And then E g => E k Slide 10-7 Discussion of energy conservation: car & inclined ramp

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 10-7 Discussing Energy Bar Charts

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Should Dr. Saul be worried? A.Yes B.No Slide 10-7 Demonstration: Smash the Professor - Part 1