Chapter 7 Work & Energy Classical Mechanics beyond the Newtonian Formulation

Introduction: Our approach New quantities, frameworks, systems, level of knowing Work and Energy; and the Work-Energy principle (or relation) Defining descriptions which are used as physics goes beyond Classical Mechanics (Comment: In QM, motion is described and explained without trajectories as in CM.)

Something new New quantities – Work, Energy, Kinetic Energy, Potential Energy, Momentum, Impulse New frameworks – Work-Energy Principle, Impulse-Momentum Principle, Conservation of Energy, Conservation of Momentum New systems – Objects with more than translational motion, or only characterized by geometry and mass New level of knowing – constructed knowing

Work Done by Constant Forces Exploration of Work for simple case(s) Activities – Sketch situation corresponding to W=Fd – …corresponding to W=FdcosΘ – Work done in situation 1, 2, 3 – Synthesis Definition of net-Work on an object Definition of net-Work by an object

Key points regarding Work The sign of the Work does not depend on the coordinate system. The displacement in the definition of Work is based on the point at which the force is applied. The net Work is not necessarily derived from the net Force. Journal entry: reflect on, make sense of above

Scalar Product of Two Vectors General definition of scalar (dot) product Use in the definition of work by a constant force Examples of scalar product EXERCISE

Work Done by a Varying Force Using calculus reasoning to get a general definition – break up path – look at F vs. x graph General definition in terms of the F vs. x graph using language you know

Introducing the Idea of the Integral From the sum from the graph Notation EXERCISE As anti-derivative Examples

Kinetic Energy and the Work-Energy Principle Tutorial discussion Translational Kinetic Energy definition Work by a constant force and the difference in translational kinetic energy Work-Energy Principle Lab

the end