#### Transcript Work and Energy

Work and Energy Chapter 5 in S&F Equations W F r cos 1 2 K mv 2 U g mgh ***Wnet KEi PEi KE f PE f *** P Fv cos TSWBAT! Apply these appropriately to physical situations Definitions and Units • Contrary to what you might think, solving word problems is no longer considered “work” in this class, solving word problems will hereafter be referred to as “play” or “fun.” • Work, physical work, is an energy exchange, we will add it to a “system”… Work and Energy • Yes, we have equations for it… • Work = Force times distance – Or more appropriately the “dot” product of a force vector and the displacement vector of the object it acts on. • What are the units? Work and Energy • Joules! – You were probably thinking Newton’s times meters, huh? You are correct, we just have a special name for the units of work and energy. • Since work is an energy exchange, they both have the same units. Work and Energy • In the real world you can exchange dollars for doughnuts, but in the physical world it’s more like dollars for euros, yen, pounds(!) etc. – Work, kinetic, potential, heat, sound, light… • Let’s look at the dot product a little more… Work Work F d F d Were interested in the component of force that actually moves the object in the direction it goes. The other component, perpendicular to the displacement, is “wasted.” Work Work F d Fcos Fsin F d Work Work F d F Fcos d Work Work F r cos F Fcos r Let’s Apply this puppy. Tleash angle displacement Puppy Pull • Tension in leash = 100 N • Angle with ground = 30 degrees • Displacement along the ground = 20 meters (this puppy is stubborn) So what’s the work? Work F d cos W= 100 N x 20 m x cos(30) = 1730 Joules We did 1730 joules of work on the puppy. Energy • So what is energy? • The physical state of an object that gives it the capacity to do work. Energy • You can probably mention two types, maybe more… • Kinetic – translational, rotational • Potential – gravitational, electrical, internal (temp) • Let’s just do Translational Kinetic and Gravitational Potential for now and save the others for later in this course. Kinetic Energy 1 2 K mv 2 Work and KE Wnet KE f KEi Work Kinetic energy theorem Where’s this come from? • Think back to kinematics v f v0 2ax 2 2 mv f mv0 2max 2 2 1 1 2 2 mv f mv0 max 2 2 1 1 2 2 mv f mv0 F x 2 2 How fast is it going? • Given work done and mass, and starts from rest. vf Wnet 1 1 2 mv f mv0 2 2 2 2Wnet 2 v0 m Start from rest Energy 1 2 Kinetic Energy, K mv 2 Potential Energy, U g mgh S&F use: KE= and PE= Potential Energy • Gravitational energy. • Let’s think this one through. If I lift 100 N one meter what work did I do? • Yeah, 100 Joules • How fast is it moving now? • What’s up? (besides the 100 N weight) PE • The energy went somewhere, where? • We say the weight gained Potential energy equal to the change in vertical position, altitude, or height, times its weight (the force it took to get it there). U g mgh Work raising a weight • How much work is done raising a bucket from a well? W PE f PEi W mg (h f h0 ) Conservative vs. Nonconservative forces Conservative – we can get it back So I lifted the 100N one meter, what happens when I drop it? It speeds up until it hits the ground. The work transforms into KE of the weight, so gravity is a conservative force. Conservative vs. Nonconservative forces Non-conservative Think back to the puppy pull. Let’s make it a box now, even though I did work on the box, friction also did work on the box. Due to Newton’s IIId law, friction did negative work on the box! What happens when we let go of the leash? Will the box spontaneously spring back to where it was? NO! Friction is non-conservative. Con vs non • Conservative forces store the energy when you work against them. You can get it back later. – Gravity, electrical force, springs. • Non-conservative Forces dissipate the energy of work done against them. You can’t get it back. It turns into; sound, heat etc. – Friction, airplane drag… Book definition • Conservative – path independent – Gravity, doesn’t matter where, just how high. • Non-conservative – path dependent – Longer path, more friction loss All together • KE and PE as well as work all in one Wnet KE0 PE0 KE f PE f Fin. • Questions?? To Cover on site • Power = work per time • P=Fvcos Review W F r cos 1 2 K mv 2 U g mgh ***Wnet KEi PEi KE f PE f *** P Fv cos • Conserve - get it back, non – don’t