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Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Introduction Section 0 Lecture 1 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 1 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet Date Day Lecture Chapter Jan 5 M Class Admin: Intro.Physics Phenomena 1 6 T Problem solving and math App. B, C 7 W Units, Scalars, Vectors, 1 9 F* Speed and Velocity 2 Jan 12 M Acceleration 2 14 W Free Falling Objects 3 16 F* Projectile Motion 3 Jan 19 M Martin Luther King No Class 21 W Newton’s Laws 4 23 F* Mass and Weight 4 Jan 26 M Motion with Friction 4 28 W Review 1-4 1-4 29 Th Test 1 30 F Circular Motion 5 Feb 2 M Planetary Motion and Gravity 5 4 W Energy 6 6 F* Harmonic Motion 6 Feb 9 M Momentum 7 11 W Impulse and Collisions 7 13Introduction F* Rotational 8 Section 0 Motion Lecture 1 Slide 2 Feb 16 M Presidents Day No Class 17 Tu Angular Momentum (Virtual Monday) 8 18 W Review 5-8 19 5-8 H Test 2 INTRODUCTION TO Modern Physics PHYX 2710 20 F* Static Fluids, Pressure 9 Fall 2004 Feb 23 M Flotation 9 25 W Fluids in Motion 9 27 F* Temperature and Heat 10 Mar 2 M First Law of Thermodynamics 10 Physics of Technology—PHYS 1800 4 W Spring 2009Heat flow and Greenhouse Effect Conservation 10 of Energy *Homework Handout 6 F* Climate Change - Homework Due - 1 2 3 4 5 - 6 Lecture 14 Slide 2 7 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Introduction Section 0 Lecture 1 Slide 3 Introduction INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 3 Describing Motion and Interactions Position—where you are in space (L or meter) Velocity—how fast position is changing with time (LT-1 or m/s) Acceleration—how fast velocity is changing with time (LT-2 or m/s2) Force— what is required to change to motion of a body (MLT-2 or kg-m/s2) Introduction Section 0 Lecture 1 Slide 4 In this chapter we will develop on of the most useful concepts in science…ENERGY…and learn what it means to conserve energy. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 4 Defining Work • Work is equal to the force applied times the distance moved. – Work = Force x Distance: – Work output = Work input W=Fd • units: 1 joule (J) = 1 Nm = 1 kg m2 / s2 [ML2T-2] Introduction Section 0 Lecture 1 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 5 Work and Power • Only forces parallel to the motion do work. • Power is the rate of doing work – Power = Work divided by Time: P=W/t units: 1 watt (W) = 1 J / s = 1 kg m2 / s3 [ML2T-3] Introduction Section 0 Lecture 1 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 6 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Introduction Section 0 Lecture 1 Slide 7 Kinetic Energy INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 7 Kinetic Energy • Kinetic energy is the energy associated with an object’s motion. – Doing work on an object increases its kinetic energy. – Work done = change in kinetic energy 1 2 KE mv 2 Introduction Section 0 Lecture 1 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 8 Kinetic Energy • Negative work is the work done by a force acting in a direction opposite to the object’s motion. – For example, a car skidding to a stop – What force is acting to slow the car? Introduction Section 0 Lecture 1 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 9 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Introduction Section 0 Lecture 1 Slide 10 Potential Energy INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 10 Potential Energy • If work is done but no kinetic energy is gained, we say that the potential energy has increased. – For example, if a force is applied to lift a crate, the gravitational potential energy of the crate has increased. – The work done is equal to the force (mg) times the distance Section 0 Lecture 1 Slide 11 liftedIntroduction (height). – The gravitational potential energy PEgravity=mgh. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 11 Potential Energy Work is done on a large crate to tilt the crate so that it is balanced on one edge, rather than sitting squarely on the floor as it was at first. Has the potential energy of the crate increased? a) Yes b) No Yes. The weight of the crate has been lifted slightly. If it is Introduction Lectureand 1 Slide 12 released it willSection fall 0back convert the potential energy into kinetic energy. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 12 Potential Energy • The term potential energy implies storing energy to use later for other purposes. – For example, the gravitational potential energy of the crate can be converted to kinetic energy and used for Introduction Section 0 Lecture 1 Slide 13 other purposes. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 13 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Introduction Lecture 1 Slide 14 Conservation of Energy Section 0 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 14 Conservation of Energy Energy Energy: The potential to do work. Conservation of Energy: The total energy of a closed system remains constant. – Energy can be converted from one form to another. – Not all forms of energy can be fully recovered. Introduction Section 0 Lecture 1 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Time Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 15 Work Input ≤ Work Out A lever is used to lift a rock. Will the work done by the person on the lever be greater than, less than, or equal to the work done by the lever on the rock? a) b) c) d) Greater than Less than Equal to Unable to tell from this graph Introduction Section 0 Lecture 1 Slide 16 The work done by the person can never be less than the work done by the lever on the rock. If there are no dissipative forces they will be equal. This is a consequence of the conservation of energy. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 16 Work Input ≤ Work Out – Work done in pulling a sled up a hill produces an increase in potential energy of the sled and rider. – This initial energy is converted to kinetic energy as they slide down the hill. Introduction Section 0 Lecture 1 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 17 Work Input ≤ Work Out • Conservative forces are forces for which the energy can be completely recovered. – Gravity and elastic forces are conservative. – Friction is not conservative. Introduction Section 0 Lecture 1 Slide 18 – Any work done by frictional forces is negative. – That work removes mechanical energy from the system. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 18 A sled and rider with a total mass of 40 kg are perched at the top of the hill shown. Suppose that 2000 J of work is done against friction as the sled travels from the top (at 40 m) to the second hump (at 30 m). Will the sled make it to the top of the second hump if no kinetic energy is given to the sled at the start of its motion? a) b) c) yes no It depends. Yes. The difference between the potential energy at the first point and the second point, plus Introduction Section 0 Lecture loss to friction is less than the kinetic energy given at the start of the motion. 1 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 19 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Hooke’s Potential Energy Section 0 Law Lecture 1and Slide Spring 20 Introduction INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 20 Potential Energy of a Spring • An elastic force is a force that results from stretching or compressing an object. • Elastic potential energy is the energy gained when work is done to stretch a spring. – The spring constant, k, is a number describing the stiffness of the spring. Introduction Section 0 Lecture 1 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 21 Hooke’s Law and Potential Energy • Hooke’s Law: The increase in elastic potential energy is equal to the work done by the average force needed to stretch the spring. PE work done = average force distance 1 average force = kx 2 1 2 PE kx Introduction 2 Section 0 Lecture 1 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 22 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Introduction Lecture 1 Slide 23 Energy and Oscillations Section 0 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 23 • A restoring force is a force that exerts a push or a pull back towards equilibrium. • A restoring force that increases in direct proportion to the distance from equilibrium results in simple harmonic motion. Introduction Section 0 Lecture 1 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 24 Springs and Simple Harmonic Motion • Simple harmonic motion occurs when the energy of a system repeatedly changes from potential energy to kinetic energy and back again. Energy added by doing work to stretch the spring is Introductionback Section and 0 Lecture 1 Slide 25 transformed forth between potential energy and kinetic energy. INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 25 The horizontal position x of the mass on the spring is plotted against time as the mass moves back and forth. • The period T is the time taken for one complete cycle. • The frequency f is the number of cycles per unit time. F=1/T • The amplitude is Introduction Section 0 the maximum distance from equilibrium. Lecture 1 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 X(t) = A sin (2π f t) Conservation of Energy Lecture 14 Slide 26 Energy and Oscillations Why does a swinging pendant return to the same point after each swing? Introduction Section 0 Lecture 1 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 27 Energy and Oscillations The force does work to move the ball. This increases the ball’s energy, affecting its motion. Introduction Section 0 Lecture 1 Slide 28 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 28 • Conservative forces are forces for which the energy can be completely recovered. – Gravity and elastic forces are conservative. – Friction is not conservative. Introduction Section 0 Lecture 1 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 29 Conservation of Energy • Conservation of energy means the total energy (the kinetic plus potential energies) of a system remain constant. – Energy is conserved if there are no forces doing work on Section the system. Introduction 0 Lecture 1 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 30 Physics of Technology Next Lab/Demo: Energy & Oscillations Momentum and Collisions Thursday 1:30-2:45 ESLC 53 Ch 6 and 7 Next Class: Wednesday 10:30-11:20 BUS 318 room Review Ch 6 Slide 31 Read Ch 7 Introduction Section 0 Lecture 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservation of Energy Lecture 14 Slide 31
