1. Conservation of Energy Introduction Section 0 Lecture 1 Slide 1 Lecture 14 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy

2. Introduction Section 0 Lecture 1 Slide 2 Lecture 14 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

3. Conservation of Energy Introduction Section 0 Lecture 1 Slide 3 Lecture 14 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Introduction

4. Conservation of Energy Introduction Section 0 Lecture 1 Slide 4 Lecture 14 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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/s 2 ) Force— what is required to change to motion of a body (MLT -2 or kg-m/s 2 ) In this chapter we will develop on of the most useful concepts in science…ENERGY…and learn what it means to conserve energy.

5. Conservation of Energy Introduction Section 0 Lecture 1 Slide 5 Lecture 14 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Work is equal to the force applied times the distance moved. –Work = Force x Distance: W = F d –Work output = Work input units: 1 joule (J) = 1 Nm = 1 kg m 2 / s 2 [ML 2 T -2 ] Defining Work

6. Conservation of Energy Introduction Section 0 Lecture 1 Slide 6 Lecture 14 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 m 2 / s 3 [ML 2 T -3 ] Work and Power

7. Conservation of Energy Introduction Section 0 Lecture 1 Slide 7 Lecture 14 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Kinetic Energy

8. Conservation of Energy Introduction Section 0 Lecture 1 Slide 8 Lecture 14 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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

9. Conservation of Energy Introduction Section 0 Lecture 1 Slide 9 Lecture 14 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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?

10. Conservation of Energy Introduction Section 0 Lecture 1 Slide 10 Lecture 14 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Potential Energy

11. Conservation of Energy Introduction Section 0 Lecture 1 Slide 11 Lecture 14 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 lifted (height). –The gravitational potential energy PE gravity =mgh.

12. Conservation of Energy Introduction Section 0 Lecture 1 Slide 12 Lecture 14 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 released it will fall back and convert the potential energy into kinetic energy. Potential Energy

13. Conservation of Energy Introduction Section 0 Lecture 1 Slide 13 Lecture 14 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 other purposes.

14. Conservation of Energy Introduction Section 0 Lecture 1 Slide 14 Lecture 14 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy

15. Introduction Section 0 Lecture 1 Slide 15 Lecture 14 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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. Conservation of Energy Time  Energy 

16. Conservation of Energy Introduction Section 0 Lecture 1 Slide 16 Lecture 14 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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)Greater than b)Less than c)Equal to d)Unable to tell from this graph 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. Work Input ≤ Work Out

17. Conservation of Energy Introduction Section 0 Lecture 1 Slide 17 Lecture 14 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 –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. Work Input ≤ Work Out

18. Conservation of Energy Introduction Section 0 Lecture 1 Slide 18 Lecture 14 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 –Any work done by frictional forces is negative. –That work removes mechanical energy from the system. Conservative forces are forces for which the energy can be completely recovered. –Gravity and elastic forces are conservative. –Friction is not conservative. Work Input ≤ Work Out

19. Conservation of Energy Introduction Section 0 Lecture 1 Slide 19 Lecture 14 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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)yes b)no c)It depends. Yes. The difference between the potential energy at the first point and the second point, plus loss to friction is less than the kinetic energy given at the start of the motion.

20. Conservation of Energy Introduction Section 0 Lecture 1 Slide 20 Lecture 14 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Hooke’s Law and Spring Potential Energy

21. Conservation of Energy Introduction Section 0 Lecture 1 Slide 21 Lecture 14 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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.

22. Conservation of Energy Introduction Section 0 Lecture 1 Slide 22 Lecture 14 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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.

23. Conservation of Energy Introduction Section 0 Lecture 1 Slide 23 Lecture 14 Slide 23 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 14 Conservation of Energy Energy and Oscillations

24. Conservation of Energy Introduction Section 0 Lecture 1 Slide 24 Lecture 14 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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.

25. Conservation of Energy Introduction Section 0 Lecture 1 Slide 25 Lecture 14 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 transformed back and forth between potential energy and kinetic energy.

26. Conservation of Energy Introduction Section 0 Lecture 1 Slide 26 Lecture 14 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 the maximum distance from equilibrium. X(t) = A sin (2π f t)

27. Conservation of Energy Introduction Section 0 Lecture 1 Slide 27 Lecture 14 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Why does a swinging pendant return to the same point after each swing? Energy and Oscillations

28. Conservation of Energy Introduction Section 0 Lecture 1 Slide 28 Lecture 14 Slide 28 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The force does work to move the ball. This increases the ball’s energy, affecting its motion. Energy and Oscillations

29. Conservation of Energy Introduction Section 0 Lecture 1 Slide 29 Lecture 14 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Conservative forces are forces for which the energy can be completely recovered. –Gravity and elastic forces are conservative. –Friction is not conservative.

30. Conservation of Energy Introduction Section 0 Lecture 1 Slide 30 Lecture 14 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 the system.

31. Conservation of Energy Introduction Section 0 Lecture 1 Slide 31 Lecture 14 Slide 31 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 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 Read Ch 7