PreClass Notes: Chapter 7, Sections

Transcription

1 PreClass Notes: Chapter 7, Sections From Essential University Physics 3 rd Edition by Richard Wolfson, Middlebury College 2016 by Pearson Education, Inc. Narration and extra little notes by Jason Harlow, University of Toronto This video is meant for University of Toronto students taking PHY131. Outline A conservative force is a force that gives back energy that was transferred by doing work. R.Wolfson 7.1 Conservative and Nonconservative Forces 7.2 Potential Energy 7.3 Conservation of Mechanical Energy 1

2 Conservative and Nonconservative Forces A conservative force stores any work done against it, and can give back the stored work as kinetic energy. For a conservative force, the work done in moving between two points is independent of the path. B A Conservative and Nonconservative Forces Because the work done by a conservative force is path independent, the work done in going around any closed path is zero: F d r = 0 2

3 Conservative and Nonconservative Forces A nonconservative force does not store work done against it, the work done may depend on path, and the work done going around a closed path need not be zero. Conservative and Nonconservative Forces Examples of conservative forces include Gravity The electric force The force of an ideal spring Nonconservative forces include Friction Pushing force of a human or animal Automobile engine 3

4 Potential Energy Stored energy held in readiness with a potential for doing work Examples: A stretched bow has stored energy that can do work on an arrow. A stretched rubber band of a slingshot has stored energy and is capable of doing work. Gravitational Potential Energy Potential energy due to elevated position Examples: coffee mug on the top shelf water at the top of Niagara Falls 4

5 Potential Energy Demo video Potential Energy Consider two particles A and B that interact with each other and nothing else. There are two ways to define a system. System 1 consists only of the two particles, the forces are external, and the work done by the two forces change the system s kinetic energy. 5

6 Potential Energy System 2 includes the interaction within the system. Since W ext = 0, we must define an energy associated with the interaction, called the potential energy, U. When internal forces in the system do work, this changes the potential energy. Potential Energy The change in potential energy is defined as the negative of the work done by a conservative force acting over any path between two points: B U F dr AB A Potential energy change is independent of path. Only changes in potential energy matter. We re free to set the zero of potential energy at any convenient point. 6

7 Elastic Potential Energy Elastic potential energy stores the work done in stretching or compressing springs or spring-like systems: U 1 2 kx2 Elastic potential energy increases quadratically with stretch or compression x. Here the zero of potential energy is taken in the spring s equilibrium configuration. Elastic Potential Energy 7

8 Got it? A spring has a spring constant of 100 N/m. How much potential energy does it store when stretched by 10 cm? A. 50 J B. 10 J C. 5 J D. 0.5 J E. 0.1 J Potential Energy 8

9 Gravitational Potential Energy Gravitational potential energy stores the work done against gravity: U mg y Gravitational potential energy increases linearly with height y. This reflects the constant gravitational force near Earth s surface. Mechanical Energy Mechanical Energy is defined as the sum of the kinetic plus potential energy: E mech = K + U 9

10 Conservation of Mechanical Energy K 1 + U 1 = K 2 + U 2 K 1 = 0 U 1 = 10,000 J K 2 = 2,500 J U 2 = 7,500 J K 3 = 7,500 J U 3 = 2,500 J K 4 = 10,000 J U 4 = 0 Energy Bar Charts Slide

11 Conservation of Mechanical Energy Got it? Can a system have negative potential energy? A. No, because a negative potential energy is unphysical. B. No, because the kinetic energy of a system must be equal to its potential energy. C. Yes, as long as the total energy remains positive. D. Yes, as long as the total energy remains negative. E. Yes, because the choice of the zero of potential energy is arbitrary. 11

12 The Zero of Potential Energy Problem Solving with Conservation of Energy Interpret the problem to make sure all forces are conservative, so conservation of mechanical energy applies. Identify the quantity you re being asked to find, which may be an energy or some related quantity. Draw the object in a situation where you can determine both its kinetic and potential energy, then again in the situation where one quantity is unknown. Set up the equation: E 1 = E 2 Evaluate to solve for the unknown quantity, which might be an energy, a spring stretch, a velocity, etc. Assess your solution to see that your answer makes sense, has the right physical units, and is consistent with your intuition. 12

13 Example Problem Note that I have worked out Exercise 21 from Chapter 7. The 5-minute video is available at 13