PHY 113 C General Physics I 11 AM12

PHY 113 C General Physics I 11 AM-12: 15 PM MWF Olin 101 Plan for Lecture 8: Chapter 8 -- Conservation of energy 1. Potential and kinetic energy for conservative forces 2. Energy and non-conservative forces 3. Power 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 1

9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 2

Comments on preparation for next Thursday’s exam 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 3

Comments on preparation for next Thursday’s exam -- continued 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 4

Comments on preparation for next Thursday’s exam – continued What you should bring to the exam (in addition to your well-rested brain): Ø A pencil or pen Ø Your calculator Ø An 8. 5”x 11” sheet of paper with your favorite equations (to be turned in together with the exam) What you should NOT use during the exam Ø Electronic devices (cell phone, laptop, etc. ) Ø Your textbook 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 5

Problem solving skills Math skills Equation Sheet Advice: 1. Keep basic concepts and equations at the top of your head. 2. Practice problem solving and math skills 3. Develop an equation sheet that you can consult. 8/27/2013 PHY 113 A Fall 2013 -- Lecture 1 6

iclicker question Which of the following best describes your opinion about the equation sheet: A. I have not prepared my equation sheet yet but hope to do so soon B. I have a preliminary equation sheet but have not used it for doing homework C. I have a preliminary equation sheet and have used it for doing homework D. I am dreaming about preparing the equation sheet, but have not done it yet E. In my opinion, the equation sheet is not really necessary 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 7

Review of energy concepts: 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 8

Some questions from webassign Assignment #7 In 1990 Walter Arfeuille of Belgium lifted a 281. 5 -kg object through a distance of 17. 1 cm using only his teeth. (a) How much work was done on the object by Arfeuille in this lift, assuming the object was lifted at constant velocity? T yf T mg yi mg 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 9

Some questions from webassign Assignment #7 In 1990 Walter Arfeuille of Belgium lifted a 281. 5 -kg object through a distance of 17. 1 cm using only his teeth. How much work was done on the object by gravity? T yf T mg yi mg 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 10

Some questions from webassign Assignment #7 What is the work done as the particle moves from x=0 to x=3 m? 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 11

Some questions from webassign Assignment #7 -continued What is the work done as the particle moves from x=8 to x=10 m? 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 12

Some questions from webassign Assignment #7 A 4. 34 -kg particle is subject to a net force that varies with position as shown in the figure. The particle starts from rest at x = 0. What is its speed at x = 5. 00 m? 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 13

Work and potential energy Note: It is assumed that F is conservative 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 14

Work and potential energy -- continued Example – gravity near the surface of the Earth: y mg yref mg 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 15

Work and potential energy for gravity (near Earth’s surface) yf mg yi mg yref 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 16

Work and potential energy continued iclicker question Why is there a strange “-” sign in the definition of potential energy? A. Physicists like to be annoying B. No reason at all C. There is a somewhat good reason 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 17

Work and potential energy continued For the case that the total force acting on the system is conservative, we can use the definition of potential energy with the work-kinetic energy theorem 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 18

Summary of work, potential energy, kinetic energy relationships 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 19

Example i A block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity? h=0. 5 m h f 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 20

Energy diagram E U, K, E (J) K U m yf 9/19/2013 yi PHY 113 C Fall 2013 -- Lecture 8 21

k 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 22

Energy diagrams 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 23

Example: Model potential energy function U(x) representing the attraction of two atoms 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 24

Comment on relationship between potential energy and (conservative) force: 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 25

Example: Mass sliding on frictionless looping track i 9/19/2013 iclicker exercise: In order for the ball completes the loop at A, what must the value of h? A. h=R B. h=2 R C. h>2 R D. Not enough information. PHY 113 C Fall 2013 -- Lecture 8 26

Example: Mass sliding on frictionless looping track i 0 0 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 27

Another example; first without friction Mass m 1 (=0. 2 kg) slides horizontally on a frictionless table and is initially at rest. What is its velocity when it moves a distance Dx=0. 1 m (and m 2 (=0. 3 kg) falls Dy=0. 1 m)? iclicker exercise: What is the relationship of the final velocity of m 1 and m 2? A. They are equal B. m 2 is faster than m 1. C. m 1 is faster than m 2. 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 28

Another example; first without friction T Mass m 1 (=0. 2 kg) slides horizontally on a frictionless table and is T initially at rest. What is its velocity when it moves a distance Dx=0. 1 m (and m 2 (=0. 3 kg) falls Dy=0. 1 m)? m 2 g 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 29

Another example; now with friction T f Mass m 1 (=0. 2 kg) slides horizontally on a table with kinetic friction and is T initially at rest. What is its velocity when it moves a distance Dx=0. 1 m (and m 2 (=0. 3 kg) falls Dy=0. 1 m)? m 2 g 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 30

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iclicker exercise: Assume a mass m starts at rest at A and moves on the frictionless surface as shown. At what position is the speed the largest? A. A B. B C. C D. none of these. 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 32

Power 9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 33

9/19/2013 PHY 113 C Fall 2013 -- Lecture 8 34