Quiz information on the course website Include : Quiz answers (posted by ~5pm Tuesdays) Quiz problems Quiz rubrics (posted by 5pm following Tuesdays) Quiz score will also be posted by the end of the following week. Quizzes will be returned in your DL section that meet after the following quiz. (I.e. Quiz3 will be returned later next week)

What about Quiz 1? Average 8.69 Those who has not gotten them back will get them in the first DLM this week. Answer, rubrics are on the course web site. Request regrade? => Submit your quiz along with Quiz Re- evaluation Request Form (available from the course website) to me AFTER the lecture by lecture 6 (Feb12) What about Quiz 2? Quiz 2 will be returned in DLM 7 this week.

Quiz 3 8:30-8:50am TODAY Have your calculator ready Closed book Next lecture February 5 Quiz 4 will cover the material from today’s lecture, FNT’s from DLM 5, material from DLM6&7 this week, including FNTs for DLM7 but NOT FNT’s for DLM8.

Energy systems so far E therma l T E bond Phase KESpeed PE gra v height E electri c E mass-spring Distance from the equilibrium position E nuclea r Energy is converted from one form to another, but NEVER created nor destroyed. If the energy of an object increases, something else must have given that object its energy.

Conservation of Energy 5 2 E tot = 10 Joule 3 Nature happens…

Energy Interaction Model E tot = 10 Joule 7 1 2

Energy Interaction Model (-3J) + (+5J) + (-2J) = 0 ∆E orange + ∆ E melon + ∆ E grape = 0 E tot = 10 Joule E total = E orange + E melon + E grape

FNT Equal mass, identical initial speeds Which rock has the greatest speed just Before it hits the ground? Conservation of Energy

FNT Increase in the KE system is the same as the decrease in the PE grav system ∆PE grav X + ∆ KE X = 0 Equal mass, identical initial speeds Which rock has the greatest speed just Before it hits the ground? (KE X ) initial = (KE Y ) initial = (KE Z ) initial (PE grav X ) initial = (PE grav Y ) initial = (PE grav Z ) initial (PE grav X ) final - (PE grav X ) initial + (KE X ) final - (KE X ) initial = (PE grav X ) initial + (KE X ) final - (KE X ) initial = 0 => (KE X ) final = (KE X ) initial + (PE grav X ) initial Wait a minute! Conservation of Energy

FNT Total energy of the system remains unchanged E tot X = PE grav X + KE X = Constant Equal mass, identical initial speeds Which rock has the greatest speed just Before it hits the ground? How do the total energies of the three rocks compare initially? Same How do the total energies of the three rocks compare finally (or at anytime) ? Same Conservation of Energy

Bowling Ball What is the height of the bowling ball after one full swing? (a) Same (b) Higher (c) Lower

Bowling Ball What is the height of the bowling ball after one full swing? (a) Same (Assume friction is negligable)

Bowling Ball (a) Starting point (b) When rope is vertical (c) At point c. When is the speed of the bowling ball maximum? a b c

Bowling Ball (b) When rope is vertical When is the speed of the bowling ball maximum? a b c

Bowling Ball (a) Starting point (b) When rope is vertical (c) At point c When is the PE gravity of the bowling ball maximum? a b c

Bowling Ball (a) Starting point (c) At point c. When is the PE gravity of the bowling ball maximum? a b c

Conservation of Energy  PE gravity = -  KE mg  h = - (1/2) m  v 2 E total = PE grav + KE = constant At the height (peak) of the amplitude, the object is at rest. PE gravity = mgh (define h above the low point) At the bottom of the motion, the object is moving quickly, and h=0. KE = (1/2) m  v 2 Conservation of Energy dictates that: All of the PE goes into KE, and then back again! Consider a simple pendulum:

Bowling Ball Initial Final (Still in motion) PE grav Height KE Speed

Bowling Ball PE grav Height KE Speed Final Initial (In motion)

Bowling Ball PE grav Height KE Speed Initial Final (Still in motion)

Potential Energy: Springs Springs contain energy when you stretch or compress them. We will use them a lot in Physics 7. The indicator is how much the spring is stretched or compressed,  x, from its equilibrium position. k is a measure of the “stiffness” of the spring, with units [k] = kg/s 2.  x: Much easier to stretch a spring a little bit than a lot!  PE spring = (1/2) k  x 2 x

Mass-Spring Systems k is a property of the spring only PE mass-spring does not depend on mass PE = 0 arbitrary  PE mass- spring = (1/2) k  y 2 +C

Mass-Spring Systems PE mass- spring ∆y KE Speed

Mass-Spring Systems PE mass- spring ∆y KE Speed

Conservation of Energy  PE spring-mass = -  KE (1/2)k  y 2 = - (1/2) m  v 2 E total = PE spring-mass + KE = constant Just like a simple pendulum: At the peak of the amplitude, the object is at rest. PE mass-spring = (1/2) m  y 2 (define y from the equilibrium position) At the equilibrium position, the object is moving quickly, and  y =0. KE = (1/2) m  v 2 Conservation of Energy dictates that: All of the PE goes into KE, and then back again!

Graphing Energies What are the x-axis, y axis? Units? x axis (independent variable: height) y axis (dependent variable: PE grav ) Which quantity (energy) is the easiest to graph? E tot ? PE grav? What about KE? Where should the origin (0) be placed? Where does it most make sense? Should the floor be 0m?

Potential Energy and Forces: Springs, Gravitational The indicator is how much the spring is stretched or compressed,  x, from its equilibrium position.  PE spring = (1/2) k  x 2 x ∆PE grav = h The indicator is the change in vertical distance that the object moved (I.e. change in the distance between the center of the Earth and the object)

PE vs displacement: Force Displacement from equilibrium y[+][-]

PE vs displacement: Force Displacement from equilibrium y[+][-] direction of force

PE vs displacement: Force direction of force Displacement from equilibrium y[+][-]

PE vs displacement: Force On this side force pushes up On this side force pushes down Equilibrium Forces from potentials point in direction that (locally) lowers PE Displacement from equilibrium y[+][-]

Potential Energy vs r and Forces Force is always in direction that decreases PE Force is related to the slope -- NOT the value of PE The steeper the PE vs r graph, the larger the force

Why does it take more energy to vaporize than to melt? Whst is E bond ? We will model real atoms of liquids and solids as oscillating masses and springs Particle Model of Matter What does this to do with real world?? Three-phase model of matter Energy-interaction model Mass-spring oscillator Particle model of matter  Particle model of bond energy  Particle model of thermal energy Thermodynamics Ideal gas model Statistical model of thermodynamics r

Introduction to the Particle Model Potential Energy between two atoms separation Flattening: atoms have negligible forces at large separation. Repulsive: Atoms push apart as they get too close r PE Distance between the atoms

Closed Book Make sure above boxes are filled!