Physics 218 Lecture 13 Dr David Toback Physics

Physics 218 Lecture 13 Dr. David Toback Physics 218, Lecture XIII 1

The Schedule Today: • Finish up Chapters 6&7 • Chapter 6 in recitation if you haven’t already Next week: (10/16) • Chapter 6 HW due • Chapter 8 in lecture (reading questions due) • Chapter 7 in recitation Following week: (10/23) • HW 7 due • Chapter 9 in lecture on Tues (reading questions due) • Exam 2 on Thursday October 26 th Physics 218, Lecture XIII 2

Energy • Potential Energy & Conservation of Energy problems • The relationship between potential energy and Force • Energy diagrams and Equilibrium Physics 218, Lecture XIII 3

Physics 218, Lecture XIII 4

Energy Review If there is net work on an object, it changes the kinetic energy of the object (Gravity forces a ball falling from height h to speed up Work done. ) Wnet = DK If there is a change in the potential energy, some one had to do some work: (Ball falling from height h speeds up→ work done → loss of potential energy. I raise a ball up, I do work which turns into potential energy for the ball) DUTotal = WPerson =-WGravity Physics 218, Lecture XIII 5

Energy Review If work is done by a non-conservative force it is negative work (slows something down), and we get heat, light, sound etc. EHeat+Light+Sound. . = -WNC If work is done by a non-conservative force, take this into account in the total energy. (Friction causes mechanical energy to be lost) K 1+U 1 = K 2+U 2+EHeat… K 1+U 1 = K 2+U 2 -WNC Physics 218, Lecture XIII 6

Friction and Springs A block of mass m is traveling on a rough surface. It reaches a spring (spring constant k) with speed Vo and compresses it a total distance D. Determine m Physics 218, Lecture XIII 7

Force and Potential Energy If we know the potential energy, U, we can find the force This makes sense… For example, the force of gravity points down, but the potential increases as you go up Physics 218, Lecture XIII 8

Force and Potential Energy Draw some examples… –Gravity –Spring Physics 218, Lecture XIII 9

Potential Energy Diagrams • For Conservative forces can draw energy diagrams • Equilibrium points – Motion will move “around” the equilibrium – If placed there with no energy, will just stay (no force) Physics 218, Lecture XIII 10

Stable vs. Unstable Equilibrium Points The force is zero at both maxima and minima but… – If I put a ball with no velocity there would it stay? – What if it had a little bit of velocity? Physics 218, Lecture XIII 11

Bungee Jump You are standing on a platform high in the air with a bungee cord (spring constant k) strapped to your leg. You have mass m and jump off the platform. 1. How far does the cord stretch, l in the picture? 2. What is the equilibrium point around which you will bounce Physics 218, Lecture XIII l l 12

Next Week… • Chapter 8: Momentum – Reading Questions for Tuesday: Q 8. 6 and Q 8. 13 • Homework 6 Due Monday • Recitation on Chapter 7 th • Exam 2 is Thursday October 26 Physics 218, Lecture XIII 13

Physics 218, Lecture XIII 14

Roller Coaster with Friction A roller coaster car of mass m starts at rest at height y 1 and falls down the path with friction, then back up until it hits height y 2 (y 1 > y 2). Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path? Physics 218, Lecture XIII 15

Roller Coaster with Friction A roller coaster car of mass m starts at rest at height y 1 and falls down the path with friction, then back up until it hits height y 2 (y 1 > y 2). An odometer tells us that the total scalar distance traveled is d. Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path? Assuming that the magnitude and angle of the force of friction, F, between the car and the track is constant, find |F|. Physics 218, Lecture XIII 16

Bungee Jump A jumper of mass m sits on a platform attached to a bungee cord with spring constant k. The cord has length l (it doesn’t stretch until it has reached this length). How far does the cord stretch Dy? Physics 218, Lecture XIII l 17

A football is thrown A 145 g football starts at rest and is thrown with a speed of 25 m/s. 1. What is the final kinetic energy? 2. How much work was done to reach this velocity? We don’t know the forces exerted by the arm as a function of time, but this allows us to sum them all up to calculate the work Physics 218, Lecture XIII 18

Robot Arm A robot arm has a funny Force equation in 1 -dimension where F 0 and X 0 are constants. What is the work done to move a block from position X 1 to position X 2? Physics 218, Lecture XIII 19