1. Physics 101: Lecture 12, Pg 1 Physics 101: Lecture 12 Work and Energy l Chapter 6: Work and Energy l Reminders: è Exam I, Tuesday September 30 th at 5 PM è See PHY101 Web page for room assignments è Do not forgot to bring your UB ID card !

2. Physics 101: Lecture 12, Pg 2 Work & Energy l An important concept in physics è Alternative approach to mechanics l Many applications beyond mechanics è Thermodynamics (movement of heat) è Quantum mechanics... l Very useful tools è You will learn new (sometimes much easier) ways to solve problems

3. Physics 101: Lecture 12, Pg 3 Work done by a Constant Force l The work done on an object by a constant (i.e. displacement independent) force F is given by W = F s s Unit : [W] = N m = J (Joule) s : magnitude of displacement F s : magnitude of the force in the direction of the displacement (F s =F cosΘ) W can be positive or negative: W = + F s s if F s points in the same direction as s W = - F s s if F s is opposite of s

4. Physics 101: Lecture 12, Pg 4 Lecture 9, Preflight 1 & 2 You are towing a car up a hill with constant velocity. The work done on the car by the normal force is: 1. positive 2. negative 3. zero W T FNFN V The normal force is perpendicular to the displacement, hence, does no work. correct

5. Physics 101: Lecture 12, Pg 5 Concept Question You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is: 1. positive 2. negative 3. zero With the surface defined as the x-axis, the x component of gravity is in the opposite direction of the displacement, therefore work is negative. W T FNFN V correct

6. Physics 101: Lecture 12, Pg 6 Concept Question You are towing a car up a hill with constant velocity. The work done on the car by the tension force is: 1. positive 2. negative 3. zero Tension is in the same direction as the displacement. W T FNFN V correct

7. Physics 101: Lecture 12, Pg 7 Work/Kinetic Energy Theorem: NetWork {Net Work done on an object} = changekinetic energy {change in kinetic energy of object} l Also works for a variable force ! Work done by a constant net force: W net = F net s = m a s = m (v f 2 –v 0 2 )/2 KE = m v 2 /2 is called the kinetic energy of an object. W net = ΔKE = KE f - KE 0 = ½ m v f 2 – ½ m v 0 2

8. Physics 101: Lecture 12, Pg 8 Work done by Gravity l Object falling vertically upward or downward : W gravity = F gravity s = m g (h 0 -h f ) PE = m g h is called gravitational potential energy Object falling downward: W gravity > 0 Object moving upward: W gravity < 0 Gravity is an example for a conservative force: work done is independent of path or force does no net work on object moving around a closed path.

9. Physics 101: Lecture 12, Pg 9 Conservation of Mechanical Energy l Total mechanical energy of an object remains constant provided the net work done by non-conservative forces is zero: E tot = KE + PE = constant or KE f + PE f = KE 0 + PE 0 => ΔKE + ΔPE = 0 Otherwise, in the presence of a net work done by non-conservative forces (e.g. friction): W nc = ΔKE + ΔPE = KE f – KE 0 + PE f -PE o