USC2001 Energy Lecture 1 Energy and Work Wayne M. Lawton Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore 117543 Email matwml@nus.edu.sg http://www.math.nus.edu.sg/~matwml/courses/Undergraduate/USC/2006/USC2001/ Tel (65) 6516-2749 1

SUMMARY OF THREE DYNAMICS LECTURES Lecture 1. Energy and Work : work as lifting, levers and pulleys, gravitational force, springs, statics. Lecture 2. Kinetic Energy in Motion : Newton’s 2nd Law, falling bodies, work-kinetic energy theorem, oscillators, collisions, momentumm Newton’s 3rd Law Lecture 3. Thermodynamics of Heat : thermometers, mechanical derivation of ideal gas law, work and heat, thermodynamic processes, entropy, 1st and 2nd Laws Related Focus Topics : mechanical engines, steam and internal combustion engines, refrigeration and energy conversion, biomechanics. 2

WHAT IS ENERGY ? [1] The American Heritage Dictionary of the English Language, Houghton Mifflin, Boston, 1992. 1 The capacity for work or vigorous activity, strength 2 Exertion of vigor or power ‘a project requiring a great deal of time and energy’ 3 Usable heat or power ‘Each year Americans consume a high percentage of the world’s energy’ 4 Physics. The capacity of a physical system to do work -attributive. energy – conservation, efficiency 3

4 WORK IS ENERGY [1] Appendix: PIE http://www.bartleby.com/61/roots/IE577.html (old form 5.5-7 thousand years ago) Werg – to do (suffixed form) Werg-o derivatives handiwork,boulevard,bulwark, energy, erg, ergative,-urgy; adrenergic,allergy,argon,cholinergic,demiurge, dramaturge,endergonic, endoergic,energy,ergograph,ergometer, ergonomics,exergonic,exergue, exoergic,georgic,hypergolic,lethargy,liturgy,metallurgy,surgery,synergidsynergism,thaumaturge,work Greek: ergon  energos  energeia  Latin: energia  French:energie Germanic: werkam  Old High German: werc, Old English: weorc,werc (zero-grade form) Wig derivatives wrought, irk, wright (o-grade form) Worg derivatives organ, organon (= tool), orgy 4

5 WEIGHT LIFTING Physicists define or in energy units called is force required to lift the object in is the mass of an object in is the acceleration of gravity = is the distance that the object is lifted Questions What is weight? Can F be exactly constant? 5

6 ARCHIMEDES “ Give me a place to stand and I will move the Earth” lightweight braggart load arm Earth effort arm fulcrum http://www.shu.edu/projects/reals/history/archimed.html https://www.cs.drexel.edu/~crorres/Archimedes/contents.html http://wow.osu.edu/experiments/simplemachines/levers.html Questions The Earth’s mass is 5.98E24 kg, if Archimedes’ is 65 Kg what is the geometry of his lever? What is his lever principle and what are some tools that employ it? 6

PULLEYS In the balance shown below, the heavier/lighter mass may be lifted by lowering the lighter/heavier mass. 1m 2kg 1kg 2m The objects move in opposite directions by distances that are inversely proportional to their masses ? Question What is the golden rule of mechanics? http://www.hp-gramatke.net/pmm_physics/english/page0200.htm 7

Distance Dependent Forces The Earth’s radius is Our formula is only an approximation valid for objects whose distance r from the Earth’s centre is very close to Isaac Newton’s Universal Law of Gravitation gives where is the Earth’s mass and is the gravitational constant Question Why is ? 8

9 How to Compute Work where F is in the s-direction and are the initial and final values of s This integral is the area between the graphs of and Question What work is required to lift an object, having mass m, from the Earth’s surface to height d? Answer 9

WORK TO COMPRESS A SPRING The figure below shows a spring being compressed. k = spring constant Compressed Uncompressed Question What is the compression work integral? Answer Since Hook’s Law gives 10

NEWTON’S 1st LAW If no force acts on a body, then the body’s velocity cannot change; that is, the body cannot accelerate. Note: force is a vector quantity – it has both magnitude and direction! What happens if two or more people pull on an object? This question leads to the following more precise statement If no net force acts on a body, then the body’s velocity cannot change; that is, the body cannot accelerate. 11

STATICS Why is this object static (not moving) ? Hint: What are the forces acting on this object? What is the net force acting on this object? 12

VECTOR ALGEBRA FOR STATICS The tension forces are The gravity force is 13

14 TUTORIAL 1 Design a pulley that a strong person who weights 70 kg can use to lift a 700 kg object. 2. Compute the work required to lift an object with mass 7 kg from the Earth’s surface to ‘outer space’. 3. Compute the work required to compress gas with volume V and pressure P to volume V/2. 4. Compute the work required to stretch a spring with stiffness k by distance L. 14

TUTORIAL 1 5. A 100 kg woman stands with her legs making 45 degree angles with respect to the vertical direction. What is the compressive force in her knees ? 6. How is biomechanics important for orthopaedics ? 7. What is Pascal’s law for fluid statics ? 8. Compute the mass of the object on the side of the block below that has length 4m so that the system is in equilibrium (there is no movement). ? 15