1. 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/~matwml Tel (65) 6874-2749 1

2. WHAT IS ENERGY ? 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 [1] The American Heritage Dictionary of the English Language, Houghton Mifflin, Boston, 1992. 2

3. WORK IS ENERGY (old form 5.5-7 thousand years ago) Werg – to do 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,synergids ynergism,thaumaturge,work [1] Appendix: PIE (suffixed form) Werg-o Greek: ergon  energos  energeia  Latin: energia  French:energie Germanic: werkam  Old High German: werc, Old English: weorc,werc http://www.bartleby.com/61/roots/IE577.html (zero-grade form) Wig derivatives wrought, irk, wright (o-grade form) Worg derivatives organ, organon (= tool), orgy 3

4. WEIGHT LIFTING Physicists define or is the distance that the object is lifted is the acceleration of gravity = is force required to lift the object in Questions What is weight? Can F be exactly constant? in energy units called is the mass of an object in 4

5. ARCHIMEDES “ Give me a place to stand and I will move the Earth” http://www.shu.edu/projects/reals/history/archimed.html effort arm fulcrum Earth lightweight braggart https://www.cs.drexel.edu/~crorres/Archimedes/contents.html http://wow.osu.edu/experiments/simplemachines/levers.html load arm 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? 5

6. In the balance shown below, the heavier/lighter mass may be lifted by lowering the lighter/heavier mass. The objects move in opposite directions by distances that are inversely proportional to their masses ? PULLEYS 2kg 2m 1m 1kg Question What is the golden rule of mechanics? http://www.hp-gramatke.net/pmm_physics/english/page0200.htm 6

7. Distance Dependent Forces Our formula for objects whose distance r from the Earth’s centre is is only an approximation valid Isaac Newton’s Universal Law of Gravitation gives very close to is the gravitational constant is the Earth’s mass The Earth’s radius is where and Question Why is? 7

8. How to Compute Work and where F is in the s-direction This integral is the area between the graphs of are the initial and final values of s Question What work is required to lift an object, having mass m, from the Earth’s surface to height d? 8 Answer and

9. WORK TO COMPRESS A SPRING The figure below illustrates a spring being compressed Initial DistanceFinal Distance Hook’s Law states that therefore k = spring constant Question What is the compression work integral? Answer 9

10. TUTORIAL 1 1.Compute the work to lift an object, having mass 1kg, from the Earth’s surface to ‘infinite’ height. 2. Compute the work to compress a spring by 1m if the final force equals 5N. 4. Compute the work to compress a volume V of gas with pressure P by a small amount dV. Compute the work to compress it to one tenth of its initial volume at constant temperature under ideal gas law assumptions. 5. Compute the work that the force of gravity does to an object having mass m as it slides a distance d along an inclined plane. How are vectors involved? 10 3. How do snakes crush prey with > 6 x their strength?