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 R:\public_html\courses\Undergraduate\USC\2008\USC2001 Tel (65) 6516-2749 1

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

3. 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. 3

4. 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 4

5. 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 5

6. 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? 6

7. 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 7

8. 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? 8

9. 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? 9 Answer and

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

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

12. 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

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

14. TUTORIAL 1 2. Compute the work required to lift an object with mass 7 kg from the Earth’s surface to ‘outer space’. 1.Design a pulley that a strong person who weights 70 kg can use to lift a 700 kg object. 14 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.

15. TUTORIAL 1 6. How is biomechanics important for orthopaedics ? 15 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 ? 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). ? 7. What is Pascal’s law for fluid statics ?