1. USC2001 Energy Lecture 1 Energy and Work
Wayne M. Lawton
Department of Mathematics
National University of Singapore
2 Science Drive 2
Singapore
Tel (65) 1

2. 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

3. 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. 4 WORK IS ENERGY [1] Appendix: PIE
(old form 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. 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. 6 ARCHIMEDES “ Give me a place to stand and I will move the Earth”
lightweight braggart
load arm
Earth
effort arm
fulcrum
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. 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? 7

8. 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. 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

10. 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

11. 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

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. 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

15. 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