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SSCP 1143 : MECHANICSSSCP 1143 : MECHANICS

DR. RAMLI BIN ARIFIN

Week Topic

Week 11. Units, Physical QuantitiesBasic and Derived quantities, units & standards, systems of units, conversion of units, dimensional analysis.

Week 2 2. Motion in Two dimensionsDisplacement, velocity and acceleration

Week 3 Free-fall, Projectile.3 ' f iWeek 4 3. Newton's Laws of MotionForce and interactions, Newton's 1st, 2nd and 3rd law of motion.

Week 5 4. Application of Newton's LawsParticles in equilibrium, tension in a rope, lifts, frictional forces.

Week 6 5. Work and Kinetic EnergyWork, Kinetic energy and Work-Energy theorem, Power.

Week 76. Potential Energy and Conservation of EnergyGravitational potential energy, Conservative and non-conservativeWeek 7 Gravitational potential energy, Conservative and non conservative forces, Law of conservation of energy.

Week 87. Momentum, Impuls and CollisionsMomentum, impulse, Conservation of momentum, Elastic and inelastic collisions.

Week 9 MID-TERM HOLIDAYS

Week 10 8. Rotation of Rigid BodiesAngular velocity and acceleration, Energy in rotational motion.

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Week 119. Dynamics of Rotational motionTorque, angular acceleration, Work and Power in rotational motion, angular momentum, conservation of angular momentum.

Week 1210. Equilibrium and ElasticityEquilibrium conditions, centre of gravity, Young's modulus, Shear modulus and Bulk modulus

Week 1311. GravitationNewton's law of gravitation, g value, weight, Satellites, Kepler's law, Apparent weight, weightlessness.

Week 1412. Periodic MotionOscillation, Simple harmonic motion, equations of SHM, Energy in SHM, Physical pendulum.

13 Fl id M h i

Week 15

13. Fluid MechanicsDensity, relative density, pressure in a fluid, Pascal's law, measurement of pressure, buoyancy, continuity equation, Bernoulli's equation, viscosity.

Week 16 Study leave

Week 17-19 Examination weeks

References

1. Young and Freedman, Sears and Zemansky's University Physics(with Modern Physics), Pearson Int. Edition, 12th Edition.1999.

2 James S Walker PHYSICS Second Edition Pearson and Prentice2. James S.Walker, PHYSICS, Second Edition., Pearson and Prentice Hall.2009

3. Fishbane, Gasiorowicz & Thornton, PHYSICS FOR SCIENTISTS & ENGINEERS, Extended Version, Prentice Hall. 2004.

4. Giambattista, Richardson and Richardson, PHYSICS, 2nd Edition, McGraw Hill. 2008.

5. Halliday Resnick & Walker, FUNDAMENTALS OF PHYSICS, Eighth Edition, Wiley. 2008

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Assessment

No Type of Assessment Number % each % total Date

1 Quiz W3 W101 Quiz 2 5 10 W3, W10

2 Test 2 15 30 W7, W13

3 Assignment 2 5 10 W4, 15

4 Final Examination 1 50 50 W17-19

Total 100Total 100

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Measurement and Uncertainty; Significant FiguresNo measurement is exact; there is always some uncertainty due to limited

MEASUREMENTS AND UNITS

No measurement is exact; there is always some uncertainty due to limited instrument accuracy and difficulty reading results.

The photograph to the left illustrates this– it would be difficult to measure thewidth of this board more accurately than± 1 mm.

The uncertainty is about ±1 mm.

Estimated uncertainty is written with a ± sign; for example:8.8 ± 0.1 cm.

Percent uncertainty is the ratio of the uncertainty to the measured value, multiplied by 100:

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The number of significant figures is the number ofreliably known digits in a number. It is usually possibleto tell the number of significant figures by the way thenumber is written:

23.21 cm has four significant figures.

0.062 cm has two significant figures (the initial zeroesdon’t count).

80 km is ambiguous—it could have one (roughly) ortwo significant figures . If it has three, it should bewritten 80 0 kmwritten 80.0 km.

When multiplying or dividing numbers, the result has asmany significant figures as the number used in thecalculation with the fewest significant figures.calculation with the fewest significant figures.

Example: 11.3 cm x 6.8 cm = 76.84 cm2

≈ 77 cm2.

When adding or subtracting, the answer is no moreaccurate than the least accurate number used.

3.6 – 0.57 = 3.0 (not 3.03)

The number of significant figures may be off by one; usethe percentage uncertainty as a check.

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Calculators will not give you the right number ofsignificant figures; they usually give too many but

ti i t f ( i ll if th t ilisometimes give too few (especially if there are trailingzeroes after a decimal point).

The top calculator shows the result of 2.0/3.0.

The proper answer is 0.67

The bottom calculator shows the result of 2.5 x 3.2.The proper answer is 8.0

Using a protractor, you measure an angle to be 30°.(a) How many significant figures should you quote inthis measurement? (two) (b) Use a calculator to findth i f th l dthe cosine of the angle you measured.Cos 30° = 0.866025

Correctly given by 0.87

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Scientific notation is commonly used in physics; it allowsthe number of significant figures to be clearly shown.g g y

For example, we cannot tell how many significant figuresthe number 36,900 has. However, if we write 3.69 x 104,we know it has three; if we write 3.690 x 104, it has four.

Much of physics involves approximations; these can affectthe precision of a measurement also.

Accuracy vs. Precision

Accuracy is how close a measurement comes to the truevalue.

Precision is the repeatability of the measurement using thesame instrument.

It is possible to be accurate without being precise and tobe precise without being accurate!

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Units, Standards, and the SI SystemQuantity Unit StandardLength Meter Length of the path traveled

by light in 1/299,792,458 y g , ,second

Time Second Time required for 9,192,631,770 periods of radiation emitted by cesium atoms

Mass Kilogram Platinum cylinder in International Bureau of Weights and Measures, Paris

The values of a quantities issometimes a very large or very smallnumber. It is convenient to introducelarger or smaller units that are related

h l i b l i l fto the normal units by multiples often

These are the standard SIprefixes for indicating powers of10. Many are familiar; yotta, zetta,exa, hecto, deka, atto, zepto, andyocto are rarely used.

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We will be working in the SI system, in which the basicunits are kilograms, meters, and seconds. Quantities notin the table are derived quantities, expressed in terms ofthe base units.the base units.

Other systems: cgs; units are centimeters, grams, and seconds.

British engineering system hasforce instead of mass as one ofits basic quantities, which arefeet, pounds, and seconds.

SI CGS BELengthMass

meter (m)kilogram (kg)

centimeter (cm)gram (g)

foot (ft)slug (sl)Mass

TimeElectric currentTemperatureAmount of

kilogram (kg)second (s)

ampere (A)kelvin (K)

gram (g)second (s)

slug (sl)second (s)

substanceLuminous intensity

mole (mol)

candela (cd)

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•The base units are used along with various laws to defineadditional units for other important physical quantities referred asderived units.D i d i bi i f h b i E l f•Derived units are combinations of the base units. Example: force

[N], energy [J]

Converting UnitsTo convert a number from one unit to another, multiply thenumber by the ratio of the two units (conversion factor).

Unit conversions always involve a conversion factor.

Example: 1 in. = 2.54 cm.

Written another way: 1 = 2.54 cm/in.

So if we have measured a length of 21.5 inches, and wishto convert it to centimeters, we use the conversion factor:

•Example: to convert 979 meters to feet, multiply 979 meters by thefactor (3.281foot/1 meter)•Problem: 1 m is equivalent to 3.281 ft. A cube with an edge of 1.5 fthas a volume of: [Answer: 9.6 x 10-2m3]

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Dimensions and Dimensional AnalysisDimensions of a quantity are the base units that make itup; they are generally written using square brackets.

The term dimension is used to refer to the physical nature of aquantity and the type of unit used to specify it. Three suchquantity and the type of unit used to specify it. Three suchdimensions are length [L], time [T] and mass [M].

Many physical quantities can be expressed in terms of acombination of fundamental dimensions such as [L], [T] and[M].

Example: Speed = distance/time

Dimensions of speed: [L/T]

Quantities that are being added or subtracted must havethe same dimensions. In addition, a quantity calculated asthe solution to a problem should have the correctdimensions.

Dimensional analysis is the checking of dimensions of allquantities in an equation to ensure that those which areadded, subtracted, or equated have the same dimensions.

Example: Is this the correct equation for velocity?

Check the dimensions:

Wrong!

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•Dimensional analysis is used to check mathematical relations forthe consistency of their dimension.•By checking the quantities on both sides of the equals sign towhether they have the same dimensions. If the dimensions are notsame, the relation is incorrect.

•Example:

•Problem: During a short interval of time the speed v in m/s of anautomobile is given by v = at2 + bt3, where the time t is in seconds.The units of a and b are respectively:[ Answer: m/s3; m/s4][ Answer: m/s ; m/s ]

•Problem: Suppose A = BC, where A has the dimension L/M andC has the dimension L/T. Then B has the dimension:[Answer: T/M]

•Suppose A = BnCm, where A has dimensions LT, B hasdimensions L2T−1, and C has dimensions LT2. Then the exponentsn and m have the values:[ Answer : 1/5; 3/5]