Vectors.pdf
- 1. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.4 Scalars and Vectors • Scalar quantities are quantities that have magnitude only. Two examples are shown below: Measuring Mass Measuring Temperature
- 2. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.4 Scalars and Vectors • Scalar quantities are added or subtracted by using simple arithmetic. Example: 4 kg plus 6 kg gives the answer 10 kg + = 4 kg 6 kg 10 kg
- 3. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.4 Scalars and Vectors • Vector quantities are quantities that have both magnitude and direction Magnitude = 100 N Direction = Left A Force
- 4. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.4 Scalars and Vectors • Examples of scalars and vectors Scalars Vectors distance displacement speed velocity mass weight time acceleration pressure force energy momentum volume density
- 5. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.4 Scalars and Vectors Adding Vectors using Graphical Method • Parallel vectors can be added arithmetically 2 N 4 N 6 N 4 N 2 N 2 N
- 6. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.4 Scalars and Vectors Adding Vectors using Graphical Method • Non-parallel vectors are added by graphical means using the parallelogram law – Vectors can be represented graphically by arrows – The length of the arrow represents the magnitude of the vector – The direction of the arrow represents the direction of the vector – The magnitude and direction of the resultant vector can be found using an accurate scale drawing 5.0 cm 20.0 N Direction = right
- 7. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 • The parallelogram law of vector addition states that if two vectors acting at a point are represented by the sides of a parallelogram drawn from that point, their resultant is represented by the diagonal which passes through that point of the parallelogram 1.4 Scalars and Vectors
- 8. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.4 Scalars and Vectors Another method of Adding Vectors • To add vectors A and B – place the starting point of B at the ending point of A – The vector sum or resultant R is the vector joining the starting point of vector A to the ending point of B – Conversely, R can also be obtained by placing the starting point of A at the ending point of B – Now the resultant is represented by the vector joining the starting point of B to the ending point of A • See next slide
- 9. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.4 Scalars and Vectors A B A B A B
- 10. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1. Scalar quantities are quantities that only have magnitudes 2. Vector quantities are quantities that have both magnitude and direction 3. Parallel vectors can be added arithmetically 4. Non-parallel vectors are added by graphical means using the parallelogram law
- 11. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1
- 12. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.5 Measurement of Length and Time Accurate Measurement • No measurement is perfectly accurate • Some error is inevitable even with high precision instruments • Two main types of errors – Random errors – Systematic errors
- 13. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 1.5 Measurement of Length and Time Accurate Measurement • Random errors occur in all measurements. • Arise when observers estimate the last figure of an instrument reading • Also contributed by background noise or mechanical vibrations in the laboratory. • Called random errors because they are unpredictable • Minimize such errors by averaging a large number of readings • Freak results discarded before averaging
- 14. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 Accurate Measurement • Systematic errors are not random but constant • Cause an experimenter to consistently underestimate or overestimate a reading • They Due to the equipment being used – e.g. a ruler with zero error • may be due to environmental factors – e.g. weather conditions on a particular day • Cannot be reduced by averaging, but they can be eliminated if the sources of the errors are known 1.5 Measurement of Length and Time
- 15. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 Least count of instruments The smallest value that can be measured by the measuring instrument is called its least count or resolution.
- 16. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 LC of length measuring instruments Least count = 1 mm Ruler scale Vernier Calliper Least count = 0.1 mm
- 17. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 Least count = 0.01 mm Screw Gauge Spherometer Least count = 0.01 mm LC of length measuring instruments
- 18. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 Least count = 1 kg Weighing scale Electronic balance Least count = 1 g LC of length measuring instruments
- 19. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 Least count = 1 s Wrist watch Stopwatch Least count = 0.01 s LC of length measuring instruments
- 20. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 Length • Measuring tape is used to measure relatively long lengths • For shorter length, a metre rule or a shorter rule will be more accurate 1.5 Measurement of Length and Time
- 21. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 • Correct way to read the scale on a ruler • Position eye perpendicularly at the mark on the scale to avoids parallax errors • Another reason for error: object not align or arranged parallel to the scale 1.5 Measurement of Length and Time
- 22. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 • Many instruments do not read exactly zero when nothing is being measured • Happen because they are out of adjustment or some minor fault in the instrument • Add or subtract the zero error from the reading shown on the scale to obtain accurate readings • Vernier calipers or micrometer screw gauge give more accurate measurements 1.5 Measurement of Length and Time
- 23. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1
- 24. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1
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