Chapter 1 units,physicalquantities and vectors
- 1. CHAPTER 1 UNITS, PHYSICAL QUANTITIES AND VECTORS ENGR. PAOULO H. DEVEGA ME Department
- 2. WHAT IS PHYSICS? Is a branch of science traditionally defined as the study of matter, energy, and the relation between them; it was called natural philosophy until the late 19th century and is still known by this name at a few universities. Physics (from the Greek, phusikos, "natural", and phusis, "nature") is the science of nature in the broadest sense. INTRODUCTION
- 3. WHAT IS PHYSICS? Physics is in some senses the oldest and most basic pure science; its discoveries find applications throughout the natural sciences, since matter and energy are the basic constituents of the natural world.The other sciences are generally more limited in their scope and may be considered branches that have split off from physics to become sciences in their own right. INTRODUCTION
- 4. •Scientific notation is simply a method for expressing, and working with, very large or very small numbers. It is a short hand method for writing numbers, and an easy method for calculations. This is made possible with the use of powers of ten notation called exponential notation • Mass of earth = 5 970 000 000 000 000 000 000 000 000 kg = 5.97 x 1027 kg ( in scientific notation) • Mass of electron = 0.000 000 000 000 000 000 000 000 000 000 911 kg = 9.11 x 10-31 kg ( in scientific notation) Fundamental Tools Needed in Studying PhysicsScientific notation
- 5. Some simple rules govern the use of significant figures. 1. Nonzero digits are always significant. Examples: 38.47 mL has four significant figures. 369 g has three significant figures 2. Zeroes are sometimes significant, and sometimes they are not. a. Zeroes at the beginning of a number ( used just to position the decimal point ) are never significant. Examples: 0.023 g has two significant figures. 0.00596 m has three significant figures. b. Zeroes between nonzero digits are always significant. Examples: 3007 g has four significant figures. 8.03 km has three significant figures Fundamental Tools Needed in Studying PhysicsSignificant Figures
- 6. c. Zeroes at the end of a number that contains a decimal point are always significant. Examples: 47.0 cm has three significant figures. 440.0 m has four significant figures. d. Zeroes at the end of a number that does not contain a decimal point may or may not be significant. Examples: 24 300 km could represent three, four, or five significant figures. If written as 2.43 x 104 km, it has three significant figures. If written as 2.430 x 104 km, it has four significant figures. If written as 2.4300 x 104 km, it has five significant figures. Fundamental Tools Needed in Studying PhysicsSignificant Figures
- 7. 3. When numbers are added/subtracted, the number of decimal places in the result equal the smallest number of decimal places of any term in the sum/difference. Examples: Add 37.24 mL and 10.3 mL 37.24 mL + 10.3 mL 47.54 mL is reported as 47.5 mL 4. When numbers are multiplied or divided, the number of significant figures in the result can be no greater than in the factor with the fewest significant figures. Examples: 3.1416 x 2.34 x 0.58 = 4.3 Fundamental Tools Needed in Studying PhysicsSignificant Figures Subtract 21.2342 g from 27.87 g 27.87 g - 21.2342 g 6.6358 g is reported as 6.64 g
- 8. Fundamental and Derived Quantities Fundamental quantities are physical quantities which cannot anymore be expressed in terms of other quantities. In mechanics, these are length , mass and time. Derived quantities are quantities which are defined in terms of other quantities.They are combination of one or two or all of the fundamentals quantities. Examples are: area , volume , speed , density , velocity , acceleration , and force. DEFINITION
- 9. •Area – •Volume – •Speed /Velocity – •Acceleration – •Force – Can you name the fundamental quantities combined to derive these quantities? Fundamental and Derived Quantities
- 10. System of Units Commonly Used •Length – meter (m) • Mass – kilogram (kg) • time – second (s) System International (SI)
- 11. System of Units Commonly Used •Length – centimeter (cm) •Mass – gram (g) •time – second (s) The cgs or Gaussian system
- 12. System of Units Commonly Used •Length – foot (ft) • Mass – slug •time – seconds (s) English or British system/ US Customary system (USCS)
- 13. System of Units Commonly Used SI UNIT CGS ENGLISH UNIT LENGTH Meter (m) Centimeter (cm) Foot (ft) MASS Kilogram (kg) Gram (g) slug TIME Second (s) Second (s) Second (s) Comparison
- 14. Prefix Meaning Symbol Tera 1012 T Giga 109 G Mega 106 M Kilo 103 k Centi 10-2 c Milli 10-3 m Micro 10-6 Nano 10-9 n Common Prefixes Used in the Metric System System of Units NOTE: In the metric system, various units are related by factors of ten.This makes conversion from one unit to another easy to handle within the metric system.
- 15. System of Units Conversion of Units If the statement of a problem includes a mixture of different units, the units must be converted to a single ,consistent set before the problem is solved. Quantities to be added or subtracted must be expressed in the same units. • Units of length 1 mile = 5280 ft 1 in. = 2.54 cm 1 m = 100 cm 1 ft = 12 in. 1 km = 1000 m • Units of mass: 1 kg = 1000 g = 0.06852 slug = 2.205 lb • Units of time: 1 min = 60 sec 1 hr = 3600 sec
- 16. • The world land speed record is 763.0 mi h, set on October 15, 1997, by Andy Green in the jet-engine carThrust SSC. Express this speed in meters per second. ANS. 341.0 m/s • The world’s largest cut diamond is the First Star of Africa (mounted in the British Royal Sceptre and kept in theTower of London). Its volume is 1.84 cubic inches. What is its volume in cubic centimeters? In cubic meters? Ans. 30.2 cubic cm. System of Units Conversion of Units
- 17. Scalar Quantities Physical quantities having MAGNITUDE only. Examples: distance – 5 km mass – 3 kg Speed – 60 km / h area – 225 m2 Time – 18 sec temperature – 32 oC
- 18. Vector Quantities Quantities having MAGNITUDE AND DIRECTION. Examples: Displacement – 5 km east Velocity – 60 km/h southward Acceleration – 30 m/s2 upward Force – 100 N west
- 19. Scalar Operations Addition and Subtraction Scalar quantities are added or subtracted arithmetically. Only similar quantities are added or subtracted and they must be expressed in the same unit.
- 20. Vector Quantities Graphical Representation of Vectors A vector is graphically represented by arrow. The length of the arrow ( measured from tail to tip ) with respect to some chosen scale indicates the magnitude or size of the vector, while the direction to which the arrow points indicates the direction.
- 21. 1.Rectangular Coordinate Reference Frame The direction of a given vector is specified by an angle measured with respect to the x – and y – axes. 2.Geographic Reference Frame The angle is measured with respect to the N-S and W-E axes. Vector Quantities Reference Frames
- 22. Vector Quantities EXAMPLES :Reference Frames RECTANGULAR COORDINATE: A: 30 m , 40 0 counterclockwise from the + x axis B: 40 m , 30 0 clockwise from the - x axis GEOGRAPHIC: A: 30 m , 40o N of E B: 40 m , 30o N ofW
- 23. ►Equal vectors Two or more vectors are said to be equal if they have the same magnitude and the same direction. ►Resultant It is that single vector which would produce the same effect as the original vectors taken together. Mathematically, the resultant is the sum of two or more vectors. Vector Quantities Vector Addition
- 24. Example: 1.) 30o N of E is equivalent to 60o E of N 2. )The direction of 40o counterclockwise from the (+) x-axis is equivalent to the following a) 50o Clockwise from the (+) y-axis b) 130o Counterclockwise from the (-) y-axis c) 140o Clockwise from the (-) x-axis Vector Quantities EQUAL VECTORS
- 25. A. Graphical Method The vectors to be added are drawn to a convenient scale in their specified directions. a. Parallelogram Method (tail to tail) b. Polygon Method (tail to tip) B. Analytical Method In this method the vectors need not be drawn to scale. a. Method ofTrigonometry b. Component Method Vector Quantities Methods of Finding the Resultant
- 26. In this method, the vectors are drawn tail to tail. Step 1: Using a scale 10 m = 1 cm , draw the vectors from a common point O. Step 2: Using these two vectors , draw a parallelogram of which the given vectors are two adjacent sides of the said parallelogram. Step 3: Draw the diagonal of the parallelogram from the common point O.This diagonal is the resultant R of the vectors A and B. Step 4: To determine the magnitude of R, measure the length of R using a ruler.Then, convert this measurement to the desired unit. Step 5: To specify the direction of R, measure the smallest angle that R makes with the horizontal using a protractor. Step 6: Combine the results from the steps 4 and 5 to state the final answer. Graphical Method Parallelogram Method
- 27. • In this method, the vectors are drawn successively ( tail to tip ) keeping their magnitude and directions unchanged.The vectors are drawn in any order. • The closing side of the polygon is the resultant R in which its tail coincides with the tail of the first vector drawn and the tip of its arrowhead coincides with the tip of the last vector drawn.To find the magnitude and direction of R, measure the length of R and the smallest angle θ.( Same as in the parallelogram method) Graphical Method Polygon Method
- 28. • Using graphical method, find the resultant of the following two displacements: 2.0 m at 400 and 4.om at 1270, the angles being taken relative to the (+) x- axis, as is customary. Give your answer to two significant figures. • Four coplanar forces act on a body at point O as shown in the figure below. Find their resultant. Graphical Method SAMPLE PROBLEMS
- 29. Analytical Method Method of Trigonometry SINE LAW 𝑅 sin∝ = 𝐵 sin 𝛾 COSINE LAW 𝑅2 = 𝐴2 + 𝐵2 − 2𝐴𝐵𝑐𝑜𝑠𝛼
- 30. Method of Trigonometry Sample Problem Determine the resultant vector R, given the following displacement: A = 30 m 400 CW from (-) x- axis B = 40 m 300 CCW from the (+) x- axis Using method of trigonometry.
- 31. • The components of a given vector are the set of vectors whose sum is the given vector.They may be called the parts of the given vector.The components of a vector are determined by its projection on the x-axis and on the y-axis as shown in figure: Graphical Method Component method
- 32. Quadrant No. x-component y-component 2 negative (- ) positive (+ ) 3 negative (- ) negative ( - ) 4 positive ( + ) negative ( - ) Graphical Method Component method
- 33. What are the components of a vectorV = 300 km/h, 36o N ofW? Ans. Vx = - 242.71 km/h Vy = 176.34 km/h Determine the resultant of the following vectors. Use the component method. A: 19 N east B: 15 N , 60o N of E C: 16 N , 45o N ofW D: 11 N , 30o S ofW E: 22 N , South F: 10 N , 500 S of E Graphical Method Component method
- 34. It is a process of subtracting one vector from another vector. Finding the vector difference A – B is just the same as getting the sum of vector A and the negative vector of B.That is, A – B =A + ( - B ) Vector Quantities Vector Subtraction
- 35. Consider that A is 45 N 35o N of E and B is 30 N west. a. What is the negative of vector A? vector B? The negative of vector A is 40 N , 35o S ofW located in the third quadrant. The negative of vector B is 30 N east. b. Determine the magnitude and direction of the vector difference A – B. Use the parallelogram method ( scale: 10 N = 1 cm) Ans. A – B is 71.67 N , 21.11o N of E c. Check your answer using the method of trigonometry. Vector Quantities SEATWORK