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### mechanics

1. 1. Mechanics
2. 2. MechanicsThe branch of physics that deals with theaction of forces on bodies and with motion,comprised of kinetics, statics, andkinematics.
3. 3. Vector and Scalar QuantitiesIn your study of physics, you will encounter scalar andvector quantities.Examples of Vector quantities 1. Displacement: An airplane flies a distance of 100 km in a easterly direction. 2. Velocity A car moves 60 km/h, 350 east of north. 3. Force A force of 15 newtons acts on a body in an upward direction
4. 4. Examples of Scalar quantities 1. Mass A load has a mass of 5 kg 2. Time The car has reached its destination after 1 hour 3. Distance The train has traveled a distance of 80 km.
5. 5. Some quantities are expressed as (a number and a unitof measure) only. These quantities are calledSCALAR.Quantities that are expressed by a magnitude anddirection are called VECTORSVECTOR is represented by an arrow. The arrow hasthree important parts: 1. Arrowhead – indicates the direction of the vector. 2. Length of the arrow – represents the magnitude of the vector 3. Tail – represents the origin of the vector
6. 6. The Direction Guide
7. 7. Example 1: The ship sails 25 km north. N d = 25 kmVector diagram Given: d= 25km north Scale: 1 cm = 10 km
8. 8. Example 2:The ship sails 20 km south, then 15 km east. d1 = 20kmGiven: d1 = 20km south d2 = 15km eastScale: 1 cm = 10 km N d2 = 15kmW E d1 = 20km d2 = 15km S
9. 9. Resultant VectorScalar quantities can be added and subtracted likeordinary numbers provided the scalars have the sameunit.For vectors, the sum depends on the direction of thevectors.The sum of two or more vectors is represented by asingle vector called RESULTANT.This vector may be found by using the Graphicalmethod, the Pythagorean theorem, or the componentmethod.
10. 10. Graphical MethodCarlito was observing an ant that crawled along atabletop. With a piece of chalk, he followed its path.He determined the ant’s displacements using a rulerand protractor. The displacement were as follows:2cm east; 3.5cm,320 north of east; and 2.3 cm, 220 westof north.Given: d1 = 2 cm east d2 = 3.5 cm, 320 north of east d3 = 2.3 cm, 220 west of north dR = ?
11. 11. Given: d1 = 2 cm eastSolution: d2 = 3.5 cm, 320 north of east d3 = 2.3 cm, 220 west of north dR = ? N 220 ___0 d3 = 2.3 cm dr = 320 d2 = 3.5 cmW E
12. 12. Assignment:Given the following displacement find the resultantdisplacement: d1 = 3.5 cm, 320 north of east d2 = 2.3 cm, 220 west of north d3 = 2 cm eastAnswer: dr = 5.5 cm, 420 north of east.
13. 13. Pythagorean TheoremA plane flying due north at 100 m/s isblown by a 500 m/s strong wind due east.What is the plane’s resultant velocity? Given: v2 v1 = 100 m/s north v2 = 500 m/s east v1 vrc2 = a2 + b2 Scale: 1cm = 100 mvR2 = v1 2 + b2 2vR2 = (100m/s) 2 + (500m/s) 2vR = 509.90 m/s
14. 14. To determine the direction of the resultant velocity, use theequation: tan Ø = opposite side / adjacent side tan Ø = 100m/s / 500m/s = 0.2 tan Ø = 0.2 = 11.310 north of eastvR = 509.90 m/s, 11.310 north of east
15. 15. KinematicsMotion may be defined as a continuous change of positionwith respect to a certain reference point. Down - Up +
16. 16. Speed and VelocitySpeed is scalar quantity, it represents the rateof change of displacement.It represents only the magnitude of velocity.Most vehicles have a device called aSPEEDOMETER which measures speed.
17. 17. Average Speed (vs)The average speed may be defined as thetotal distance traveled divided by the time ittook to travel this distance. distance vs = dAverage t time Average speed
18. 18. Average Velocity (v) Another difference between speed and velocity is that the magnitude of the average velocity is calculated in terms of displacement rather than total distance traveled distanceaverage time velocity change
19. 19. A car travels a distance of 40km from manila to atown in Quezon. What is its average speed in(km/h) if traveling time is from 7:00am to7:30am? Its average velocity? (km/h) Average speed Given: d= 40 km t = 7:00am to 7:30 am = 30 minutesvs = d / t 1.3km/min x 60 min/h = 40km / 30 min = 78 km/h = 1.3 km/min
20. 20. A car travels a distance of 40km from manila to atown in Quezon. What is its average speed in(km/h) if traveling time is from 7:00am to7:30am? Its average velocity? (km/h) Average velocity Given: d= 40 km t = 7:00am to 7:30 am = 30 minutesv =d/t 1.3km/min x 60 min/h = 40km / 30 min = 78 km/h from Manila = 1.3 km/min to Quezon
21. 21. AccelerationAcceleration is a vector quantity since it involvesa change in velocity which is vector.An increase or decrease in the magnitude ofvelocity is called acceleration although the worddeceleration is sometimes used to indicate adecrease in the magnitude of velocity.The average acceleration of an object may bedefined as: Change in velocityAverage acceleration = Elapsed time
22. 22. Initial final velocity velocity change Final time Averageacceleration initial time
23. 23. What is the average acceleration of the car in the figure: 0s 1s 2s 3s 4s 5s 6sStart, v = 0 v1 = 5km/h v2 = 10km/h v3 = 15km/h v4 = 20km/h v5 = 25km/h v6 = 30km/h Given: v=0 v0 = 30km/h t=0 = 30 km/h – 0 / 6 s – 0 t0 = 6 s = 5 km/h/s
24. 24. Energy Energy is the capacity to do work. Energy can exists in many forms. The chemical energy in a battery is changed into electrical energy that runs the engine motor. The engine motor converts the electrical energy into mechanical energy by making the other parts of the engine work to make the car move.
25. 25. Kinetic Energy Energy possess by any moving object. The work done by the moving object is equal to the change in its kinetic energy. 1 KE = mv2 2 VelocityKinetic energy mass
26. 26. A 98-kg basketball player runs at a speed of 7m/s. a) what is his KE? Given: mass = 98-kg v = 7 m/s KE = ? KE = ½ mv2 = (1) (98-kg) (7 m/s)2 / 2 = 2,401 Joules.
27. 27. Potential Energy Energy possess by any object at rest. Types of Potential Energy a) Gravitational Potential Energy Energy possess by an object due to its position. It is determined by the heightGPE = mgh of an object above the earth’s center of gravity.mass heightGravity (9.8m/s2 )
28. 28. Types of Potential Energy b) Chemical energy the energy possessed by theatoms or molecules of a substance andis released or changed into anotherforms when the substance is involved ina chemical reaction. this energy depends on thecomposition of the substance.
29. 29. Types of Potential Energy c. Elastic Potential Energy this is the energy possessedby an object like a spring or any otherelastic materials due to its condition. The energy depends on theaverage required to compress it and thedistance from its normal lengthElastic Potential Energy = kx2 / 2
30. 30. Law of Conservation of Energy “Energy can neither be created nor destroyed but can only be changed from one form to another.”∆KE + ∆PE + ∆(other forms of energy) = 0
31. 31. For example, when the fuel used by a thermalpower plant is burned, its chemical energy isconverted into heat energy.The heat produced causes the water to boiland can be converted into steam.The energy of the steam is transformed in thesteam turbine to mechanical energy.This energy is changed in the generator toelectrical energy which is distributed to theconsumers.The electrical energy is converted into lightenergy in electrical lamps, sound energy in aradio, or heat energy in an electric stove.
32. 32. Heat
33. 33. Sources of HeatA. Natural Sources a) The Sun b) The interior of the EarthB. Artificial Sources a) Chemical Action b) Mechanical Action c) Electrical Energy d) Nuclear energy
34. 34. Effects of HeatHeat affects materials in various ways:1. When substance absorbed heat, its temperature rises.2. Solid usually melts or change to liquid state when heated.3. Liquid may absorb enough heat when heated to change to the vapor state.4. Almost all objects expands when heated.5. A change in the heat content of a substance can cause chemical change.6. Heat causes many changes in bodily functions of living organisms.
35. 35. Electricity andMagnetism
36. 36. Electrical Nature of MatterWhen a glass rod is rubbed with silk, some of the freemoving electrons in the glass transfer to the silk cloth.This breaks the neutral state of both the glass rod andthe silk.The rod becomes deficient in electrons and is said to bepositively charged.The silk having gained the electrons lost by the rod, hasan excess of electrons and becomes negatively charged.In the example given, the number of proton remains thesame throughout.The object never lose or gain proton.An object becomes charged with whatever particles ithas in excess.
37. 37. The Coulomb’s LawThe first Law of Electrostatics states that: Likecharges repel and unlike charges attract.How large is this charge that repels or attracts?The quantity of charge in the SI system isexpressed in Coulombs ( C ), named afterCharles Augustine de Coulomb. 1 coulomb = 6.25x1018 electrons q1 q 2 Measured in F=k Coulomb 9x109 N.m2 /C2 d2 Distance in meter
38. 38. If q1 has a positive charge and q2 a negativecharged, F will therefore be a force ofattraction which will bring the two bodiescloser to each other.If q1 and q2 are both negative chargedbodies, F will be a force of repulsion whichwill make the two charged bodies moveaway from each other.
39. 39. The two objects are both negatively chargedwith 0.02 C each and are 70 cm apart. Whatkind of force exists between them and howmuch? Given: q1 = q2 = -0.02 C d = 70 cm = 0.70 m k = 9 x 109 N.m2 /C2Solution:F = 9 X109 N.m2 /C2x = (9x109 N.m2 ) (-0.02C) (0.02C) / (0.70m)2x = 7.3x106 N (force of repulsion)
40. 40. OHM’S LAWThe current flowing through a circuit is directlyproportional to the potential difference andinversely proportional to the resistance of thecircuit.The first part of the law may be represented as I(current)  V (potential difference.The second law may be expressed as I  I/R Current or E Potential difference (emf) the rate of low I= Volts (V) of electricity R resistance in Ohms
41. 41. What is the potential difference (emf) in anelectric circuit with a current of 15 amperesand a resistance of 4.0 ohms? Given: I = 15 amperes R = 4.0 ohms V= ?Solution: I = E/R 15 A = E/ 4.0 Ώ E = 60 volts (emf)