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Mechanics
Mechanics
The branch of physics that deals with the
action of forces on bodies and with motion,
comprised of kinetics, statics, and
kinematics.
Vector and Scalar Quantities
In your study of physics, you will encounter scalar and
vector 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
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.
Some quantities are expressed as (a number and a unit
of measure) only.      These quantities are called
SCALAR.
Quantities that are expressed by a magnitude and
direction are called VECTORS
VECTOR is represented by an arrow. The arrow has
three 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
The Direction Guide
Example 1:
  The ship sails 25 km north.
            N

                 d = 25 km




Vector diagram

                             Given: d= 25km north
                             Scale: 1 cm = 10 km
Example 2:
The ship sails 20 km south, then 15 km east.
                                         d1 = 20km
Given: d1 = 20km south
       d2 = 15km east
Scale: 1 cm = 10 km
         N
                                     d2 = 15km



W                           E
    d1 = 20km


                    d2 = 15km
                S
Resultant Vector
Scalar quantities can be added and subtracted like
ordinary numbers provided the scalars have the same
unit.
For vectors, the sum depends on the direction of the
vectors.
The sum of two or more vectors is represented by a
single vector called RESULTANT.

This vector may be found by using the Graphical
method, the Pythagorean theorem, or the component
method.
Graphical Method
Carlito was observing an ant that crawled along a
tabletop. With a piece of chalk, he followed its path.
He determined the ant’s displacements using a ruler
and protractor. The displacement were as follows:
2cm east; 3.5cm,320 north of east; and 2.3 cm, 220 west
of north.
Given:
      d1 = 2 cm east
      d2 = 3.5 cm, 320 north of east
      d3 = 2.3 cm, 220 west of north
      dR = ?
Given:
                           d1 = 2 cm east
Solution:                  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 cm

W                                                     E
Assignment:

Given the following displacement find the resultant
displacement:
       d1 = 3.5 cm, 320 north of east
       d2 = 2.3 cm, 220 west of north
       d3 = 2 cm east




Answer:
     dr = 5.5 cm, 420 north of east.
Pythagorean Theorem
A plane flying due north at 100 m/s is
blown 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
                                               vr

c2 = a2 + b2                       Scale: 1cm = 100 m

vR2 = v1 2 + b2 2
vR2 = (100m/s) 2 + (500m/s) 2
vR = 509.90 m/s
To determine the direction of the resultant velocity, use the
equation:
      tan Ø = opposite side / adjacent side

       tan Ø = 100m/s / 500m/s

             = 0.2

       tan Ø = 0.2
             = 11.310 north of east

vR = 509.90 m/s, 11.310 north of east
Kinematics
Motion may be defined as a continuous change of position
with respect to a certain reference point.



                       Down -                     Up +
Speed and Velocity


Speed is scalar quantity, it represents the rate
of change of displacement.


It represents only the magnitude of velocity.


Most vehicles have a device called a
SPEEDOMETER which measures speed.
Average Speed (vs)
The average speed may be defined as the
total distance traveled divided by the time it
took to travel this distance.
                                      distance
          vs =         d
Average                t               time




    Average speed
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

                                      distance
average
                                      time
 velocity          change
A car travels a distance of 40km from manila to a
town in Quezon. What is its average speed in
(km/h) if traveling time is from 7:00am to
7:30am? Its average velocity? (km/h)
        Average speed
        Given:
        d= 40 km
        t = 7:00am to 7:30 am
          = 30 minutes

vs = d / t                1.3km/min x 60 min/h
   = 40km / 30 min        = 78 km/h
   = 1.3 km/min
A car travels a distance of 40km from manila to a
town in Quezon. What is its average speed in
(km/h) if traveling time is from 7:00am to
7:30am? Its average velocity? (km/h)
        Average velocity
        Given:
        d= 40 km
        t = 7:00am to 7:30 am
          = 30 minutes

v =d/t                     1.3km/min x 60 min/h
  = 40km / 30 min          = 78 km/h from Manila
  = 1.3 km/min             to Quezon
Acceleration
Acceleration is a vector quantity since it involves
a change in velocity which is vector.
An increase or decrease in the magnitude of
velocity is called acceleration although the word
deceleration is sometimes used to indicate a
decrease in the magnitude of velocity.
The average acceleration of an object may be
defined as:
                       Change in velocity
Average acceleration =   Elapsed time
Initial   final velocity
     velocity
                               change




                     Final time
  Average
acceleration    initial time
What is the average acceleration of the car in the
    figure:
     0s          1s           2s            3s           4s          5s         6s
Start, 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
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.
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                    Velocity

Kinetic energy         mass
A 98-kg basketball player runs at a speed of 7
m/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.
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 height
GPE = mgh      of an object above the earth’s
               center of gravity.
mass     height
Gravity (9.8m/s2 )
Types of Potential Energy
      b) Chemical energy
           the energy possessed by the
atoms or molecules of a substance and
is released or changed into another
forms when the substance is involved in
a chemical reaction.
           this energy depends on the
composition of the substance.
Types of Potential Energy
      c. Elastic Potential Energy
            this is the energy possessed
by an object like a spring or any other
elastic materials due to its condition.
            The energy depends on the
average required to compress it and the
distance from its normal length

Elastic Potential Energy = kx2 / 2
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
For example, when the fuel used by a thermal
power plant is burned, its chemical energy is
converted into heat energy.
The heat produced causes the water to boil
and can be converted into steam.
The energy of the steam is transformed in the
steam turbine to mechanical energy.
This energy is changed in the generator to
electrical energy which is distributed to the
consumers.
The electrical energy is converted into light
energy in electrical lamps, sound energy in a
radio, or heat energy in an electric stove.
Heat
Sources of Heat
A. Natural Sources
           a) The Sun
           b) The interior of the Earth
B. Artificial Sources
           a) Chemical Action
           b) Mechanical Action
           c) Electrical Energy
           d) Nuclear energy
Effects of Heat
Heat 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.
Electricity
   and
Magnetism
Electrical Nature of Matter
When a glass rod is rubbed with silk, some of the free
moving electrons in the glass transfer to the silk cloth.
This breaks the neutral state of both the glass rod and
the silk.
The rod becomes deficient in electrons and is said to be
positively charged.
The silk having gained the electrons lost by the rod, has
an excess of electrons and becomes negatively charged.
In the example given, the number of proton remains the
same throughout.
The object never lose or gain proton.
An object becomes charged with whatever particles it
has in excess.
The Coulomb’s Law
The first Law of Electrostatics states that: Like
charges repel and unlike charges attract.

How large is this charge that repels or attracts?

The quantity of charge in the SI system is
expressed in Coulombs ( C ), named after
Charles Augustine de Coulomb.
     1 coulomb = 6.25x1018 electrons
                       q1 q 2     Measured in
                  F=k             Coulomb
  9x109 N.m2 /C2         d2      Distance in meter
If q1 has a positive charge and q2 a negative
charged, F will therefore be a force of
attraction which will bring the two bodies
closer to each other.

If q1 and q2 are both negative charged
bodies, F will be a force of repulsion which
will make the two charged bodies move
away from each other.
The two objects are both negatively charged
with 0.02 C each and are 70 cm apart. What
kind of force exists between them and how
much?
     Given:
          q1 = q2 = -0.02 C
          d = 70 cm
            = 0.70 m
          k = 9 x 109 N.m2 /C2
Solution:
F = 9 X109 N.m2 /C2
x = (9x109 N.m2 ) (-0.02C) (0.02C) / (0.70m)2
x = 7.3x106 N (force of repulsion)
OHM’S LAW
The current flowing through a circuit is directly
proportional to the potential difference and
inversely proportional to the resistance of the
circuit.

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
What is the potential difference (emf) in an
electric circuit with a current of 15 amperes
and 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)

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mechanics

  • 2. Mechanics The branch of physics that deals with the action of forces on bodies and with motion, comprised of kinetics, statics, and kinematics.
  • 3. Vector and Scalar Quantities In your study of physics, you will encounter scalar and vector 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. 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. Some quantities are expressed as (a number and a unit of measure) only. These quantities are called SCALAR. Quantities that are expressed by a magnitude and direction are called VECTORS VECTOR is represented by an arrow. The arrow has three 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
  • 7. Example 1: The ship sails 25 km north. N d = 25 km Vector diagram Given: d= 25km north Scale: 1 cm = 10 km
  • 8. Example 2: The ship sails 20 km south, then 15 km east. d1 = 20km Given: d1 = 20km south d2 = 15km east Scale: 1 cm = 10 km N d2 = 15km W E d1 = 20km d2 = 15km S
  • 9. Resultant Vector Scalar quantities can be added and subtracted like ordinary numbers provided the scalars have the same unit. For vectors, the sum depends on the direction of the vectors. The sum of two or more vectors is represented by a single vector called RESULTANT. This vector may be found by using the Graphical method, the Pythagorean theorem, or the component method.
  • 10. Graphical Method Carlito was observing an ant that crawled along a tabletop. With a piece of chalk, he followed its path. He determined the ant’s displacements using a ruler and protractor. The displacement were as follows: 2cm east; 3.5cm,320 north of east; and 2.3 cm, 220 west of north. Given: d1 = 2 cm east d2 = 3.5 cm, 320 north of east d3 = 2.3 cm, 220 west of north dR = ?
  • 11. Given: d1 = 2 cm east Solution: 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 cm W E
  • 12. Assignment: Given the following displacement find the resultant displacement: d1 = 3.5 cm, 320 north of east d2 = 2.3 cm, 220 west of north d3 = 2 cm east Answer: dr = 5.5 cm, 420 north of east.
  • 13. Pythagorean Theorem A plane flying due north at 100 m/s is blown 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 vr c2 = a2 + b2 Scale: 1cm = 100 m vR2 = v1 2 + b2 2 vR2 = (100m/s) 2 + (500m/s) 2 vR = 509.90 m/s
  • 14. To determine the direction of the resultant velocity, use the equation: tan Ø = opposite side / adjacent side tan Ø = 100m/s / 500m/s = 0.2 tan Ø = 0.2 = 11.310 north of east vR = 509.90 m/s, 11.310 north of east
  • 15. Kinematics Motion may be defined as a continuous change of position with respect to a certain reference point. Down - Up +
  • 16. Speed and Velocity Speed is scalar quantity, it represents the rate of change of displacement. It represents only the magnitude of velocity. Most vehicles have a device called a SPEEDOMETER which measures speed.
  • 17. Average Speed (vs) The average speed may be defined as the total distance traveled divided by the time it took to travel this distance. distance vs = d Average t time Average speed
  • 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 distance average time velocity change
  • 19. A car travels a distance of 40km from manila to a town in Quezon. What is its average speed in (km/h) if traveling time is from 7:00am to 7:30am? Its average velocity? (km/h) Average speed Given: d= 40 km t = 7:00am to 7:30 am = 30 minutes vs = d / t 1.3km/min x 60 min/h = 40km / 30 min = 78 km/h = 1.3 km/min
  • 20. A car travels a distance of 40km from manila to a town in Quezon. What is its average speed in (km/h) if traveling time is from 7:00am to 7:30am? Its average velocity? (km/h) Average velocity Given: d= 40 km t = 7:00am to 7:30 am = 30 minutes v =d/t 1.3km/min x 60 min/h = 40km / 30 min = 78 km/h from Manila = 1.3 km/min to Quezon
  • 21. Acceleration Acceleration is a vector quantity since it involves a change in velocity which is vector. An increase or decrease in the magnitude of velocity is called acceleration although the word deceleration is sometimes used to indicate a decrease in the magnitude of velocity. The average acceleration of an object may be defined as: Change in velocity Average acceleration = Elapsed time
  • 22. Initial final velocity velocity change Final time Average acceleration initial time
  • 23. What is the average acceleration of the car in the figure: 0s 1s 2s 3s 4s 5s 6s Start, 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. 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. 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 Velocity Kinetic energy mass
  • 26. A 98-kg basketball player runs at a speed of 7 m/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. 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 height GPE = mgh of an object above the earth’s center of gravity. mass height Gravity (9.8m/s2 )
  • 28. Types of Potential Energy b) Chemical energy the energy possessed by the atoms or molecules of a substance and is released or changed into another forms when the substance is involved in a chemical reaction. this energy depends on the composition of the substance.
  • 29. Types of Potential Energy c. Elastic Potential Energy this is the energy possessed by an object like a spring or any other elastic materials due to its condition. The energy depends on the average required to compress it and the distance from its normal length Elastic Potential Energy = kx2 / 2
  • 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. For example, when the fuel used by a thermal power plant is burned, its chemical energy is converted into heat energy. The heat produced causes the water to boil and can be converted into steam. The energy of the steam is transformed in the steam turbine to mechanical energy. This energy is changed in the generator to electrical energy which is distributed to the consumers. The electrical energy is converted into light energy in electrical lamps, sound energy in a radio, or heat energy in an electric stove.
  • 32. Heat
  • 33. Sources of Heat A. Natural Sources a) The Sun b) The interior of the Earth B. Artificial Sources a) Chemical Action b) Mechanical Action c) Electrical Energy d) Nuclear energy
  • 34. Effects of Heat Heat 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. Electricity and Magnetism
  • 36. Electrical Nature of Matter When a glass rod is rubbed with silk, some of the free moving electrons in the glass transfer to the silk cloth. This breaks the neutral state of both the glass rod and the silk. The rod becomes deficient in electrons and is said to be positively charged. The silk having gained the electrons lost by the rod, has an excess of electrons and becomes negatively charged. In the example given, the number of proton remains the same throughout. The object never lose or gain proton. An object becomes charged with whatever particles it has in excess.
  • 37. The Coulomb’s Law The first Law of Electrostatics states that: Like charges repel and unlike charges attract. How large is this charge that repels or attracts? The quantity of charge in the SI system is expressed in Coulombs ( C ), named after Charles 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. If q1 has a positive charge and q2 a negative charged, F will therefore be a force of attraction which will bring the two bodies closer to each other. If q1 and q2 are both negative charged bodies, F will be a force of repulsion which will make the two charged bodies move away from each other.
  • 39. The two objects are both negatively charged with 0.02 C each and are 70 cm apart. What kind of force exists between them and how much? Given: q1 = q2 = -0.02 C d = 70 cm = 0.70 m k = 9 x 109 N.m2 /C2 Solution: F = 9 X109 N.m2 /C2 x = (9x109 N.m2 ) (-0.02C) (0.02C) / (0.70m)2 x = 7.3x106 N (force of repulsion)
  • 40. OHM’S LAW The current flowing through a circuit is directly proportional to the potential difference and inversely proportional to the resistance of the circuit. 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. What is the potential difference (emf) in an electric circuit with a current of 15 amperes and 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)