mechanics
-
Upload
manuel-s-enverga-university-foundation -
Category
Education
-
view
542 -
download
1
Transcript of mechanics
![Page 1: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/1.jpg)
Mechanics
![Page 2: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/2.jpg)
The branch of physics that deals with the action of forces on bodies and with motion, comprised of kinetics, statics, and kinematics.
Mechanics
![Page 3: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/3.jpg)
Vector and Scalar Quantities In your study of physics, you will encounter
scalar and vector quantities.
Examples of Vector quantities1. Displacement:
An airplane flies a distance of 100 km in a easterly direction.
2. VelocityA car moves 60 km/h, 350 east of north.
3. ForceA force of 15 newtons acts on a body in an upward direction
![Page 4: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/4.jpg)
Examples of Scalar quantities
1. MassA load has a mass of 5 kg
2. TimeThe car has reached its destination after 1 hour
3. Distance
The train has traveled a distance of 80 km.
![Page 5: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/5.jpg)
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 VECTORSVECTOR 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
![Page 6: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/6.jpg)
The Direction Guide
![Page 7: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/7.jpg)
Example 1:
The ship sails 25 km north.
Given: d= 25km north Scale: 1 cm = 10 km
N
d = 25 km
Vector diagram
![Page 8: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/8.jpg)
Example 2:The ship sails 20 km south, then 15 km east.Given: d1 = 20km south d2 = 15km east Scale: 1 cm = 10 km
N
EW
S
d1 = 20km
d1 = 20km
d2 = 15km
d2 = 15km
![Page 9: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/9.jpg)
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.
![Page 10: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/10.jpg)
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 eastd2 = 3.5 cm, 320 north of eastd3 = 2.3 cm, 220 west of northdR = ?
![Page 11: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/11.jpg)
Solution:
N
WS
E
Given: d1 = 2 cm eastd2 = 3.5 cm, 320 north of
eastd3 = 2.3 cm, 220 west of
northdR = ?
320dr =
220 d3 = 2.3 cm
d2 = 3.5 cm
___0
![Page 12: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/12.jpg)
Assignment:
Given the following displacement find the resultant displacement:
d1 = 3.5 cm, 320 north of eastd2 = 2.3 cm, 220 west of northd3 = 2 cm east
Answer:dr = 5.5 cm, 420 north of east.
![Page 13: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/13.jpg)
Pythagorean TheoremA 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:v1 = 100 m/s
northv2 = 500 m/s
east Scale: 1cm = 100 m
v1
v2
vr
c2 = a2 + b2
vR2 = v1 2 + b2 2
vR2 = (100m/s) 2 +
(500m/s) 2 vR = 509.90 m/s
![Page 14: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/14.jpg)
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
![Page 15: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/15.jpg)
KinematicsMotion may be defined as a continuous change of position with respect to a certain reference point.
Up +
Down -
![Page 16: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/16.jpg)
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.
![Page 17: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/17.jpg)
Average Speed (vs)
The average speed may be defined as the total distance traveled divided by the time it took to travel this distance.
vs
=td
Average speed
Average
distance
time
![Page 18: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/18.jpg)
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
velocity
average
distance
time
change
![Page 19: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/19.jpg)
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 kmt = 7:00am to 7:30 am = 30 minutes
vs = d / t = 40km / 30 min = 1.3 km/min
1.3km/min x 60 min/h= 78 km/h
![Page 20: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/20.jpg)
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 kmt = 7:00am to 7:30 am = 30 minutes
v = d / t = 40km / 30 min = 1.3 km/min
1.3km/min x 60 min/h= 78 km/h from Manila to Quezon
![Page 21: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/21.jpg)
AccelerationAcceleration 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:
Average acceleration =
Change in velocityElapsed
time
![Page 22: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/22.jpg)
Average accelerati
on
Initial velocity
final velocity
initial time
Final time
change
![Page 23: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/23.jpg)
What is the average acceleration of the car in the figure:0 s 1 s 2 s 3 s 4 s 5 s 6 s
Start, v = 0
v1 = 5km/h
v2 = 10km/h
v3 = 15km/h
v4 = 20km/h
v5 = 25km/h
v6 = 30km/h
Given:v = 0v0 = 30km/ht = 0t0 = 6 s
= 30 km/h – 0 / 6 s – 0 = 5 km/h/s
![Page 24: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/24.jpg)
EnergyEnergy 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.
![Page 25: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/25.jpg)
Kinetic Energy Energy possess by any moving object.The work done by the moving object is equal to the change in its kinetic energy.
KE =1
2mv2
Kinetic energy
mass
Velocity
![Page 26: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/26.jpg)
A 98-kg basketball player runs at a speed of 7 m/s.
a) what is his KE?
Given:mass = 98-kgv = 7 m/s
KE = ?
KE = ½ mv2
= (1) (98-kg) (7 m/s)2 / 2 = 2,401 Joules.
![Page 27: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/27.jpg)
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 of an object above the earth’s center of gravity.
GPE = mghmass
Gravity (9.8m/s2 )
height
![Page 28: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/28.jpg)
Types of Potential Energyb) 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.
![Page 29: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/29.jpg)
Types of Potential Energyc. 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
![Page 30: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/30.jpg)
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
![Page 31: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/31.jpg)
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.
![Page 32: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/32.jpg)
Heat
![Page 33: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/33.jpg)
Sources of HeatA. Natural Sources
a) The Sunb) The interior of the Earth
B. Artificial Sourcesa) Chemical Actionb) Mechanical Actionc) Electrical Energyd) Nuclear energy
![Page 34: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/34.jpg)
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.
![Page 35: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/35.jpg)
Electricity and
Magnetism
![Page 36: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/36.jpg)
Electrical Nature of MatterWhen 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.
![Page 37: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/37.jpg)
The Coulomb’s LawThe 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 q2
F = k d2
9x109 N.m2 /C2
Measured in Coulomb
Distance in meter
![Page 38: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/38.jpg)
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.
![Page 39: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/39.jpg)
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 Cd = 70 cm = 0.70 mk = 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)
![Page 40: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/40.jpg)
OHM’S LAWThe 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
E I =
R
Current orthe rate of
low of electricity resistance in
Ohms
Potential difference (emf)
Volts (V)
![Page 41: mechanics](https://reader035.fdocuments.us/reader035/viewer/2022070317/55622ce6d8b42ac6588b55a6/html5/thumbnails/41.jpg)
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 amperesR = 4.0 ohmsV = ?
Solution: I = E/R
15 A = E/ 4.0 Ώ
E = 60 volts (emf)