Mechanics

The branch of physics that deals with the action of forces on bodies and with motion, comprised of kinetics, statics, and kinematics.

Mechanics

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

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.

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

The Direction Guide

Example 1:

The ship sails 25 km north.

Given: d= 25km north Scale: 1 cm = 10 km

N

d = 25 km

Vector diagram

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

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 eastd2 = 3.5 cm, 320 north of eastd3 = 2.3 cm, 220 west of northdR = ?

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

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.

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

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

KinematicsMotion may be defined as a continuous change of position with respect to a certain reference point.

Up +

Down -

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.

vs

=td

Average speed

Average

distance

time

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

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

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

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

Average accelerati

on

Initial velocity

final velocity

initial time

Final time

change

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

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.

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

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.

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

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.

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

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 HeatA. Natural Sources

a) The Sunb) The interior of the Earth

B. Artificial Sourcesa) Chemical Actionb) Mechanical Actionc) Electrical Energyd) Nuclear energy

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.

Electricity and

Magnetism

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.

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

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 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)

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)

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)