Pysics form three topic one

 Scalar and Vector Quantities

Difference between Scalar and Vector QuantitiesDistinguish between scalar and vector quantities

Scalar QuantitiesThese

are physical quantities which have magnitude only. Examples of scalar
quantities include mass, length, time, area, volume, density, distance,
speed, electric current and specific heat capacity.Vector QuantitiesThese
are physical quantities which have both magnitude and direction.
Examples of vector quantities include displacement, velocity,
acceleration, force, pressure, retardation, and momentum.Addition of Vectors Using Graphical MethodAdd vectors using graphical methodScalar physical quantities have magnitude only. Thus, they can be added, multiplied, divided, or subtracted from each other.Example 1If you add a volume of 40cm3 of water to a volume of 60cm3 of water, then you will get 100cm3 of water.Vectors can be added, subtracted or multiplied conveniently with the help of a diagram.Vectors RepresentationA vector quantity can be represented on paper by a direct line segment.

1. The length of the line segment represents the magnitude of a vector.
2. The arrow head at the end represents the direction.

Methods of Vector AdditionThere are two methods that are used to sum up two vectors:

1. Triangle method
2. Parallelogram method.

Triangle MethodA step-by-step method for applying the head-to-tail method to determine the sum of two or more vectors is given below.1.Choose
a scale and indicate it on a sheet of paper. The best choice of scale
is one that will result in a diagram that is as large as possible, yet
fits on the sheet of paper.2.Pick a starting location and draw the first vectorto scalein the indicated direction. Label the magnitude and direction of the scale on the diagram (e.g., SCALE: 1 cm = 20 m).3.Starting from where the head of the first vector ends, draw the second vectorto scalein the indicated direction. Label the magnitude and direction of this vector on the diagram.4.Draw the resultant from the tail of the first vector to the head of the last vector. Label this vector as Resultantor simplyR.5.
Using a ruler, measure the length of the resultant and determine its
magnitude by converting to real units using the scale (4.4 cm x 20 m/1
cm = 88 m).6.Measure the direction of the resultant using the counterclockwise convention.Resultant vector: This
is the vector drawn from the starting point of the first vector to the
end point of the second vector which is the sum of two vectors.

Where:

• Vi – First vector
• V2 – Second vector
• R – Resultant vector

Example 2Suppose a man walks starting from point A, a distance of 20m due North, and then 15m due East. Find his new position from A.SolutionUse scale1CM Represents 5mThus20m due to North Indicates 4 cm15m due to East Indicates 3cm.Demonstration

The position of D is represented by Vector AD of magnitude 25M or 5CM at angle of 36051”Since

• Tan Q = (Opposite /Adjacent)
• Tan Q = 3cm /4cm
• Q = Tan -1 (3/4)
• Q = Tan -1(0.75)
• Q = 35º51”

The Resultant displacement is 25m ad direction Q = 36º51”The Triangle and Parallelogram Laws of ForcesState the triangle and parallelogram laws of forcesTriangle Law of ForcesTriangle
Law of Forces states that “If three forces are in equilibrium and two
of the forces are represented in magnitude and direction by two sides of
a triangle, then the third side of the triangle represents the third
force called resultant force.”Example 3A
block is pulled by a force of 4 N acting North wards and another force
3N acting North-East. Find resultant of these two forces.Demonstration

Scale1Cm Represents 1NDraw a line AB of 4cm to the North. Then, starting from B, the top vectorofAB, draw a line BC of 3 CM at 45oEast of North.Join
the line AC and measure the length (AC = 6.5 cm) which represents 6.5N.
Hence, AC is the Resultant force of two forces 3N and 4N.Parallelogram MethodIn
this method, the two Vectors are drawn (usually to scale) with a common
starting point , If the lines representing the two vectors are made to
be sides of s parallelogram, then the sum of the two vectors will be the
diagonal of the parallelogram starting from the common point.The
Parallelogram Law states that “If two vectors are represented by the
two sides given and the inclined angle between them, then the resultant
of the two vectors will be represented by the diagonal from their common
point of parallelogram formed by the two vectors”.Example 4Two
forces AB and AD of magnitude 40N and 60N respectively, are pulling a
body on a horizontal table. If the two forces make an angle of 30o between them find the resultant force on the body.Solutiuon

Choose a scale.1cm represents10NDraw a line AB of 4cmDraw a line AD of 6cm.Make an angle of 30o between AB and AD. Complete the parallelogram ABCD using the two sides AB and include angle 30O.Draw the lineAC with a length of9.7 cm, which is equivalent to 97 N.The lineAC of the parallelogram ABCD represents the resultant force of AB and AD in magnitude and direction.Example 5Two
ropes, one 3m long and the other and 6m long, are tied to the ceiling
and their free ends are pulled by a force of 100N. Find the tension in
each rope if they make an angle of 30o between them.Solution1cm represents 1NThus3cm = represent 3m6cm = represents 6mDemonstration

By using parallelogram method

Tension, determined by parallelogram method, the length of diagonal using scale is 8.7 cm, which represents 100N force.Thus.Tension in 3m rope = 3 X 100 / 8.7 = 34.5NTension in 6m rope = 6 x 100 / 8.7 =69NTension force in 3m rope is 34.5N and in 6m rope is 69N.Note: Equilibrant forcesare those that act on a body at rest and counteract the force pushing or pulling the body in the opposite direction.Relative MotionThe Concept of Relative MotionExplain the concept of relative motionRelative motion is the motion of the body relative to the moving observer.The Relative Velocity of two BodiesCalculate the relative velocity of two bodiesRelative velocity (Vr) is the velocity relative to the moving observer.CASE
1: If a bus in overtaking another a passenger in the slower bus sees
the overtaking bus as moving with a very small velocity.CASE 2: If the passenger was in a stationary bus, then the velocity of the overtaking bus would appear to be greater.CASE 3: If the observer is not stationary, then to find the velocity of a body B relative to body A add velocity of B to A.Example 6If
velocity of body B is VB and that of body A is VA, then the velocity of
B with respect to A , the relative velocity VBA is Given by:VBA = VB + (-VA)That isVBA = VB – VANOTE:The relative velocity can be obtained Graphically by applying the Triangle or parallelogram method.For same directionVrBA = VB – (+VA)= VB – VA ___________________ (I)For different directionVrBA = VB – (-VA)VrBA = VB + VA _______________________ (II)Example 7A
man is swimming at 20 m/s across a river which is flowing at 10 m/s.
Find the resultant velocity of the man and his course if the man
attempted to swim perpendicular to the water current.SolutionScale1cmrepresents 2m/s

• The length of AC is 11.25 cm which is 22.5 m/s making a angle of 65º25’ with the water current.
• The diagonal AC represent (in magnitude and direction) the resultant velocity of the man.

The Concept of Relative Motion in Daily LifeApply the concept of relative motion in daily lifeKnowledge
of relative motion is applied in many areas. In the Doppler effect, the
received frequency depends on the relative velocity between the source
and receiver. Friction force is determined by the relative motion
between the surfaces in contact. Relative motions of the planets around
the Sun cause the outer planets to appear as if they are moving
backwards relative to stars in universe.Resolution of VectorsThe Concept of Components of a VectorExplain the concept of components of a vectorIs
the Splits or separates single vector into two vectors (component
vectors) which when compounded, provides the resolved vector.Resolved vector is asingle vector which can be split up into component vectors.Component vectorsare vectors obtained after spliting up or dividing a single vector.Resolution of a Vector into two Perpendicular ComponentsResolve a vector into two perpendicular componentsComponents of a vector are divided into two parts:

1. Horizontal component
2. Vertical component

Take angle OACCase 1SinQ = FX/FThusFX = F SinQHorizontal component, FX = FSinQCase 2Cos Q = Fy/FThus:Fy = FCosQVertical component: Fy = FCosQResolution of Vectors in Solving ProblemsApply resolution of vectors in solving problemsExample 8Find the horizontal and vertical components of a force of 10N acting at 300 to the vertical.Solution

FX = FCOS 60ºSinceCos 60º /F =(FX)FX = F CoS60º _________________(1)FX = 10NCos 60ºFy = ?Sinq = FyFy =F SinQ __________________________ (ii)Fy= 10N Sin 60º