4. LESSON OBJECTIVES
At the end of the lesson, I should be able to:
Explain the concept scalar & vector quantities.
Distinguish between scalar & vector quantities. And their representations
Compose at least two vectors
Resolve a vector into a given direction.
Resolve vectors (e.g. forces) using any analytical method.
6. SUCCESS CRITERIA
• ALL: should be able to differentiate between scalar and
vector quantities.
• MOST: should be able to explain the.
• SOME: should be able to solve analytical problems on.
7. INTRODUCTION
Physical quantities in Physics are classified either as:
a. Scalars
b. Vectors
Scalars are added algebraically only (i.e. using arithmetic method)’
The volume of water in beaker A is 5 cm cm3 and the volume of water in
beaker B is 10 cm cm3, the total volume is (5+10) cm cm3 = 15cm cm3
On the other hand, vectors are added using geometrical and analytical
methods.
8. Vector Representations
Vector is represented using a straight line/arrow-head indicating the direction of the given vector.
Scales are used for representing vectors.
Example
Draw the vector diagram of a car at 50 km/h in a direction of N60ºE.
Solution
Say 1cm = 10km/h
9. Addition of Vectors
Case of two Vectors:
P = 5N & Q = 4N
Say P & Q moving in the same direction. Their sum or resultant is given by:
R = P + Q
R = 5N + 4N
R = 9N
If P & Q moving in the opposite direction. Their sum or resultant is given by:
R = P – Q =5N – 4N = 1N
11. RESOLUTION OF VECTORS
1. A man walks 3km eastwards and then 4km southwards, using scale drawing
method, what is his resultant displacement?
2. Two forces 5N and 4N are inclined to each other at 30º. Find the resultant force by
the triangle method.
12. RESOLUTION OF VECTORS, COMPONENTS
The horizontal component of a vector, V, is VX = V cos θ
The vertical component of a vector, V, is Vy = V sin θ
13. PROBLEMS ON RESOLUTION OF
VECTORS, COMPONENTS
A boy is pulling his toy car with a rope attached to the toy car
at 30º to the horizontal direction. If the boy pulls with a force
of F (Newtons) , Find the effective force that pulls the toy in
a horizontal direction.
A plane flies with a velocity of 1000km/h in a direction
N60ºE. Find its effective velocity in the easterly and
northerly directions.
14. INDEPENDENT TASK
A nail on a vertical wall is pulled by means of a cord
attached to its head. If the cord makes an angle of 60º to
the horizontal and it exerts a force of 80N on the nail; Find:
i. The effective force which tends to pull the nail out of
the wall.
ii. The force which tends to bend the nail.
15. THE RESULTANT OF MORE THAN TWO VECTORS.
To find the resultant of more than two vectors, we resolve each vector in two
perpendicular directions;
vertical components
horizontal components
Magnitude of resultant vector is given by: R = √ X2 + Y2
Direction of resultant vector is given by: tan α = Y/X
16. PROBLEMS ON COPLANAR
NON-PARALLEL FORCES
Calculate the resultant of five coplanar forces of values 10N,
12N, 16N, 20N, 15N on an object, O as shown below:
SOLUTION
The force are resolved into the horizontal and vertical
components as given below:
17. SOLUTION OF COPLANAR FORCES
FORCE [N] Inclination
to the
horizontal
HORIZONTAL
COMPONENT (X)
VERTICAL COMPONENT(Y)
10 0 +10 cos 0 = +10.000 + 10 sin 0 = 0.000
12 50◦ +12 cos 50◦ = +7.713 +12 sin 50◦ = +9.193
20 40◦ -20 cos 40◦ = -15.321 + 20 sin 40◦ =+12.856
16 90◦ +16 cos 90◦ = 0.000 - 16 sin 90◦ = - 16.000
15 60◦ + 15 cos 60◦ = +7.500 - 15 sin 60◦ = - 12.990
ΣX = +9.892 ΣY = - 6.941
18. SOLUTION OF COPLANAR FORCES
Magnitude of resultant vector is given by: R = √ ΣX2 + Σ Y2
• R = √ [+9.892]2 + [-6.941]2
• R = √146.016 = 12.084
R = 12.08N
Direction of resultant vector is given by: tan α = ΣY/ Σ X
tan α = [-6.941/9.892]
α = tan-1 [-0.7017]
α = -35.3º
The direction of the resultant is S 54.7 º E
