# Lesson Notes By Weeks and Term - Senior Secondary 1

Vector resolution

Term: 3rd Term

Week: 8

Class: Senior Secondary School 1

Age: 15 years

Duration: 40 minutes of 5 periods each

Date:

Subject:      Physics

Topic:-       Vector resolution

SPECIFIC OBJECTIVES: At the end of the lesson, pupils should be able to

1. Define vector resolution
2. Explain the methods of vector resolution
3. Calculate the resultant of two or more vectors by resolution

INSTRUCTIONAL TECHNIQUES: Identification, explanation, questions and answers, demonstration, videos from source

INSTRUCTIONAL MATERIALS: Videos, loud speaker, textbook, pictures

INSTRUCTIONAL PROCEDURES

PERIOD 1-2

 PRESENTATION TEACHER’S ACTIVITY STUDENT’S ACTIVITY STEP 1 INTRODUCTION The teacher reviews the previous lesson on vectors Students pay attention STEP 2 EXPLANATION He defines and explains vector resolution. He explains the methods of vector resolution Students pay attention and participates STEP 3 DEMONSTRATION He explains the guidelines for finding the resultant of two or more vectors and carries out some calculations Students pay attention and participate STEP 4 NOTE TAKING The teacher writes a summarized note on the board The students copy the note in their books

NOTE

VECTOR RESOLUTION

The process of determining the magnitude of a vector is known as vector resolution. The two methods of vector resolution are:

1. the parallelogram method
1. the trigonometric method

Parallelogram law of vector addition states that if two vectors acting at a common point are represented in magnitude and direction by the adjacent sides of a parallelogram, their resultant is represented in magnitude and direction by the diagonal of the parallelogram drawn from their common point of intersection and direct away from that point.

Example: Two forces with magnitudes of 25N and 18N respectively are inclined at an angle of 1200 to each other. Calculate the resultant force and the angle it makes with the 18N force.

R2 = A2 + B2 – 2ABcos(1800-ϴ)

R2 = 252 + 182 – 2 x 25 x 18cos(1800-1200)

R2 = 625 + 324 – 900cos600

R2 = 499

Resultant, R = 22.34N

RESULTANT OF TWO OR MORE VECTORS BY RESOLUTION

The resultant of two or more vectors can be found by taking the following simple steps:

1. Resolving each vector into vertical and horizontal component.
2. Summing all the components along vertical axis to obtain vertical resultant i.e. ΣFx
3. Summing all the components along horizontal axis to obtain horizontal resultant i.e. ΣFy
4. The final Resultant of the vectors is the vector sum of the vertical and horizontal resultants F = ΣFx + ΣFy
5. The direction (ϴ) of the resultant with the horizontal is given by tanϴ = ΣFy

ΣFx

Example: Three coplanar forces act simultaneously at a point as shown below

Find the resultant of the forces and its direction with respect to x-axis.

(Take sin600 = 0.87, cos600 = 0.50

Solution:

 VERTICAL COMPONENT Ry HORIZONTAL COMPONENT Rx 107 sin900 107cos900 -100sin600 -100cos600 80sin00 80cos00 ΣFy= 20N ΣFx = 30N

R = √302+ 202

R = √1300

R = 36.1N

Direction is given as tanϴ = ΣFy

ΣFx

tanϴ =       ΣFy

ΣFx

=       20

30

ϴ = 33.7˚

EVALUATION:   1. Define vector resolution

1. Discuss two methods of vector resolution
2. Find the resultant of the vectors having magnitudes of 5 units, 6 units, and are inclined to each other at an angle of 60 degrees.
3. find the resultant of two vectors where the first vector has a magnitude of 30 and the second vector has a magnitude of 40 with 50° has the inclination between the two vectors.

CLASSWORK: As in evaluation

CONCLUSION: The teacher commends the students positively