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SS2: PHYSICS - 1ST TERM

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  1. Scalars & Vectors | Week 1
    5 Topics
    |
    1 Quiz
  2. Equations of Motion | Week 2
    3 Topics
    |
    1 Quiz
  3. Projectile | Week 3
    5 Topics
  4. Equilibrium of Forces I | Week 4
    4 Topics
  5. Equilibrium of Forces II | Week 5
    4 Topics
  6. Stability of a Body | Week 6
    4 Topics
    |
    1 Quiz
  7. Simple Harmonic Motion (SHM) | Week 7
    4 Topics
  8. Speed, Velocity & Acceleration & Energy of Simple Harmonic Motion | Week 8
    5 Topics
    |
    1 Quiz
  9. Linear Momentum | Week 9
    6 Topics
    |
    1 Quiz
  10. Mechanical Energy & Machines | Week 10
    2 Topics
    |
    1 Quiz



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Scalar Quantities:

Scalar quantities are physical quantities which have magnitude only or numerical value but no direction.

Examples of Scalar Quantities are

  • Mass
  • Length
  • density
  • Time
  • Distance
  • Temperature
  • Speed
  • Volume
  • Density
  • Area
  • Current

Addition of Scalar Quantities:

With scalar addition, all you have to do is add the values of each scalar item to obtain the total 

Examples of Addition of scalar Quantities:


            • V1 + V2 = 10 cm³ + 30 cm³ = 40 cm³
            • T1 + T2 =  273K + 100K = 373K
            • A1 + A2 = 200 m² + 250 m² = 450 m²

Vector Quantities:

Vector quantities are those quantities that have both magnitude and direction.

Examples of Vector Quantities are

  • Force
  • Gravitational field
  • Momentum
  • Weight
  • Velocity
  • Acceleration due to gravity
  • Magnetic field
  • Electric field
  • Displacement
  • Acceleration

Representation of Vector:

A vector is always represented by a straight line with an arrow at the one end pointing in a particular direction. The length of the line represents the magnitude of the vector e.g.

vector e1603702124639

The vector is 10N in the Eastern direction.

vect

Addition of Vector Quantities:

1. If two vectors \( \scriptsize \vec{B} \) and \( \scriptsize \vec{D} \) moved in the same direction and are 10N and 12N respectively, then, their resultant R is

VECT5 e1603711443422

R = 22N

2. If  \( \scriptsize \vec{B} \) and  \( \scriptsize \vec{D} \) are in the opposite direction.

VECT6 e1603711792610

R = 2N

\( \scriptsize \vec{D} \: -\:  \scriptsize \vec{B} = R \)

The resultant is in the direction of the larger force i.e. \( \scriptsize \vec{D}\)

Example 1:

Given that 40 N force F1 travels from west to east and 25 N force F2 travels in the opposite direction to that of 40 N force. Find the resultant of the two vectors.

Solution:

Resultant Vector R = vector F1 + ( – vector F2)
Resultant vector R = vector F1 – vector F2
Resultant vector R = 40 N – 25 N = 15 N

Example 2:

90 N force travelled from east to west. If 35 N travelled in a direction that is opposite to that of 90 N, what is the force?

Solution:

Let 90 N be F1 and 35 N be F2
East to West is a negative direction of travel, therefore F1 = – 90 N
35 N travelled in the opposite direction to 90 N, 
therefore F2 = +35 N

Resultant vector R = – vector F1 + vector F2
Resultant vector R = – 90N + 35N = – 55N

Example 3:

Two vectors of equal magnitude that are pointing in opposite directions will sum to zero.   \( \scriptsize \vec{B} \: – \: \scriptsize \vec{D} = 0\)

VECT7 e1603716252880

   

R = 0.

Example 4:

In the vector diagram below, find the resultant of the two vectors.

Screenshot 2022 07 01 at 19.13.46

Solution:

When two vectors are inclined at 90° (perpendicular) to each other, their resultant is obtained using the Pythagoras theorem.

The resultant of the vectors is represented by the hypotenuse of the triangle in such a way that the direction of the resultant vector is opposite to the direction of the two vectors. The length of the hypotenuse represents the magnitude/size of the resultant vector.

Screenshot 2022 07 01 at 19.04.23

Using Pythagoras,

(i)

R2 = 102 + 122

R2 = 100 + 144

R2 = 244

R = \( \scriptsize \sqrt{244} \)

   = 15.6N

(ii) The direction is given by

\( \scriptsize tan \theta = \normalsize \frac{opp}{adj} = \frac{10}{12} \)

\( \scriptsize tan \theta = 0.833\)

θ = tan-1 (0.833) = \( \scriptsize 39.8^{\circ} \)

The resultant can also be found by scale drawing.

The resultant vector is a single vector which would have the same effect in magnitude and direction as the original vectors acting together.

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