Grade 10 lesson on Vectors and Scalars. it is an introduction to the topic. Happy to see that all the skills i'm learning at uj is paying off.

1. Physical Sciences
grade 10
Vectors and Scalars
By
Miss Ramboda TG
200939111

2. Lesson Objectives.
 Define a vector and a scalar quantity.
 Differentiate between vector and scalar quantities.
 Understand that ⟶F represents the force factor, whereas F represents the
magnitude of the force factor.
 Graphical representation of vector quantities.
 Properties of vectors like equality of vectors, negative vectors, addition and
subtraction of vectors using the force vector as an example.
 Define resultant vector.
 Find resultant vector graphically using the tail-to- head method as well as by
calculation for a maximum of four force vectors in one dimension.

3. Introduction
 List any physical quantities that you know.
 Time,
 Mass,
 Weight,
 Force,
 Charge
Let’s play a game called pick a paper

4. SCALAR
 Scalars are physical quantities which have only a number value or a size
(magnitude). A scalar tells you how much of something there is.
 Definition
 A scalar is a physical quantity that has only a magnitude (size).
 For example, a person buys a tub of margarine which is labelled with a mass of 500
g. The mass of the tub of margarine is a scalar quantity. It only needs one number
to describe it, in this case, 500 g.

5. VECTOR
 Vectors are different because they are physical quantities which have a size
and a direction. A vector tells you how much of something there is and which
direction it is in.
 A vector is a physical quantity that has both a magnitude and a direction.
 For example, a car is travelling east along a freeway at 100 km · h −1 . What
we have here is a vector called the velocity. The car is moving at 100 km · h
−1 (this is the magnitude) and we know where it is going – east (this is the
direction). These two quantities, the speed and direction of the car, (a
magnitude and a direction) together form a vector we call velocity

6. More examples
Examples of scalar quantities:
 Mass has only a value, no direction
 Electric charge has only a value, no direction
Examples of vector quantities:
 Force has a value and a direction. You push or pull something with some
strength (magnitude) in a particular direction
 Weight has a value and a direction. Your weight is proportional to your mass
(magnitude) and is always in the direction towards the centre of the earth.

7. Exercise 1 [7 marks]
Classify the following as vectors or scalars
1. Length
2. Force
3. Direction
4. Height
5. Time
6. Speed
7. Temperature

8. Exercise Answers
1. Length- Scalar
2. Force- Vector
3. Direction – Vector/scalar
4. Height- Scalar
5. Time- Scalar
6. Speed- Vector
7. Temperature- Scalar

9. Vector notation
 Vectors are different to scalars and must have their own notation.
 There are many ways of writing the symbol for a vector.
 We will be showing vectors by symbols with an arrow pointing to the right
above it.
 For example, → F, → W and → v represent the vectors of force, weight and
velocity, meaning they have both a magnitude and a direction.
 Sometimes just the magnitude of a vector is needed. In this case, the arrow is
omitted. For the case of the force vector:
 → F represents the force vector
 F represents the magnitude of the force vector

10. Graphical representation of vectors
 Vectors are drawn as arrows. An arrow has both a magnitude (how long it is)
and a direction (the direction in which it points).
 The starting point of a vector is known as the tail and the end point is known
as the head.
 Simulations: Show vectors by drawing them.

11. Properties of vectors
 If two vectors have the same magnitude (size) and the same direction, then
we call them equal to each other.
 For example, if we have two forces, → F1= 20 N in the upward direction and →
F2= 20 N in the upward direction, then we can say that → F1= → F2.
 Defining Equal vectors
 Two vectors are equal if they have the same magnitude and the same direction.

12. Properties cont…
 Scalars can have positive or negative values, e.g. -5 or 5
 Vectors can also be positive or negative.
 A negative vector is a vector which points in the direction opposite to the reference positive
direction.
 For example, if in a particular situation, we define the upward direction as the reference positive
direction,
 then a force → F1= 30 N downwards would be a negative vector and could also be written as → F1= −30 N.
 In this case, the negative (-) sign indicates that the direction of → F1 is opposite to that of the reference
positive direction.
 A negative vector is a vector that has the opposite direction to the reference positive direction.

13. Addition and subtraction of vectors
Adding vectors
 When vectors are added, take into account both their magnitudes and
directions.
 For example, You and a friend are trying to move a heavy box. You stand behind it
and push forwards with a force → F1 and your friend stands in front and pulls it
towards them with a force → F2.
 The two forces are in the same direction (i.e. forwards) and so the total force
acting on the box is:
 [Draw the box and show the vectors, and then add them]

14. Adding and subtracting vectors cont…
Subtracting vectors
 Lets use the same example as above. You and your friend are trying to move.
 You stand behind the box and pull it towards you with a force → F1 and your friend
stands at the front of the box and pulls it towards them with a force → F2.
 In this case the two forces are in opposite directions.
 If we define the direction your friend is pulling in as positive then the force you
are exerting must be negative since it is in the opposite direction.
 We can write the total force exerted on the box as the sum of the individual
forces: [Draw to illustrate].

15. The resultant vector
 The final quantity you get when adding or subtracting vectors is called the
resultant vector.
 The resultant vector is the single vector whose effect is the same as the
individual vectors acting together.
 Lets use the box example:
 In the first case, you and your friend are applying forces in the same direction. The
resultant force will be the sum of your two applied forces in that direction.
 In the second case, the forces are applied in opposite directions. The resultant
vector will again be the sum of your two applied forces, however after choosing a
positive direction, one force will be positive and the other will be negative and the
sign of the resultant force will just depend on which direction you chose as
positive. [draw to illustrate]

16. Summary
 A scalar is a physical quantity with magnitude only.
 A vector is a physical quantity with magnitude and direction.
 Vectors may be represented as arrows where the length of the arrow indicates the
magnitude and the arrowhead indicates the direction of the vector.
 Two vectors are equal if they have the same magnitude and the same direction.
 A negative vector is a vector that has the opposite direction to the reference positive
direction.
 Addition and subtraction of vectors.
 The resultant vector is the single vector whose effect is the same as the individual
vectors acting together.
 https://youtu.be/rcDXQ-5H8mk

17. Assessment.
 Homework: inquiry-based activity.
 At home, identify quantified objects (at least 10). Then categorize them as
either scalar or vector.
 Hint: with the vector quantities, consider the distances that you normally
walk either to school or shops.