Vector Quantities CXC

​Objectives

At the end of this session students will be able to :​

​

• distinguish between scalar and vectors and give examples of each

• state that vectors can be represented using an arrow .

​SESSION 1 : Vectors

​Physical

Quantities ; Anything that can be measured

​Scalar : has magnitude only	​Vector: has magnitude and direction
​distance	​displacement
​speed	​velocity
​time	​acceleration
​energy	​force

​Difference between Vectors and scalars in tabular form

​Scalars	​Vectors
​Physical quantities have magnitude only but no direction	​Physical quantities have magnitude and direction
​These quantities are completely described by : 1 a number 2 a suitable unit	​These quantities are completely described by 1 a number 2 a suitable unit 3 a direction
​These quantities are added, subtracted , multiplied and divided by simple arithmetic rules	​These quantities cannot be added ,subtracted, multiplied and divided by simple arithmetic rules.
​	​

• The tail is the starting position.

• The head is the ending position.

• The magnitude represents how long or large the vector is.

  • For example, a vector representing 100 should be twice as long as a vector representing 50. ​

​

​How To Draw a Vector

​

Multiple Choice

Another word for "size" is...

• magnification

• magnetism

• magnitude

• magnanimity

Multiple Choice

Wind blowing at 20 mph. Vector or scalar?

• Scalar
• Vector

Multiple Select

Select the scalar quantities.

• velocity

• distance

• energy

• acceleration

• speed

Multiple Choice

A deer running 15 meters per second due west. Vector or scalar?

• Scalar
• Vector

Multiple Choice

Which of the following quantities are vectors?

• speed, velocity, acceleration
• velocity, acceleration, force
• force, acceleration, mass
• length, mass, time

Multiple Choice

 Amy runs 2 miles south, then turns around and runs 3 miles north. What is displacement?

• 5 miles
• 1 mile 
• 2 miles south
• 1 mile north 

Multiple Choice

Which symbol is used to show vector quantities?

• Circle
• Line
• Arrow
• Triangle

Multiple Choice

Sara walks from Point A to Point B. Which is true?

• Distance and displacement are EQUAL
• Distance is less than displacement

Multiple Choice

Find the distance Sara walks from A to B,  B to C then C to D?

• 11m
• 3m
• 5m

Multiple Choice

Michael walks in the following order: from Point A, to Point B, and finally to Point C. Which is true?

• Distance and displacement are EQUAL

• Distance is less than displacement

• Displacement is less than distance.

Multiple Choice

Which driver has an equal distance and displacement at B?

• 1

• 2

• 3

Multiple Choice

An example of scalar magnitude:

• velocity

• mass

• acceleration

• force

Multiple Choice

This is speed in a specific direction.

• Velocity
• Motion
• Position

Multiple Choice

 Ray runs 30 feet north, 30 feet west, and then 30 feet south. What is the displacement?

• 30 feet west
• 90 feet 
• 30 feet south
• 0 feet

Multiple Choice

The students are arguing over the differences between speed and velocity. One student says, “Speed is a vector because it describes how fast an object traveling. Velocity is a scalar because it tells how fast and what direction an object is traveling.” Which of the following statements is correct?

• The students' understanding of all four terms (speed, velocity, scalar, and vector) is correct.

• The students' understanding of all four terms (speed, velocity, scalar, and vector) is incorrect.

• The students' understanding of speed and velocity is incorrect but their

  understanding of scalar and vector is correct.

• The students’ understanding of speed and velocity is correct but their understanding of scalar and vector is incorrect.

Multiple Choice

Which symbol is used to show vector quantities?

• Circle
• Line
• Arrow
• Triangle

Multiple Choice

A quantity that has both magnitude and direction is called a scalar quantity.

• True
• False

Multiple Choice

You slowly walked 10 km West and then quickly ran 10 km North. During each part of the journey, the ______________ was the same.

• displacement

• distance

• time

• velocity

Multiple Choice

An example of scalar magnitude:

• velocity

• mass

• acceleration

• force

Multiple Select

Two cars are travelling at 10 m/s, in different directions. Select the sentences that are true.

• Their speeds are the same.

• Their speeds are different.

• Their velocities are the same.

• Their velocities are different.

​Objectives

At the end of this session students will be able to :​

​

• calculate the resultant of vectors which are parallel, anti-parallel and perpendicular;

​SESSION 2 : Vectors

In this class we will focus on calculating the resultant of vectors that are :

1. ​parallel

2. antiparallel

3. perpendicular

Multiple Choice

What's the sum of the vectors?

• 50 N -->

• 50 N <--

• 350 N -->

• 350 N <--

Multiple Choice

What's the sum of the vectors

• 13N -->

• 13 N <--

• 113 N -->

• 113 N <--

​Parallel and Antiparallel vectors

​Parallel Vectors When vectors are parallel to one another, we can simply add or subtract the vectors to find the resultant vector Examples of adding vectors: 2 (or more) vectors to the right 2 vectors to the left 2 vectors downward, etc. Examples of subtracting vectors: 1 vector to the right and 1 to the left 1 vector upward and 1 vector downward, etc.

​A 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 vector to scale in 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 vector to scale in the indicated direction. Label the magnitude and direction of this vector on the diagram.

4. Repeat steps 2 and 3 for all vectors that are to be added

5. Draw the resultant from the tail of the first vector to the head of the last vector. Label this vector as Resultant or simply R.

6. Using a ruler, measure the length of the resultant and determine its magnitude by converting to real units using the scale

​

​Find the Resultant Vector, R, of two vectors, 15 N east and 10 N at an angle of 45° from the horizontal.

​Guided Example:

​

​Objectives

At the end of this session students will be able to :​

​

• explain that a single vector is equivalent to two other vectors at right angles.

​SESSION 3 : Vectors

​Components of Vectors

• ​Sometimes a single vector needs to be changed into an equivalent set of two component vectors that are at right angles to each other

• Any vector can be “resolved” into two component vectors at right angles

• Components: two vectors at right angles that add up to a given vector

• Resolution: the process of determining the components of a vector The perpendicular components of a vector are independent of each other.

​Determining the Components

• ​Vector V represents a vector quantity First, horizontal and vertical lines are drawn from the tail of the vector Second, a rectangle is drawn that encloses the vector V.

• The sides of the rectangle are the desired components, vector.

​Guided Example:

​

​Find the Resultant Vector, R, of two vectors, 15 N east and 10 N at an angle of 45° from the horizontal.

Draw

​Find the Resultant Vector, R, of two vectors, 15 N east and 10 N at an angle of 45° from the horizontal.