Topic 1

Question 1

What are scalar quantities?

Answer 1

Scalar quantities have only a magnitude.

Question 2

What is an example of a scalar quantity?

Answer 2

Mass is an example of a scalar quantity because it has magnitude without direction.

Question 3

What are other examples of scalar quantities?

Answer 3

Energy and volume are also examples of scalar quantities.

Question 4

What are vector quantities?

Answer 4

Vector quantities have both magnitude and direction.

Question 5

What is an example of a vector quantity?

Answer 5

Weight is an example of a vector quantity because it is a force and therefore has both magnitude and direction.

Question 6

What are other examples of vector quantities?

Answer 6

Acceleration and momentum are also examples of vector quantities.

Question 7

What is distance?

Answer 7

Distance is a measure of how far an object has travelled, regardless of direction.

Question 8

What does distance measure?

Answer 8

Distance is the total length of the path taken.

Question 9

What type of quantity is distance?

Answer 9

Distance has a magnitude but no direction, so it is a scalar quantity.

Question 10

What is displacement?

Answer 10

Displacement is a measure of how far it is between two points in space, including the direction.

Question 11

How is displacement defined?

Answer 11

Displacement is the length and direction of a straight line drawn from the starting point to the finishing point.

Question 12

What type of quantity is displacement?

Answer 12

Displacement has a magnitude and a direction, so it is a vector quantity.

Question 13

What is the difference between distance and displacement?

Answer 13

Displacement is a vector quantity, while distance is a scalar quantity.

Question 14

How does distance differ from displacement in a student’s travel to school?

Answer 14

The overall distance includes the total lengths of all the roads, while the overall displacement is a straight line between their home and school.

Question 15

What is speed?

Answer 15

Speed is a measure of the distance travelled by an object per unit time, regardless of the direction.

Question 16

What type of quantity is speed?

Answer 16

Speed has magnitude but no direction, so it is a scalar quantity.

Question 17

What is velocity?

Answer 17

Velocity is a measure of the displacement of an object per unit time, including the direction.

Question 18

What type of quantity is velocity?

Answer 18

Velocity has magnitude and direction, so it is a vector quantity.

Question 19

What is the relationship between speed and velocity?

Answer 19

An object can have a constant speed but a changing velocity if the object is changing direction.

Question 20

What are some common examples of scalar and vector quantities?

Answer 20

Scalar: distance, speed, mass, energy, volume, temperature.
Vector: displacement, velocity, weight, force, acceleration, momentum.

Question 21

How should an instructor explain the difference between mass and weight?

Answer 21

Step 1: Scalars have only magnitude; Vectors have both magnitude and direction.
Step 2: Mass is a scalar quantity.
Step 3: Weight is a vector quantity.

Question 22

How does mass change with location?

Answer 22

The instructor might explain that their mass will not change as their location in the Universe changes.

Question 23

How does weight change with location?

Answer 23

The instructor might explain that their weight varies depending on their location, such as being less on the Moon than on Earth.

Question 24

How are vectors represented?

Answer 24

Vectors are represented by an arrow.

Question 25

What does the length of the arrow in a vector represent?

Answer 25

The length of the arrow represents the magnitude.

Question 26

What does the direction of the arrow in a vector indicate?

Answer 26

The direction of the arrow indicates the direction.

Question 27

How should the scale of arrows in vector diagrams be?

Answer 27

The scale of the arrows should be proportional to the relative magnitudes of the forces.

Question 28

How long should an arrow for a 4 N force be compared to a 2 N force?

Answer 28

An arrow for a 4 N force should be twice as long as an arrow for a 2 N force.

Question 29

What do vector diagrams of two forces show?

Answer 29

The length of the arrows are proportional to the magnitude of the forces and show the direction that forces act in.

Question 30

How can vector diagrams be used?

Answer 30

Vector diagrams can be used to combine vectors.

Question 31

What can be said about vectors at right angles to one another?

Answer 31

Vectors at right angles to one another can be combined into one resultant vector.

Question 32

What does the resultant vector represent?

Answer 32

The resultant vector will have the combined effect of the two original vectors.

Question 33

How are component vectors sometimes drawn?

Answer 33

Component vectors are sometimes drawn with a dotted line and a subscript indicating horizontal or vertical.

Question 34

What does F subscript V represent?

Answer 34

F subscript V is the vertical component of the force F.

Question 35

What does F subscript H represent?

Answer 35

F subscript H is the horizontal component of force F.

Question 36

What does calculating vectors graphically involve?

Answer 36

Calculating vectors graphically means carefully producing a scale drawing with all lengths and angles correct.

Question 37

What tools are needed for accurate vector calculations?

Answer 37

This should be done using a sharp pencil, ruler, and protractor.

Question 38

What is the first step to carry out calculations with vectors on graphs?

Answer 38

Choose a scale which fits the page.

Question 39

What is an example scale for vector diagrams?

Answer 39

For example, use 1 cm = 10 m or 1 cm = 1 N, so that the diagram is around 10 cm high.

Question 40

What is the next step after choosing a scale?

Answer 40

Draw the vectors at right angles to one another.

Question 41

What should be done after drawing the vectors?

Answer 41

Complete the rectangle.

Question 42

How is the resultant vector drawn?

Answer 42

Draw the resultant vector diagonally from the origin.

Question 43

How do you measure the length of the resultant vector?

Answer 43

Carefully measure the length of the resultant vector.

Question 44

What should be done with the scale factor?

Answer 44

Use the scale factor to calculate the magnitude.

Question 45

How do you measure the angle of the resultant vector?

Answer 45

Use the protractor to measure the angle.

Question 46

Can vectors be measured or calculated graphically?

Answer 46

Vectors can be measured or calculated graphically using scaled vector diagrams.

Question 47

What is a method for combining vectors by calculation?

Answer 47

In this method, a vector diagram is still essential but it does not need to be exactly to scale.

Question 48

What form can the vector diagram take in calculations?

Answer 48

The vector diagram can take the form of a sketch, as long as the resultant side and component sides are clearly labelled.

Question 49

What can be used when the magnitude of only one vector is known?

Answer 49

When the magnitude of only one vector is known, and the angle is known, then trigonometry can be used to find the magnitude of the missing vector.

Question 50

What mnemonic helps remember trigonometric functions?

Answer 50

The mnemonic 'soh-cah-toa' can be used to remember the trigonometric functions.

Question 51

When can Pythagoras' theorem be used?

Answer 51

Pythagoras' theorem can be used when the magnitudes of two of the three vectors are known.

Question 52

What is the first step in the worked example of calculating resultant force?

Answer 52

Step 1: Draw a vector diagram.

Question 53

What is the formula to calculate the magnitude of the resultant force?

Answer 53

F = √(60² + 100²) ## Footnote F = √(13600) = 117 N

Question 54

How do you calculate the direction of the resultant vector?

Answer 54

tan(θ) = opposite / adjacent ## Footnote tan(θ) = 100 / 60; θ = tan⁻¹(100/60) = 59°

Question 55

What is the final answer for the resultant force?

Answer 55

F = 117 N at 59° from the horizontal.

Question 56

What should you do if the question specifies a calculation method?

Answer 56

If the question specifically asks you to use the calculation or graphical method, you must solve the problem as asked.

Question 57

Which method is sometimes easier, graphical or calculation?

Answer 57

The graphical method sometimes feels easier than calculating, but calculating is quicker and more accurate once confident with trigonometry and Pythagoras.