2.2.2 Scalar and Vector Calculations

Question 1

How does one add and subtract scalars? What is important to note here?

Answer 1

1. Add and subtract the quantities;

2. BE CAREFUL WITH UNITS - we cannot add scalar quantities that have the same units.

Question 2

How are vectors expressed visually?

Answer 2

An arrow is used denoting:

1. Orientation of force;
2. Position of force;
3. Magnitude of force: shown by length of arrow - often SCALES ARE USED.
4. A bearing from North must be stated to show direction.

Question 3

Graphically, when would a vector be zero?

Answer 3

If a diagram had two arrows of equal magnitudes, but opposite directions: and so they would cancel each other out. These are called ‘anti-parallel’ forces.

Question 4

What is important to note when adding and subtracting vector quantities?

Answer 4

Direction: as one direction is positive and the other negative.

Question 5

What are ‘anti-parallel’ forces?

Answer 5

Forces which act in opposite directions.

Question 6

If two forces are orthogonal to each other, how should one find the resultant vector?

Answer 6

By creating a vector triangle and using Pythagoras’s theorem.

Question 7

What amount of sig fig should you round to?

Answer 7

1. The amount stated in the question;
2. If not, then the same number of sig fig that the values in the question have.
3. If there are no numbers in the question, then 3sf;

Question 8

What is a resultant vector?

Answer 8

A resultant vector is the combination of two or more single vectors.

Question 9

What is a common vector question?

Answer 9

1. Find the resultant vector of wind and airplane speed - here, you would use Pythagoras and BE CAREFUL WITH UNITS.
2. You would STATE DIRECTION IN DEGREES FROM NORTH.

Question 10

How should one add vectors not at right angles?

Answer 10

1. Construct a to-scale diagram;
2. Use a ruler to find the magnitude of the resultant vector and
3. Use a protractor to find its direction.

Question 11

How would one state direction if not in a bearing?

Answer 11

The angle must be stated with reference to a specified direction: clockwise or anti from the POSITIVE x direction.