Scalar and Vectors

Question 1

What is the difference between scalars and vectors?

Answer 1

Scalars have magnitude only while vectors have both magnitude and direction.

Question 2

Give examples of vector quantities.

Answer 2

Displacement velocity force momentum weight acceleration electric field.

Question 3

What is a resultant vector?

Answer 3

That single vector which would have the same effect in magnitude and direction as two or more vectors acting together.

Question 4

How is the resultant vector obtained?

Answer 4

By the parallelogram method or the triangle method.

Question 5

If two vectors P and Q are inclined at an angle θ what is the formula for their resultant R?

Answer 5

R² = P² + Q² + 2PQ cos θ.

Question 6

What is the component of a vector in a given direction?

Answer 6

Its effective value in that direction.

Question 7

How is a vector usually resolved?

Answer 7

In the horizontal and vertical directions.

Question 8

If a vector V is inclined at θ to the horizontal what is the horizontal component of V?

Answer 8

Vx = V cos θ.

Question 9

If a vector V is inclined at θ to the horizontal what is the vertical component of V?

Answer 9

Vy = V sin θ.

Question 10

How can the resultant of more than two vectors be found?

Answer 10

By first resolving the system into two perpendicular directions.

Question 11

If the sum of the X-components is X and the sum of the Y-components is Y how is the resultant R found?

Answer 11

R² = X² + Y².

Question 12

If the sum of the X-components is X and the sum of the Y-components is Y how is the inclination angle α to the X-direction or the horizontal direction found?

Answer 12

tan α = Y/X.

Question 13

How do you find the resultant of more than two vectors?

Answer 13

Resolve each vector in two perpendicular directions add all the horizontal components X and all the vertical components Y.

Question 14

If four forces are acting on a body and you resolve them into horizontal and vertical components what do the sums X and Y represent?

Answer 14

X = sum of horizontal components Y = sum of vertical components.

Question 15

When finding the sum of the horizontal components (X) which directions are taken as positive and negative?

Answer 15

Right hand or easterly direction is positive left hand or westerly direction is negative.

Question 16

When finding the sum of the vertical components (Y) which directions are taken as positive and negative?

Answer 16

Northerly or upward direction is positive southerly or downward direction is negative.

Question 17

How is the resultant of X and Y found?

Answer 17

R² = X² + Y² R = √(X² + Y²).

Question 18

How is the direction α of the resultant found?

Answer 18

tan α = Y/X.

Question 19

What is the reverse process of finding two vectors which have the same effect as a resultant vector called?

Answer 19

Resolution of vectors.

Question 20

What is a component of a vector in a given direction?

Answer 20

Its effective value in that direction.

Question 21

What is the horizontal component of a vector?

Answer 21

Its effective value in a horizontal direction.

Question 22

Into what directions is it most useful to resolve a vector?

Answer 22

Mutually perpendicular directions usually the horizontal or x-direction and the vertical or y-direction.

Question 23

If a vector V is inclined at an angle θ to a horizontal direction what is the horizontal component of the vector V?

Answer 23

Vx = V cos θ.

Question 24

If a vector V is inclined at an angle θ to a horizontal direction what is the vertical component of V?

Answer 24

Vy = V sin θ.

Question 25

How do you find the resultant of two vectors P and Q inclined at an angle θ to each other using the triangle method?

Answer 25

1. Starting from a point O draw OA to represent P. 2. Next draw the second vector Q placing its tail at the tip of the first vector P ensuring its magnitude and direction are correct. 3. Finally draw OB to complete the triangle.

Question 26

What does OB represent?

Answer 26

R the resultant vector in magnitude and direction.

Question 27

How can the resultant of two vectors inclined to each other be represented?

Answer 27

By the diagonal of a parallelogram drawn with the two vectors as adjacent sides.

Question 28

How are the two vectors drawn in the parallelogram method?

Answer 28

From a common origin.

Question 29

What is the shape formed using these two vectors?

Answer 29

A parallelogram.

Question 30

What represents the resultant in this method?

Answer 30

The diagonal drawn from the common origin.

Question 31

What does the Parallelogram Law of Vectors state?

Answer 31

If two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.

Question 32

How are vectors added if they are in the same direction?

Answer 32

Their sum or resultant is given by R = P + Q.

Question 33

What is the direction of the resultant vector when vectors are added in the same direction?

Answer 33

The common direction of P and Q.

Question 34

If two forces P and Q of 5 N and 4 N respectively act on a body in the same direction what is the resultant force?

Answer 34

R = P + Q = 5 N + 4 N = 9 N.

Question 35

If P and Q are in opposite directions how is the resultant given?

Answer 35

R = P - Q.

Question 36

If P > Q what is the direction of R?

Answer 36

The direction of P.

Question 37

If P = Q what is R?

Answer 37

0

Question 38

If a boy walks 2 km eastwards to a point A and then walks another 4 km westwards what is his displacement (S) from his starting point?

Answer 38

S = 4 - 2 = 2 km westwards.

Question 39

Can simple algebraic addition or subtraction be used if the two or more vectors are inclined at an angle to each other?

Answer 39

No.

Question 40

A man walks 3 km eastwards and then 4 km southwards. How can his motion be represented?

Answer 40

Graphically using scale drawings.

Question 41

What is the resultant displacement?

Answer 41

5 km in the direction inclined at α = 53.13° to AB or at 36.9° East of South.

Question 42

What theorem can be used to obtain the same result?

Answer 42

Pythagoras theorem.

Question 43

When can Pythagoras theorem be used to find the resultant vector?

Answer 43

Only when the two vectors are inclined at right angles to each other.

Question 44

What is the resultant vector?

Answer 44

That single vector which would have the same effect in magnitude and direction as the original vectors acting together.

Question 45

What are the two methods of adding or compounding vectors to find the resultant?

Answer 45

The parallelogram method and the triangle method.

Question 46

What do other measurable physical quantities have in addition to magnitude?

Answer 46

Direction.

Question 47

What are vector quantities?

Answer 47

Physical quantities that have both magnitude and direction for their complete description.

Question 48

Give examples of vector quantities.

Answer 48

Displacement velocity acceleration force weight momentum electric field intensity magnetic field intensity.

Question 49

Give an example of a vector quantity.

Answer 49

A displacement of 20 km due north.

Question 50

How are vectors represented?

Answer 50

By straight lines with an arrowhead.

Question 51

What does the length of the line represent?

Answer 51

The magnitude of the vector.

Question 52

What does the arrowhead indicate?

Answer 52

The direction of the vector quantity.

Question 53

What are the two classifications of quantities in Physics?

Answer 53

Scalars and vectors.

Question 54

How are scalar and vector quantities handled in numerical calculations?

Answer 54

Differently.

Question 55

What does the chapter aim to explain?

Answer 55

The concept of scalars and vectors.

Question 56

What does the chapter aim to help students distinguish?

Answer 56

Between scalar and vector quantities and their representation.

Question 57

What skill does the chapter aim to develop?

Answer 57

The ability to compose at least two vectors.

Question 58

What should students be able to explain after the chapter?

Answer 58

The meaning of the resultant of two vectors.

Question 59

What should students be able to do with vectors?

Answer 59

Resolve a vector into a given direction.

Question 60

What components should students be able to resolve vectors into?

Answer 60

Two components at right angles to each other.

Question 61

What problems should students be able to solve?

Answer 61

Simple problems involving resolution and addition of vectors.

Question 62

What methods should students be able to use to solve vector problems?

Answer 62

Analytical and graphical methods.

Question 63

What do many measurable physical quantities in physics have?

Answer 63

Only numerical values.

Question 64

How are scalar quantities described?

Answer 64

Completely when only their magnitudes or sizes are known.

Question 65

Give examples of scalar quantities.

Answer 65

Length distance mass volume density time speed temperature energy.

Question 66

What are scalar quantities?

Answer 66

Those which have only magnitude or numerical value but no direction.

Question 67

Give an example of a scalar quantity.

Answer 67

A speed of 50 kmhr⁻¹.

Question 68

How are scalars added?

Answer 68

By ordinary algebraic methods.