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Understand vector quantities

• State the two components of

a vector.

• Draw a directed line to

represent a vector.

Quantities such as time, temperature and mass are entirely defined by a numerical value and are called scalars or scalar quantities.› E.g. temperature in a room is 16 C.

Quantities such as velocity, force and acceleration, which have both a magnitude and a direction, are called vectors.› E.g. the velocity of a car is 90km/h due west.

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A vector quantity can be represented graphically by a line, drawn so that:› the length of the line denotes the magnitude

of the quantity, and

› the direction of the line denotes the direction in which the vector quantity acts.

An arrow is used to denote the sense, or direction, of the vector.

The arrow end of a vector is called the ‘nose’ and the other end the ‘tail’.

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For example, a force of 9N acting at 45◦

to the horizontal is shown in Fig. 1. Note

that an angle of +45◦ is drawn from the

horizontal and moves anticlockwise.

Fig. 1

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A velocity of 20m/s at −60◦ is shown in

Fig. 2. Note that an angle of −60◦ is

drawn from the horizontal and moves

clockwise.

Fig. 2

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Solve addition vectors:

• Determine the resultant vector using graphical method:

i) triangle method,

ii) parallelogram method.

Adding two or more vectors by drawing

assumes that a ruler, pencil and

protractor are available.

Results obtained by drawing are

naturally not as accurate as those

obtained by calculation.

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Triangle @ Nose-to-tail method

› Two force vectors, F1 and F2, are shown in Fig. 3.

› When an object is subjected to more than

one force, the resultant of the forces is found

by the addition of vectors.

Fig. 3

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To add forces F1 and F2:

› Force F1 is drawn to scale horizontally, shown

as Oa in Fig. 4.

› From the nose of F1, force F2 is drawn at angle θ to the horizontal, shown as ab.

› The resultant force is given by length Ob,

which may be measured.

This procedure is called the ‘nose-to-tail’

or ‘triangle’ method.

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a

b

0

Fig. 4

Fig. 3

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Parallelogram method› To add the two force vectors, F1 and F2, of Fig.

3:

› A line cb is constructed which is parallel to and equal in length to Oa (see Fig. 5).

› A line ab is constructed which is parallel to and equal in length to Oc.

› The resultant force is given by the diagonal of the parallelogram, i.e. length Ob.

This procedure is called the ‘parallelogram’ method.

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a

b

0

Fig. 5

Fig. 3

c

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A force of 5N is inclined at an angle of 45◦ to

a second force of 8 N, both forces acting at

a point. Find the magnitude of the resultant

of these two forces and the direction of the

resultant with respect to the 8N force by:

› (a) the ‘nose-to-tail’method, and

› (b) the ‘parallelogram’ method.Answer:

12N at

(approximately) 17˚ from

horizontal

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Answer:

18N at

(approximately)

34˚ from

horizontal

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Answer:

22m/s at

(approximately)

105˚ from

horizontal

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Prepare for Quiz 1 and Peer Assessment 1, for next class!

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