Basic Engineering Mathematics, Fifth Edition

132 Basic Engineering Mathematics

theyvalue. In Figure 17.3, pointBhas co-ordinates

(− 4 , 3 )and pointChas co-ordinates(− 3 ,− 2 ).

17.3 Straight line graphs

The distances travelled by a car in certain peri-

ods of time are shown in the following table of

values.

Time(s) 10 20 30 40 50 60

Distance travelled (m) 50 100 150 200 250 300

We will plot time on the horizontal (orx) axis with a

scale of 1cm=10s.

We will plot distance on the vertical (ory) axis with a

scale of 1cm=50m.

(When choosingscales itis better tochoose ones such as

1cm=1unit,1cm=2unitsor 1cm=10unitsbecause

doing so makes reading values between these values

easier.)

With the above data, the(x,y)co-ordinates become

(time, distance) co-ordinates; i.e., the co-ordinates are

(10, 50), (20, 100), (30, 150), and so on.

The co-ordinates are shown plotted in Figure 17.4

using crosses. (Alternatively, a dot or a dot and circle

may be used, as shown in Figure 17.3.)

A straight line is drawn through the plotted co-

ordinates as shown in Figure 17.4.

300

Distance Travelled (m)

Time (s)

250

200

150

100

50

10 20 30 40 50 60

Distance/ time graph

Figure 17.4

Student task

Thefollowing tablegives theforceFnewtons which,

when applied to a lifting machine, overcomes a

corresponding load ofLnewtons.

F(Newtons) 19 35 50 93 125 147

L(Newtons) 40 120 230 410 540 680

1. PlotLhorizontally andFvertically.


2. Scales are normally chosen such that the graph
   occupies as much space as possible on the
   graph paper. So in this case, the following
   scales are chosen.

Horizontal axis (i.e.L): 1cm=50N

Vertical axis (i.e.F): 1cm=10N

3. Draw the axes and label themL(newtons) for
   the horizontal axis andF(newtons) for the
   vertical axis.


4. Label the origin as 0.


5. Writeonthehorizontalscalingat100,200,300,
   and so on, every 2cm.


6. Write on the vertical scaling at 10, 20, 30, and
   so on, every 1cm.


7. Plot on the graph the co-ordinates (40, 19),
   (120, 35), (230, 50), (410, 93), (540, 125) and
   (680, 147), markingeach with a cross or a dot.


8. Usingaruler,drawthebest straight linethrough
   the points. You will notice that not all of the
   pointslieexactly ona straightline.This is quite
   normal with experimental values. In a practi-
   cal situation it would be surprising if all of the
   points lay exactly on a straight line.


9. Extend the straight line at each end.


10. From the graph, determine the force applied
    when the load is 325N. It should be close
    to 75N. This process of finding an equivalent
    value within the given data is calledinterpola-
    tion. Similarly, determine the load that a force
    of 45N will overcome. It should be close to
    170N.


11. From the graph, determine the force needed to
    overcome a 750N load. It should be close to
    161N. This process of finding an equivalent