Straight line graphs 143

Plot a graph of stress (vertically) against strain

(horizontally). Find (a) Young’s modulus of

elasticity for aluminium, which is given by the

gradient of the graph, (b) the value of the strain at a

stress of 20N/mm^2 and (c) the value of the stress

when the strain is 0.00020

The co-ordinates (0.00007, 4.9), (0.00013, 8.7), and
so on, are plotted as shown in Figure 17.20. The
graph produced is the best straight line which can be
drawn corresponding to these points. (With experimen-
tal results it is unlikelythat all the points will lie exactly
on a straight line.) The graph, and each of its axes, are
labelled. Since the straight line passes through the ori-
gin, stress is directly proportional to strain for the given
range of values.

Stress (N/mm

2 )

(^0) 0.00005
4
8
12
14
16
20
24
28
0.00015 0.00025
Strain 0.000285
0.00035
y
x
A
C B
Figure 17.20
(a) The gradient of the straight lineACis given by
AB
BC

28 − 7
0. 00040 − 0. 00010

21
0. 00030

21
3 × 10 −^4

7
10 −^4
= 7 × 104
=70000N/mm^2
Thus,Young’s modulus of elasticity for alu-
miniumis70000N/mm^2 .Since1m^2 = 106 mm^2 ,
70000N/mm^2 is equivalent to 70000× 106 N/m^2 ,
i.e. 70 × 109 N/m^2 (or pascals).
From Figure 17.20,
(b) The value of the strain at a stress of 20N/mm^2 is
0.000285
(c) The value of the stress when the strain is 0.00020
is14N/mm^2.
Problem 15. The following values of resistance
Rohms and corresponding voltageVvolts are
obtained from a test on a filament lamp.
Rohms 30 48.5 73 107 128
Vvolts 16 29 52 76 94
Choose suitable scales and plot a graph withR
representing the vertical axis andVthe horizontal
axis. Determine (a) the gradient of the graph, (b) the
Raxis intercept value, (c) the equation of the graph,
(d) the value of resistance when the voltage is 60V
and (e) the value of the voltage when the resistance
is 40 ohms. (f) If the graph were to continue in the
same manner, what value of resistance would be
obtained at 110V?
The co-ordinates (16, 30), (29, 48.5), and so on are
shown plotted in Figure 17.21, where the best straight
line is drawn through the points.
147
140
120
85
80
60
100
Resistance
R
(ohms)
40
10
20
0 2024 40 60 80 100 110 120
Voltage V (volts)
y
C B
A
x
Figure 17.21
(a) The slope or gradient of the straight lineACis
given by
AB
BC

135 − 10
100 − 0

125
100
=1.25