basic_engineering_mathematics0

92 Basic Engineering Mathematics
Now try the following exercise
Exercise 48
Further practical problems involving
straight line graphs (Answers on page 275)
1. The resistance R ohms of a copper winding is measured
at various temperatures t ◦ C and the results are as follows:
R ohms 112 120 126 131 134
t ◦ C 20 36 48 58 64
Plot a graph of R (vertically) against t (horizontally) and
find from it (a) the temperature when the resistance
is 122 and (b) the resistance when the temperature
is 52 ◦ C.
2. The speed of a motor varies with armature voltage as
shown by the following experimental results:
n (rev/min) 285 517 615 750 917 1050
V volts 60 95 110 130 155 175
Plot a graph of speed (horizontally) against voltage (vertically)
and draw the best straight line through the points.
Find from the graph (a) the speed at a voltage of 145V,
and (b) the voltage at a speed of 400 rev/min.
3. The following table gives the force F newtons which,
when applied to a lifting machine, overcomes a corresponding
load of L newtons.
Force F
newtons 25 47 64 120 149 187
Load L
newtons 50 140 210 430 550 700
Choose suitable scales and plot a graph of F (vertically)
against L (horizontally). Draw the best straight
line through the points. Determine from the graph (a)
the gradient, (b) the F-axis intercept, (c) the equation
of the graph, (d) the force applied when the load is
310 N, and (e) the load that a force of 160 N will overcome.
(f) If the graph were to continue in the same
manner, what value of force will be needed to overcome a
800 N load?
4. The following table gives the results of tests carried out
to determine the breaking stress σ of rolled copper at
various temperatures, t:
Stress σ (N/cm 2 ) 8.51 8.07 7.80
Temperature t( ◦ C) 75 220 310
Stress σ (N/cm 2 ) 7.47 7.23 6.78
Temperature t( ◦ C) 420 500 650
Plot a graph of stress (vertically) against temperature
(horizontally). Draw the best straight line through the
plotted co-ordinates. Determine the slope of the graph
and the vertical axis intercept.
5. The velocity v of a body after varying time intervals
t was measured as follows:
t (seconds) 2 5 8 11 15 18
v (m/s) 16.9 19.0 21.1 23.2 26.0 28.1
Plot v vertically and t horizontally and draw a graph of
velocity against time. Determine from the graph (a) the
velocity after 10 s, (b) the time at 20 m/s and (c) the
equation of the graph.
6. The mass m of a steel joint varies with length L as follows:
mass, m (kg) 80 100 120 140 160
length, L (m) 3.00 3.74 4.48 5.23 5.97
Plot a graph of mass (vertically) against length (horizontally).
Determine the equation of the graph.
7. The crushing strength of mortar varies with the percentage
of water used in its preparation, as shown
below.
Crushing
strength, F
(tonnes) 1.64 1.36 1.07 0.78 0.50 0.22
% of water
used, w% 6 9 12 15 18 21
Plot a graph of F (vertically) against w (horizontally).
(a) Interpolate and determine the crushing strength when
10% of water is used.
(b) Assuming the graph continues in the same manner
extrapolate and determine the percentage of water
used when the crushing strength is 0.15 tonnes.
(c) What is the equation of the graph?
8. In an experiment demonstrating Hooke’s law, the strain
in a copper wire was measured for various stresses. The
results were:
Stress
(pascals) 10.6 × 10 6 18.2 × 10 6 24.0 × 10 6
Strain 0.00011 0.00019 0.00025