Basic Engineering Mathematics, Fifth Edition

(Amelia) #1

Straight line graphs 145


n(rev/min) 285 517 615

V(volts) 60 95 110

n(rev/min) 750 917 1050
V(volts) 130 155 175

Plot a graph of speed (horizontally) against
voltage(vertically) and draw thebest 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 400rev/min.


  1. The following table gives the force F
    newtons which, when applied to a lifting
    machine, overcomes a corresponding load of
    Lnewtons.


ForceF(newtons) 25 47 64

LoadL(newtons) 50 140 210

ForceF(newtons) 120 149 187

LoadL(newtons) 430 550 700

Choose suitable scales and plot a graph of
F(vertically) againstL(horizontally).Draw
the best straight line through the points.
Determine from the graph
(a) the gradient,
(b) theF-axis intercept,
(c) the equation of the graph,
(d) the force applied when the load is
310N, and
(e) the load that a force of 160N will
overcome.
(f) If the graph were to continue in the
same manner, what value of force will
be needed to overcome a 800N load?


  1. The following table gives the results of tests
    carried out to determine the breaking stress
    σof rolledcopper at varioustemperatures,t.


Stressσ(N/cm^2 ) 8.51 8.07 7.80

Temperaturet(◦C) 75 220 310

Stressσ(N/cm^2 ) 7.47 7.23 6.78
Temperaturet(◦C) 420 500 650

Plot a graph of stress (vertically) against
temperature (horizontally). Draw the best
straight linethroughthe plottedco-ordinates.
Determine the slope of the graph and the
vertical axis intercept.


  1. The velocityvof a body after varying time
    intervalstwas measured as follows:


t(seconds) 2 5 8
v(m/s) 16.9 19.0 21.1

t(seconds) 11 15 18
v(m/s) 23.2 26.0 28.1

Plotvvertically andthorizontally and draw
a graph of velocity against time. Determine
from the graph (a) the velocity after 10s,
(b) the time at 20m/s and (c) the equation
of the graph.


  1. The massmof a steel joist varies with length
    Las follows:


mass,m(kg) 80 100 120 140 160

length,L(m) 3.00 3.744.48 5.235.97

Plot a graph of mass (vertically) against
length (horizontally). Determine the equa-
tion of the graph.


  1. The crushing strength of mortar varies with
    the percentage of water used in its prepara-
    tion, as shown below.


Crushing strength, 1.67 1.40 1.13
F(tonnes)
% of water used,w% 6 9 12

Crushing strength, 0.86 0.59 0.32
F(tonnes)
% of water used,w% 15 18 21
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