Basic Engineering Mathematics, Fifth Edition

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.

3. 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?

4. 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.

5. 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.

6. 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.

7. 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