Basic Engineering Mathematics, Fifth Edition

146 Basic Engineering Mathematics

Plot a graph of F (vertically) againstw

(horizontally).

(a) Interpolate and determine the crushing

strength when 10% water is used.

(b) Assuming the graph continues in the

same manner, extrapolate and deter-

mine the percentage of water used when

the crushing strength is 0.15 tonnes.

(c) What is the equation of the graph?

8. Inanexperiment demonstratingHooke’slaw,
   the strain in a copper wire was measured for
   various stresses. The results were

Stress 10. 6 × 10618. 2 × 10624. 0 × 106

(pascals)

Strain 0.00011 0.00019 0.00025

Stress 30. 7 × 106 39. 4 × 106

(pascals)

Strain 0.00032 0.00041

Plot a graph of stress (vertically) against

strain (horizontally). Determine

(a) Young’s modulus of elasticity for cop-

per, which is given by the gradient of

the graph,

(b) the value of strain at a stress of

21 × 106 Pa,

(c) the value of stress when the strain is

0.00030,

9. An experiment with a set of pulley blocks
   gave the following results.

Effort,E(newtons) 9.0 11.0 13.6

Load,L(newtons) 15 25 38

Effort,E(newtons) 17.4 20.8 23.6

Load,L(newtons) 57 74 88

Plot a graph of effort (vertically)against load

(horizontally). Determine

(a) the gradient,

(b) the vertical axis intercept,

(c) the law of the graph,

(d) the effort when the load is 30N,

(e) the load when the effort is 19N.

10. The variation of pressurepin a vessel with
    temperatureTis believed to follow a law of
    the formp=aT+b,whereaandbare con-
    stants. Verify this law for the results given
    below and determine the approximate values
    ofaandb. Hence, determine the pressures
    at temperatures of 285K and 310K and the
    temperature at a pressure of 250kPa.

Pressure,p(kPa) 244 247 252

Temperature,T(K) 273 277 282

Pressure,p(kPa) 258 262 267

Temperature,T(K) 289 294 300