Basic Engineering Mathematics, Fifth Edition

Solving simple equations 79

Now try the following Practice Exercise

PracticeExercise 44 Practicalproblems

involving simple equations (answers on

page 344)

1. A formulaused for calculatingresistance of a
   cableisR=

ρL

a

.GivenR= 1 .25,L= 2500

anda= 2 × 10 −^4 , find the value ofρ.

2. ForceFnewtons is given byF=ma,where
   mis the mass in kilograms andais the accel-
   erationinmetrespersecondsquared.Findthe
   acceleration when a force of 4kN is applied
   to a mass of 500kg.


3. PV=mRTis the characteristic gas equa-
   tion. Find the value ofmwhen
   P= 100 × 103 ,V= 3. 00 ,R=288 and
   T=300.


4. When three resistorsR 1 ,R 2 andR 3 are con-
   nected in parallel, the total resistanceRTis
   determined from

1

RT

=

1

R 1

+

1

R 2

+

1

R 3

(a) Find the total resistance when

R 1 = 3 ,R 2 = 6 andR 3 = 18 .

(b) Find the value ofR 3 given that

RT= 3 ,R 1 = 5 andR 2 = 10 .

5. Six digital camera batteries and 3 camcorder
   batteries cost £96. If a camcorder battery
   costs £5 more than a digital camera battery,
   find the cost of each.


6. Ohm’s law may be represented byI=V/R,
   where I is the current in amperes, V is
   the voltage in volts andRis the resistance
   in ohms. A soldering iron takes a current
   of 0.30A from a 240V supply. Find the
   resistance of the element.


7. The distance,s, travelled in timetseconds is
   given by the formulas=ut+

1

2

at^2 where

uis the initial velocity in m/s andais the

acceleration in m/s^2. Calculate the accelera-

tion of the body if it travels 165m in 3s, with

an initial velocity of 10m/s.

Here are some further worked examples on solving
simple equations in practical situations.

Problem 24. The extensionxm of an aluminium

tie bar of lengthlm and cross-sectional areaAm^2

when carrying a load ofFNewtons is given by the

modulus of elasticityE=Fl/Ax.Findthe

extension of the tie bar (in mm) if

E= 70 × 109 N/m^2 ,F= 20 × 106 N,A= 0 .1m^2

andl= 1 .4m

E=Fl/Ax,hence

70 × 109

N

m^2

=

( 20 × 106 N)( 1 .4m)

( 0 .1m^2 )(x)

(the unit ofxis thus metres)

70 × 109 × 0. 1 ×x= 20 × 106 × 1. 4

x=

20 × 106 × 1. 4

70 × 109 × 0. 1

Cancelling gives x=

2 × 1. 4

7 × 100

m

=

2 × 1. 4

7 × 100

×1000mm

=4mm

Hence,the extension of the tie bar,x=4mm.

Problem 25. Power in a d.c. circuit is given by

P=

V^2

R

whereVis the supply voltage andRis the

circuit resistance. Find the supply voltage if the

circuit resistance is 1.25and the power measured

is 320W

Since P=

V^2

R

, then 320=

V^2

1. 25

( 320 )( 1. 25 )=V^2

i.e. V^2 = 400

Supply voltage, V=

√

400 =±20V

Problem 26. A painter is paid £6.30 per hour for a

basic 36 hour week and overtime is paid at one and

a third times this rate. Determine how many hours

the painter has to work in a week to earn £319. 20

Basic rate per hour=£6.30 and overtime rate per hour

= 1

1

3

×£6. 30 =£8. 40

Let the number of overtime hours worked=x

Then, ( 36 )( 6. 30 )+(x)( 8. 40 )= 319. 20

226. 80 + 8. 40 x= 319. 20