basic_engineering_mathematics0

Calculations and evaluation of formulae 27
(b) A girl leaves Hunts Cross at 8.17 a.m. and travels
to Manchester Oxford Road. How long does
the journey take. What is the average speed of the
journey?
(c) A man living at Edge Hill has to be at work at Trafford
Park by 8.45 a.m. It takes him 10 minutes to
walk to his work from Trafford Park station. What
time train should he catch from Edge Hill?
Problem 19. The area, A, of a circle is given by A = πr 2 .
Determine the area correct to 2 decimal places, given radius
r = 5.23 m.
A = πr 2 = π(5.23) 2 = π(27.3529)
Hence area, A = 85.93 m 2 , correct to 2 decimal places.
4.4 Evaluation of formulae
The statement v = u + at is said to be a formula for v in terms
of u, a and t.
v, u, a and t are called symbols.
The single term on the left-hand side of the equation, v, is
called the subject of the formulae.
Provided values are given for all the symbols in a formula
except one, the remaining symbol can be made the subject of the
formula and may be evaluated by using a calculator.
Problem 16. In an electrical circuit the voltage V is given
by Ohm’s law, i.e. V = IR. Find, correct to 4 significant
figures, the voltage when I = 5.36 A and R = 14.76 .
V = IR = (5.36)(14.76)
Hence voltage V = 79.11V, correct to 4 significant figures.
Problem 17. The surface area A of a hollow cone is given
by A = πrl. Determine, correct to 1 decimal place, the
surface area when r = 3.0 cm and l = 8.5 cm.
A = πrl = π(3.0)(8.5) cm 2
Hence surface area A = 80.1 cm 2 , correct to 1 decimal place.
Problem 18. Velocity v is given by v = u + at. If
u = 9.86 m/s, a = 4.25 m/s 2 and t = 6.84 s, find v, correct
to 3 significant figures.
v = u + at = 9.86 + (4.25)(6.84)
= 9.86 + 29.07
= 38.93
Hence velocity υ = 38.9 m/s, correct to 3 significant
figures.
Problem 20. The power P watts dissipated in an electrical
circuit may be expressed by the formula P = V 2
R . Evaluate
the power, correct to 3 significant figures, given that
V = 17.48V and R = 36.12 .
P = V 2
R = (17.48)2
36.12 = 305.5504
36.12
Hence power, P = 8.46W, correct to 3 significant
figures.
Problem 21. The volume V cm 3 of a right circular cone
is given by V = 1 3 πr2 h. Given that r = 4.321 cm and h =
18.35 cm, find the volume, correct to 4 significant figures.
V = 1 3 πr2 h = 1 3 π(4.321)2 (18.35)
= 1 3 π(18.671041)(18.35)
Hence volume,V = 358.8 cm 3 , correct to 4 significant figures.
Problem 22. Force F newtons is given by the formula
F = Gm 1m 2
, where m
d 2
1 and m 2 are masses, d their distance
apart and G is a constant. Find the value of the force given
that G = 6.67 × 10 −11 , m 1 = 7.36, m 2 = 15.5 and d = 22.6.
Express the answer in standard form, correct to 3 significant
figures.
F = Gm 1m 2
= (6.67 × 10−11 )(7.36)(15.5)
d 2 (22.6) 2
= (6.67)(7.36)(15.5)
(10 11 )(510.76)
= 1.490
10 11
Hence force F = 1.49 × 10 −11 newtons, correct to 3 significant
figures.