OCD61
Date: Saturday 23 August 2014
INSTRUCTIONS TO CANDIDATES:
Time: 10:00 am
– 12:00 noon
There are SIX questions.
Answer any TWO Questions from Part
A and any TWO Questions from Part B.
All questions carry equal marks.
Marks for parts of questions are shown in brackets.
Electronic calculators may be used provided the data and program storage memory is cleaned prior to the examination.
CANDIDATES REQUIRE : Formula Sheet (attached)

Page 2 of 9
Ras Al Khaimah Campus
B.Eng (Hons) Mechanical Engineering
Trimester Three Examination 2013/2014
Engineering Principles 2
Module No. AME4053
Q1.
(a) A rectangular sheet of metal having dimensions 20 cm by 12 cm has squares removed from each of the four corners and the sides bent upwards to form an open box. Determine the maximum possible volume of the box.
(12 marks)
(b) A projectile is fired vertically upwards under gravity. Its velocity after t seconds is given by v(t) ms
-1
, where
V = 25- 10t.
Find a formula for the height h(t) m of the projectile above its launch point after t seconds and deduce the maximum height it reaches.
(8 marks)
(Total 20 marks)
Q2.
Evaluate the following integrals
(a)
 x
2 x


1
3 x

2 dx
(6 marks)
(b)

/

0
4 x cos xdx
(6 marks)
(c) The speed V of a rocket t seconds after launching is given by
V = at
2
+ b
Where a and b are constants. Its average speed over the first second was
10m/sec, and the average speed over the next second was 50 m/sec.
Determine the values of a and b.
(8 marks)
(Total 20 marks)
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Page 3 of 9
Ras Al Khaimah Campus
B.Eng (Hons) Mechanical Engineering
Trimester Three Examination 2013/2014
Engineering Principles 2
Module No. AME4053
Q3.
(a) Find the area enclosed by the curve y = x(x-2), the x- axis the line x = 0 and the line x= 3
(7 marks)
(b) When an object such as a mass vibrating on a string or pendulum oscillating under the action of gravity, moves in a simple harmonic motion its velocity satisfies a differential equation of the form v(dv/dx) = -k x, where x is displacement and k is a constant. Find an expression for v.
(5 marks)
(c) The concentration, C, of impurities of an oil purifier varies with time t and is described by the equation a(dC/dt) = b + dm – Cm, where a,b,d and m are constants.
Given C = c
0 when t = 0, solve the equation and show that:
C = b m d

 1
 e
 mt a


 c
0 e
 mt a
(8 marks)
(Total 20 marks)
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Page 4 of 9
Ras Al Khaimah Campus
B.Eng (Hons) Mechanical Engineering
Trimester Three Examination 2013/2014
Engineering Principles 2
Module No. AME4053
Q4.
Figure Q4 shows a T-section of dimensions 10 x 10 x 2 cm. Determine the following: i. the centroid of the section
(6 marks) ii. moment of inertia of the section about the horizontal and vertical axes passing through the centre of gravity of the section.
(10 marks) iii. Find Radius of Gyration about horizontal and vertical axes
(4 marks)
Figure Q4
Total 20 marks
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Page 5 of 9
Ras Al Khaimah Campus
B.Eng (Hons) Mechanical Engineering
Trimester Three Examination 2013/2014
Engineering Principles 2
Module No. AME4053
Q5.
(a) A steel plate of width140mm and of thickness 30mm is bent into a circular arc of radius 8m.Determine the following: i) Maximum stress induced
(5 marks) ii) Bending moment which will produce the maximum stress.
(5 marks)
Given E = 2x10
5
N/mm
2
(b) A spring loaded with 2.5kg weight is extended 360mm when in equilibrium. The mass is pulled vertically downward through a further distance of 250mm and is then released from rest so that it oscillates about the equilibrium position.
Determine : i) the stiffness constant ‘k’ of the spring and time of oscillation in seconds
(5 marks) ii) the velocity and acceleration when the weight is at a distance of
150mmbelow its equilibrium position.
(5 marks)
Total 20 marks
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Page 6 of 9
Ras Al Khaimah Campus
B.Eng (Hons) Mechanical Engineering
Trimester Three Examination 2013/2014
Engineering Principles 2
Module No. AME4053
Q6.
A block of weight 2000N is in contact with a plane inclined at 30 o
to the horizontal. A force
‘P’
parallel to the plane and acting up the plane is applied to the body. The coefficient of friction between the contact surfaces is 0.3.Find i) the value of P to just cause the motion to impend up the plane.
(7 marks) ii) the value of P to just prevent the motion down the plane.
(7 marks) iii) the magnitude and direction of frictional force if P=1200N.
(6 marks)
Figure Q6
Total 20 marks
END OF QUESTIONS
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Page 7 of 9
Ras Al Khaimah Campus
B.Eng (Hons) Mechanical Engineering
Trimester Three Examination 2013/2014
Engineering Principles 2
Module No. AME4053
FORMULA SHEET
Partial Fractions
(x

F(x) a)(x
 b)

(x
A
 a)

B
(x
 b)
F(x)
(x
 a)(x
 b)
2

(x
A
 a)

(x
B
 b)

C
(x
 b)
2
Trigonometry sin 2x = 2 sin x cos x cos 2x = cos
2 x – sin 2 x cos 2x = 2 cos
2 x – 1 cos 2x = 1 -2 sin
2 x
2 tan x tan 2x =
1
 tan
2 x sin
2
x + cos
2
x = 1 tan
2
x + 1 = sec
2 x cosec
2
x = 1 + cot
2
x
Differentiation y = uv dy dx dv
= u dx
+ v du dx
(Product Rule) u y = v dy dx
 v du
 u dx v
2 dv dx
(Quotient Rule) dy dx
 dy dt x dt dx
(Chain Rule)
Integration
 u dv dx dx
 uv
  v du dx dx (By parts)
 f
1
(x) dx f(x)
 ln f(x)
 c
Area under the curve y = f(x) between the limits x = a and x = b is
Volume of a solid of revolution of the curve y = f(x) between the limits x= a and x = b
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Page 8 of 9
Ras Al Khaimah Campus
B.Eng (Hons) Mechanical Engineering
Trimester Three Examination 2013/2014
Engineering Principles 2
Module No. AME4053
Differential equations
Linear differential equation dy/dx + Py = Q
Integrating factor is
Solution is y
Centroid and 2 nd
Moments of Area
Rectangle X = (b/2), Y= (d/2) , A=bd I
XX
= bd
3
12
I
YY
= db
3
12
Circle I XX=
πR 4
4
Hollow circle
I XX=

( D 4  d )
64
Polar J solid
=

D
4
32
J hollow
= π(D
4
–d
4
)/32
For composite sections
X =
Y
=
Parallel Axis Theorem
I xx
= I
GG
+ Ah
2
I
XX
= (I
XX
) i
+
𝜮
A i
(Y i
– Y) 2
I
YY
=
(
I
YY
) i
+
𝜮
A i
(X i
– X)
2
Energy and Momentum
Potential Energy = mgh
Kinetic Energy
Linear = ½ mv
2
Angular=½ I
 2
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Page 9 of 9
Ras Al Khaimah Campus
B.Eng (Hons) Mechanical Engineering
Trimester Three Examination 2013/2014
Engineering Principles 2
Module No. AME4053
Momentum
Linear= mv
Angular= I

Vibrations
Linear Stiffness k

F

Circular frequency
 n

Frequency f n

 n
2
 x
 r cos
 t

1
T n v
   a
  
2 x r
2  x
2    r sin
 t
T f


1
T
2

 k m
M/I = =E/R
P= 2 N
T/ J =
F=μ N
= /r
Trigonometry a
Sine Rule: sinA
 b sinB
 c sinC
Cosine Rule: a
2
= b
2
+ c
2 – 2bc cos A