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National Diploma in Engineering
Mechanical Principles for
Engineering Technicians
Assignment book
Don’t forget that when submitting work you must declare which outcome you
are claiming. (P1, M3, D2, for example)
Don’t forget to put your name on all submitted work.
When requested, work must be submitted with the assignment facing sheet,
Make sure that you understand the work you have submitted. You may be
asked questions upon submission.
Work which is not reasonably presented might not be accepted.
P1 calculate the magnitude, direction and position of the line of action of the
resultant and equilibrant of a non-concurrent coplanar force system
containing a minimum of four forces acting in different directions.
Calculate the magnitude, direction and position of the line of action of the
resultant and equilibrant of this system of non-concurrent coplanar forces.
The angles are;
a = 100°
b = 130°
c = 90°
d = 135°
P2 calculate the support reactions of a simply supported beam
carrying at least two concentrated loads and a uniformly
distributed load
Calculate the support reactions of this simply supported beam.
P3 calculate the induced direct strain and dimensional change in a
component subjected to direct uniaxial loading and the shear stress and
strain in a component subjected to shear loading
1) A strut of diameter 30mm and length 2.5m carries a direct uniaxial compressive load
of 30kN. The modulus of elasticity is for the material is 160 GPa. Find (a) the
compressive stress in the material, (b) the strain and (c) the change in length of the
2) A block of material is subjected to a shear force of 50kN and is deformed as shown
below. Find (i) the shear stress and (ii) the shear strain.
P4 solve three or more problems that require the application of kinetic and
dynamic principles to determine unknown system parameters
For P4 for this unit solve the problems in questions 1 to 4.
Question 1)
A missile has a mass of 2000 tonnes and exerts a thrust of 40 MN. Assuming the missile lifts
vertically determine the initial upward acceleration of the missile. If this thrust is maintained,
and assuming a negligible loss of mass within the first few seconds, what height will be
achieved 6 seconds from lift-off? What velocity will be achieved at this point?
Question 2)
A block of mass 60kg is pulled up an incline the angle of which is 35° from the horizontal.
(See figure 1). There is an opposing friction force of 50 N. If the linear distance from A to B is
12 metres calculate:
a) The force required to move the block at a constant velocity,
b) The work done moving the block from A to B, and
c) The average power required to do this work in a time of 20
Question 3)
A mass of 20kg is lifted to a height of 15 metres above the ground. Calculate the potential
energy gained. If the mass is allowed to fall freely under gravity what is its velocity when it
returns to the ground?
Question 4)
A wagon of mass16 tonnes moving along a track at 10 km/h, collides with a stationary
wagon of mass 12 tonnes and the conjoined wagons move on together. Calculate the
velocity of the conjoined wagons immediately after impact.
P5 Calculate the resultant thrust and overturning moment on a vertical
rectangular retaining surface with one edge in the free surface of a liquid
Part of a sea defence consists of a section of concrete wall 4 metres high and 6 metres
wide. (See figure below).
Calculate the resultant thrust on the section when the sea reaches a height of 3 metres
relative to the base of the section.
Calculate the overturning moment experienced by the section about point A.
P6 (See also D2). Determine the up-thrust on an immersed body
A steel bar of length 0.6m and diameter 70mm is suspended from a chain and lowered into
a tank of liquid whose relative density is 0.9. Determine the tension in the chain when the
bar is fully immersed. The density of the water is 1000kg/m³ and the density of steel is
P7 use the continuity of volume and mass flow for an incompressible fluid to
determine the design characteristics of a gradually tapering pipe
For this pipe the diameters are:(1) 120mm
(2) 70mm
(3) 160mm
The pipe contains oil with a density of 880kgmˉ³. Its velocity is 10msˉ¹ at point (2). Calculate
the volume flow rate, the mass flow rate, and the flow velocities at points (1) and (3).
P8 calculate dimensional change when a solid material undergoes a change in
temperature and the heat transfer that accompanies a change of
temperature and phase
(i) A brass bar has a length of 1.5 metres at 20°C. What is the increase in length of the bar at 100°C if
the coefficient of linear expansion of brass is 19.5x10ˉ6 /° C?
(ii) Calculate the heat energy required to change10kg of ice at −5°C to water at 0°C. The specific heat
capacity of ice is 2.1 kJkgˉ¹Kˉ¹ and the specific latent heat of fusion is 335 kJkgˉ¹ .
P9 solve two or more problems that require application of thermodynamic
process equations for a perfect gas to determine unknown parameters of the
(i) A mass of 0.12 kg of air has an initial temperature of 500°C and pressure 0.8 MPa. If the air is
expanded according to the law pV1.2 to a final volume of 90 litres determine (a) its initial volume, (b)
its final pressure, (c) its final temperature. For air, take R = 287 Jkgˉ¹ Kˉ¹.
(ii) Air with an initial volume of 0.12m³, pressure 1 bar and temperature 18°C is compressed
according to the law pV1.3 = c through a 8:1 compression ratio. It is then allowed to expand
isothermally back to its initial volume. Determine (a) the pressure and temperature after
compression and (b) the final pressure.
M1 calculate the factor of safety in operation for a component subjected to
combined direct and shear loading against given failure criteria
The material for the bolt shown in the angled joint shown has an ultimate tensile strength
of 460 MPa and a shear strength of 280 MPa. The diameter of the bolt is 8mm. Determine
both the tensile stress and shear stress in the bolt, and determine the factor of safety in
operation. The angle at a is 50°.
M2 determine the retarding force on a freely falling body when it impacts
upon a stationary object and is brought to rest without rebound, in a given
A pile-driver has a hammer mass of 1000 kg which is dropped onto a pile from a height of 5
metres. The pile is driven 0.5 metres into the ground. The pile has a mass of 500 kg.
Calculate the retarding force exerted by the ground on the combined mass of the pile and
M3 determine the thermal efficiency of a heat transfer process from given
values of flow rate, temperature change and input power
A coal fired steam plant takes in feed water at a temperature of 70°C and produces 15
tonnes of steam per hour at a pressure of 60 bar and temperature 400°C. The fuel
consumption rate is 1.5 tonnes per hour and the calorific value of the fuel is 40MJkgˉ¹.
Determine the power rating of the boiler and its thermal efficiency.
M4 determine the force induced in a rigidly held component that undergoes
a change in temperature.
Q2. A steel bar of length 1m and diameter of 30mm is held in a frame and experiences no
stress at 20°C. What will be the stress in the bar if the temperature rises to 80°C and any
change in length is prevented? Take E = 200GPa and α = 12 x 10 ˉ⁶ °Cˉ¹.
D1 compare and contrast the use of D’Alembert’s principle with the principle
of conservation of energy to solve an engineering problem
To gain a distinction for this assignment you need to solve the problem using two alternative
approaches, one being D`Alembert`s principle, and the other being the principle of the
conservation of energy.
The principle of conservation of energy equates work done in a system to changes in
potential energy, changes in kinetic energy, and other energy losses. D`Alembert`s principle
equates work done to the sum of all forces applied in a system. These are two alternative,
and sometimes complimentary, approaches. You are asked to compare and contrast the two
methods in relation to the problem you are solving.
A block with a mass of 5kg is pulled up an incline with an angle of 20°. (See figure 2). The
coefficient of friction is 0.2. The distance from A to B is 10 metres. The block accelerates
uniformly from 1msˉ¹ at point A to 5msˉ¹ at point B. Calculate:
a) The pulling force which is producing the acceleration
b) The work done in moving the block from A to B
c) The average power required in moving the block from A to B
D2 (See also P6) evaluate the methods that might be used to determine
the density of a solid material and the density of a liquid
Evaluate the methods that might be used to determine the density of a solid material and
the density of a liquid.