Download First Diploma in Engineering Mathematics for Engineering

First Diploma in Engineering
Mathematics for Engineering
Technicians
Assignment booklet
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,
signed.
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 use arithmetic methods to evaluate two engineering problems ensuring
answers are reasonable
a) The force required to accelerate a mechanical lift vertically is given by the formula
F = mg + ma
Where F is the force, measured in joules
m = 500kg, the mass of the lift
g = 9.81msˉ², the acceleration due to gravity
a = 1msˉ² , the acceleration of the lift.
Calculate the force applied to the lift.
How could you ensure that your answer is reasonable? Please show your method.
b) The time period of a simple pendulum is given by the formula
where T is the time period of the pendulum, L = 2m, the length of the pendulum and g =
9.81msˉ², the acceleration due to gravity.
Calculate the time period of the pendulum.
How could you ensure that your answer is reasonable? Please show your method.
P2 use algebraic methods to transpose and evaluate simple formulae
a) In an electrical circuit the voltage, current and resistance are related by the formula
V = IR
If V = 10 volts and R = 47kΩ calculate the value of the current. Please show your
method.
b) The displacement of an object in time is given by the formula
S is the distance travelled
u is the initial velocity of the object
v is the final velocity of the object
t is the time taken to travel the distance
Transpose the equation to make t the subject and then find its value if s = 12 m, u = 3
msˉ¹ and v = 7 msˉ¹.
P3 plot a graph for linear and non-linear relationships from given data
a) The following table of load and effort readings was obtained from a test on a lifting
device.
Effort,
E (N)
Load,
W (N)
20.5
25.0
29.5
35.0
40.5
45.0
49.5
55.0
60.0
200
400
600
800
1000
1200
1400
1600
1800
Plot a graph of effort (y-axis) against load (x-axis).
b) The luminosity of a lamp, I, varies with applied voltage V. Experimental values are
obtained as shown:
I
2.5
candela
V
50
voltage
4.9
8.1
12.1
16.9
22.5
27.5
34.5
44.5
70
90
110
130
150
170
190
210
Plot a graph of voltage against luminosity.
P4 determine the area of two regular shapes from given data
a) Calculate the area of a rectangle of height 2 metres and base 3.5 metres.
b) Calculate the area of a circle of radius 4.5 metres.
P5 determine the volume of two regular solid bodies from given data
a) Calculate the volume of material required to make a cylinder 5 metres long with an
outer diameter of 1.2 metres.
b) Calculate the volume of a solid sphere of radius 100mm.
P6 solve right-angled triangles for angles and lengths of sides using basic
Pythagoras’ theorem, sine, cosine and tangent functions
a) Use the tangent function to find the length of the adjacent side for this triangle. The
angle at a is 35°.
b) Use Pythagoras` theorem to calculate the length of the hypotenuse.
c) Use the sine function to calculate the length of the opposite side for the triangle below.
The angle at a is 30°.
d) Use the cosine function to calculate the length of the adjacent side. The angle at a is 30°.
e) Calculate the lengths of the unknown side and the unknown angles in this right angled
triangle.
M1 transpose and evaluate complex formulae
a) The force exerted by a jet of water as it strikes a stationary flat plate at right angles is
given by the formula
where the density of water ρ = 1000kgmˉ³ and the diameter of the jet d = 0.05 m.
Determine the velocity v, in msˉ¹, of the jet that will deliver a force of 450 N.
b) The instantaneous voltage of an alternating supply is given by the following equation:
V = V0sin2πft
Find a value for t when V = 80 volts if V0 = 110volts and f = 50Hz.
M2 identify the data required and determine the area of two compound
shapes
a) Calculate the area of this panel. Show the data you have used and show your working.
b) A panel is to be made for the front of an electronic control box. The panel will consist of
a rectangle of sheet metal of height 80mm and width 200mm. Three circular holes will be
cut from the rectangle, each with a diameter of 15mm. A further circular hole will be cut out
with a diameter of40mm. Calculate the area of the completed panel. Show the data you
have used and show your working.
M3 identify the data required and determine the volume of two compound
solid bodies
a) See figure 1. Calculate the volume of fluid required to fill this receptacle to the brim. To
some extent this will be an approximation. Treat the main body of the receptacle as a
sphere of inner diameter 120mm and the neck as a cylinder of inner diameter 30mm and
height 90mm.
Figure 1.
b) A component is to be made from mild steel. It consists of a rectangular block of height
30mm, width 70mm and depth 50mm. Two holes will be drilled through the entire height of
the block, one of diameter 10mm and one of diameter 15mm. Calculate the volume of steel
needed for the component.
M4 Use trigonometry to solve complex shapes
a) Calculate (i) the lengths of the unknown sides of this trapezium, (ii) the internal angles
and (iii) the height. Length AB = 4m, CE = 3m, DE = 9m and the internal angle at x = 65°.
b) Calculate the angles and unknown sides for triangle ABC.
The angle at a = 40°. Length AB = 2.5m. Length CD = 0.5m.
D1 transpose and evaluate combined formulae
(a) When a mass free falls in a gravitational field its motion is controlled by the following
relationship:
If g = 9.81 msˉ², m = 4kg and h = 10m calculate its velocity v.
(b) The charge relationship for a capacitor is given by the following expression:
Find V if Q = 750 x 10−6 coulombs and C = 6 x 10−6 farads.
(c) When an object is pushed across a flat, dry surface the following formulae relate to the
amount of energy needed to do this:
E = Ff s and Ff = μmg
If E = 1.57kJ, m = 80kg, s = 5m and g = 9.81msˉ² what is the value of μ?
D2 carry out chained calculations using an electronic calculator
The following question gives the student the opportunity to gain D2 by demonstrating the
ability to carry out chained calculations using an electronic calculator.
Note: to achieve D2 you will need to be observed performing the chained calculations, and a
witness statement will be signed.
a) The force required to move and accelerate a mass up an incline is given by the equation:F = mgsinθ + mgμcosθ + ma, where m is the mass, g is gravity, a is acceleration, μ is the
coefficient of friction, and θ is the angle of the incline.
If g = 9.8, m = 25kg, a = 3msˉ², μ = 0.4 and θ= 35°, calculate, in one chained calculation,
the force being applied to the mass.
The work done in moving the mass is given by the equation:-
W = Fd, where W is the work done, F is the force applied and d is the distance over which
the force has been applied.
If the mass is increased to 30kg, the angle becomes 40°, the coefficient of friction remains
at 0.4, and the acceleration becomes 2ms¯², and the block moves a distance of 6 metres up
the ramp, calculate, in one chained calculation, the work done.