city guilds model questions vol1 2021 engineering | Practical

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Question 1 View Details
A steel rectangular bar is to be used as a supporting beam. The bar is 200 mm long. Its cross‑section is approximately rectangular but the actual width (b) and height (h) vary slightly along the length. The following measurements of width (in mm) and height (in mm) were taken at five equally spaced points along the bar:
Question Parts
(a)
Determine the mean width \(\overline{b}\) and mean height \(\overline{h}\) of the bar.
(b)
Using the mean dimensions, calculate the second moment of area \(I\) of the bar about its neutral axis (use \(I = \frac{\overline{b}\,\overline{h}^{3}}{12}\)). Express your answer in \(\text{mm}^{4}\).
(c)
State two possible sources of experimental error in the measurement process and suggest one method to reduce each error.
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Question 2 View Details
In a laboratory the following two circuits were assembled using a 12.0 V DC supply and the resistors R₁ = 100 Ω and R₂ = 200 Ω. For each circuit the voltage across the supply and the current drawn from the supply were recorded:
Question Parts
(a)
Calculate the experimental equivalent resistance \(R_{eq,exp}\) of each circuit using the measured voltage and current values.
(b)
Determine the theoretical equivalent resistance for each configuration using the known resistor values.
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Question 3 View Details
A wooden block of mass 0.50 kg is placed on a smooth wooden inclined plane. The plane is gradually raised until the block just begins to slide. The angle of inclination is recorded for three successive trials as 15.0°, 16.2° and 14.5°. The experiment is to be used to determine the coefficient of static friction between the block and the plane.
Question Parts
(a)
Calculate the coefficient of static friction (μ) for each trial.
(b)
Determine the average coefficient of static friction from the three trials.
(c)
Identify two possible sources of error in this experiment and suggest one method to minimise each error.
(d)
Explain why it is important to use the same block for all three trials.
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Question 4 View Details
A student constructs a series circuit powered by a 12.0 V DC supply. The circuit consists of a single resistor (colour‑code 33 Ω) and an ammeter in series, and a voltmeter connected across the resistor. The following readings are obtained: voltage across the resistor = 9.8 V, current through the circuit = 0.30 A.
Question Parts
(a)
Calculate the experimental resistance of the resistor using the recorded readings.
(b)
Determine the percentage error of the experimental resistance relative to the colour‑code value (33 Ω).
(c)
Compute the power dissipated in the resistor using the experimental values.
(d)
List two safety precautions that should be observed when assembling and testing this circuit.
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Question 5 View Details
In the Materials laboratory a cylindrical steel specimen is to be tested for its Young's modulus using a universal testing machine (UTM). The specimen is clamped between the machine grips and the gauge length (distance between the inner faces of the grips) is 200 mm. The diameter of the specimen is measured at three equally spaced locations along its length and the readings are 12.00 mm, 11.96 mm and 12.04 mm. The UTM records the applied axial load and the corresponding extension of the specimen as follows: | Load (kN) | Measured extension (mm) | |-----------|--------------------------| | 5 | 0.15 | | 10 | 0.31 | | 15 | 0.48 | The machine has a compliance of 0.02 mm kN⁻¹, meaning that a portion of the measured extension is due to deformation of the machine itself. Using the data provided, answer the questions below.
Question Parts
(a)
Determine the average diameter of the specimen and calculate its cross‑sectional area. Express the area in m².
(b)
For each load, calculate: (i) the engineering stress (σ = P/A) in MPa; (ii) the corrected strain (ε) after removing the machine compliance, using ε = (ΔL – C·P)/L₀, where C = 0.02 mm kN⁻¹ and L₀ = 200 mm. Present the results in a table.
(c)
Using the stress–strain data obtained in part (b), determine the Young's modulus of the steel specimen. Assume a linear relationship and calculate the gradient of the best‑fit straight line through the three points (you may use the first‑ and last‑point method). Express the modulus in GPa.
(d)
The reference Young's modulus for the grade of steel used is 210 GPa. Calculate the percentage error of the experimentally obtained value.
(e)
Identify two possible sources of systematic error in this experiment and suggest one practical method to minimise each.
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