city guilds model questions vol1 2020 engineering | Practical

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Question 1 View Details
A steel rod of unknown Young's modulus is fixed vertically in a laboratory rig. Its initial length is measured as 0.500 m (to the nearest 0.001 m). A series of axial loads are applied and the corresponding extensions recorded: Load (N): 500, 1000, 1500, 2000 Extension (mm): 0.24, 0.49, 0.73, 0.98 The cross‑sectional area of the rod is 20 mm² (to the nearest 1 mm²).
Question Parts
(a)
Plot load against extension and determine the gradient (ΔLoad/ΔExtension).
(b)
Using the gradient, calculate Young's modulus of the steel rod.
(c)
Estimate the percentage uncertainty in the calculated Young's modulus, considering uncertainties: length ±0.001 m, area ±1 mm², each extension reading ±0.01 mm, and each load reading ±5 N.
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Question 2 View Details
A copper wire of length 0.250 m and diameter 1.0 mm is connected directly to a DC power supply. The following measurements are recorded for three different currents:
Question Parts
(a)
Determine the resistance of the wire for each current and comment on the constancy of the resistance.
(b)
Using the data for I = 3.0 A (ΔT = 12 °C), calculate the resistivity of copper at the measured temperature, then obtain the resistivity at the reference temperature of 20 °C. (Take α = 0.0039 °C⁻¹ for copper.)
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Question 3 View Details
A wooden block of mass 2.5 kg is placed on a smooth wooden inclined plane that can be set to any angle. The plane is 1.20 m long. The experimenter varies the angle and records the smallest angle at which the block begins to slide down the plane. The recorded angle of repose is 22°. The block is then pulled up the plane at constant speed using a spring‑scale over a distance of 0.80 m along the plane.
Question Parts
(a)
Determine the coefficient of static friction (µs) between the block and the plane using the angle of repose.
(b)
Calculate the magnitude of the pulling force required to move the block up the plane at constant speed over the 0.80 m distance.
(c)
Determine the work done by the pulling force in moving the block the 0.80 m distance up the plane.
(d)
List two possible sources of experimental error that could affect the value of µs obtained and briefly explain their effect.
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Question 4 View Details
A circuit is assembled on a breadboard as follows: a 12 V DC power supply is connected to a series combination of a 4 Ω resistor (R1) and a parallel network consisting of a 6 Ω resistor (R2) in parallel with a 12 Ω resistor (R3). An ammeter is placed in series with the whole circuit to measure the total current, and a voltmeter is connected across R2 to measure its voltage.
Question Parts
(a)
Draw a clear schematic diagram of the described circuit, indicating the positions of the ammeter and voltmeter.
(b)
Calculate the theoretical total resistance of the circuit.
(c)
If the ammeter reads 1.45 A and the voltmeter across R2 reads 6.8 V, determine:
() The actual total resistance of the circuit based on the measured current.
() The percentage error between the theoretical and measured total resistance.
(d)
Explain why the voltage across R2 (6.8 V) is not equal to the voltage across R3, and state the voltage across R3.
(e)
If R3 were to fail open (i.e., become an infinite resistance), predict qualitatively how the ammeter reading and the voltmeter reading across R2 would change.
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Question 5 View Details
A wooden rod is to be tested for its Young's modulus using a simple tensile set‑up. The rod has a measured length of 0.500 m and a diameter of 20 mm. The set‑up consists of a fixed clamp at the upper end, a spring balance attached to the lower end, and a metre rule to read the extension. Five different loads are applied and the extension is recorded three times for each load as shown in the table below. | Load (N) | Extension readings (mm) | |----------|--------------------------| | 10 | 0.45, 0.48, 0.46 | | 20 | 0.92, 0.95, 0.94 | | 30 | 1.38, 1.41, 1.40 | | 40 | 1.84, 1.86, 1.85 | | 50 | 2.31, 2.34, 2.33 | Using this data, answer the following:
Question Parts
(a)
List all the apparatus required for the experiment and give a brief description (one or two sentences) of how the set‑up is arranged.
(b)
Calculate the average extension for each load and present the results in a table.
(c)
Using the average values, determine the gradient (slope) of the best‑fit straight line for a load‑extension graph (load on the y‑axis, extension on the x‑axis). State the method you used.
(d)
Calculate the Young's modulus (E) of the wood using the slope obtained in part (c). Show all steps and give the final answer in scientific notation (Pa).
(e)
Identify two possible sources of error in this experiment and suggest a practical way to minimise each error.
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