city guilds model questions vol1 2023 engineering | Practical

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Question 1 View Details
A student uses a two‑component force sensor to measure the horizontal (Fx) and vertical (Fy) components of a force acting on a test rig. Five independent readings are obtained as shown in the table. | Trial | Fx (N) | Fy (N) | |-------|--------|--------| | 1 | 30 | 40 | | 2 | 28 | 42 | | 3 | 32 | 38 | | 4 | 31 | 39 | | 5 | 29 | 41 | Using these data, determine the overall magnitude of the force and the reliability of the measurement.
Question Parts
(a)
Calculate the resultant force magnitude for each trial.
(b)
Find the mean resultant force from the five trials.
(c)
Determine the standard deviation of the resultant forces and express the percent uncertainty of the mean resultant (percent uncertainty = (SD / mean) × 100%).
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Question 2 View Details
In a steady‑state heat‑conduction experiment, a uniform metal rod of length 0.500 m and cross‑sectional area 2.0 × 10⁻⁴ m² is heated at one end by an electric heater. The heater is powered by a 10.0 V supply drawing a current of 1.0 A. After the system reaches thermal equilibrium, the temperature at the heated end is 80 °C and at the opposite end is 30 °C. Using the data provided, evaluate the thermal performance of the rod and discuss experimental reliability.
Question Parts
(a)
Calculate the rate of heat flow (in watts) supplied by the electric heater.
(b)
Determine the thermal conductivity (k) of the rod using Fourier’s law for steady‑state conduction (Q = k A ΔT / L).
(c)
Identify two possible sources of error in this experiment and suggest a practical method to reduce each error.
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Question 3 View Details
A compound pulley system is set up to lift a load. The system consists of a fixed pulley and two movable pulleys arranged such that four rope segments support the load. The load weight is 200 N. During the experiment the following data were recorded: - Effort force measured on the rope: 55 N - When the load is raised by 0.20 m, the effort rope moves through 1.00 m. Using this information: (a) Determine the theoretical mechanical advantage (TMA) of the pulley arrangement. (b) Calculate the actual mechanical advantage (AMA) based on the measured forces. (c) Compute the efficiency of the system as a percentage. (d) Identify two probable sources of error in the experiment and suggest one way to reduce each error.
Question Parts
(a)
Determine the theoretical mechanical advantage (TMA) of the pulley arrangement.
(b)
Calculate the actual mechanical advantage (AMA) based on the measured forces.
(c)
Compute the efficiency of the system as a percentage.
(d)
Identify two probable sources of error in the experiment and suggest one way to reduce each error.
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Question 4 View Details
A copper wire of length 2.00 m and cross‑sectional area 0.50 mm² is connected in a simple circuit with a voltmeter and an ammeter as shown. The following readings are obtained: - Voltage across the wire (V): 3.60 V - Current through the wire (I): 0.50 A Using these data: (a) Determine the resistance of the wire. (b) Calculate the resistivity of the copper material. (c) If the temperature of the wire rises by 30 °C and the temperature coefficient of resistance for copper is 0.004 °C⁻¹, estimate the new resistance. (d) Suggest two practical precautions that could be taken to minimise experimental error in the resistance measurement.
Question Parts
(a)
Determine the resistance of the wire.
(b)
Calculate the resistivity of the copper material.
(c)
If the temperature of the wire rises by 30 °C and the temperature coefficient of resistance for copper is 0.004 °C⁻¹, estimate the new resistance.
(d)
Suggest two practical precautions that could be taken to minimise experimental error in the resistance measurement.
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Question 5 View Details
A student is required to determine the tensile strength and Young’s modulus of a cylindrical steel rod using a universal testing machine (UTM). The rod has a measured length of 300 mm (to the nearest 0.5 mm) and a diameter of 12.0 mm (to the nearest 0.1 mm). The UTM records the load applied and the corresponding extension of the rod as shown in the table. | Load (N) | Extension (mm) | |----------|----------------| | 0 | 0.00 | | 2000 | 0.12 | | 4000 | 0.24 | | 6000 | 0.36 | | 8000 | 0.48 | | 10000 | 0.60 | | 12000 | 0.85 | | 14000 | 1.20 | | 16000 | 1.80 | | 18000 | 2.55 | | 20000 | 3.60 | The data up to a load of 10 000 N are considered to lie within the elastic region. Answer the following questions:
Question Parts
(a)
Calculate the original cross‑sectional area of the rod. Show how the uncertainty in the diameter measurement propagates to give the uncertainty in the area (express the result as A ± ΔA in mm²).
(b)
Using the data for the elastic region (loads up to 10 000 N), calculate: (i) the engineering stress (σ) in MPa for each of the five points; (ii) the engineering strain (ε) for each of the five points; (iii) the Young’s modulus (E) of the material by determining the gradient of the stress‑strain curve (use the first and the fifth point). Show all intermediate steps.
(c)
Identify two possible sources of systematic error in this tensile test and suggest one method to minimise each error.
(d)
State one important precaution that must be observed when mounting the specimen on the UTM to avoid bending stresses.
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