city guilds model questions vol1 2024 engineering | Practical

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Question 1 View Details
A civil engineering student constructs a scale model of a rectangular steel beam to determine its load‑bearing capacity. The drawing uses a scale of 1 cm : 0.5 m (1 cm on the drawing represents 0.5 m in reality). In the drawing the beam measures length 12 cm, width 2 cm and height 3 cm.
Question Parts
(a)
Determine the actual (real‑world) dimensions of the beam.
(b)
Calculate the cross‑sectional area of the beam in square metres.
(c)
Using the allowable stress for the steel (σ_allow = 250 MPa) and the formula for bending stress σ = (M·y)/I, where for a simply supported beam with a central point load W, the maximum bending moment M = W·L/4, y = h/2 and I = (b·h³)/12, determine the maximum load W_max the beam can support without exceeding the allowable stress.
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Question 2 View Details
In a laboratory, a 2.5 kg block of aluminium is heated using an electric heater rated at 500 W. The heater is switched on for 10 minutes. The initial temperature of the block is 25 °C and after heating the recorded temperature is 85 °C. The specific heat capacity of aluminium is 900 J·kg⁻¹·K⁻¹.
Question Parts
(a)
Calculate the total electrical energy supplied to the heater during the experiment.
(b)
Determine the theoretical temperature rise of the aluminium block if all the electrical energy were transferred to it.
(c)
State the actual temperature rise observed in the experiment.
(d)
Calculate the overall efficiency of the heating process.
(e)
Identify two possible sources of error that could account for the difference between the theoretical and actual temperature rises.
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Question 3 View Details
A single fixed pulley is used to lift a load. The load weight is 150 N. The effort force applied to the rope is measured as 45 N. During the lift the effort end of the rope moves 0.80 m while the load rises 0.20 m. All measurements are taken with a calibrated spring‑scale and a metre rule. Using the data provided, answer the following:
Question Parts
(a)
Calculate the ideal mechanical advantage of the pulley system.
(b)
Determine the actual mechanical advantage from the measured distances and compute the overall efficiency of the system (expressed as a percentage to two decimal places). State briefly why the actual MA differs from the ideal MA.
(c)
Identify two possible sources of error in the experiment and suggest one practical way to minimise each error.
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Question 4 View Details
A copper wire of length 2.00 m and diameter 0.50 mm is connected to a DC power supply. The voltage across the wire and the corresponding current are recorded as follows: | Voltage (V) | 2 | 4 | 6 | 8 | |------------|---|---|---|---| | Current (A) | 0.50 | 1.00 | 1.50 | 2.00 | Using the data, answer the questions below. Assume the temperature of the wire during the measurements is 20 °C and the temperature coefficient of resistivity for copper is 0.004 °C⁻¹.
Question Parts
(a)
Plot the V–I graph on graph paper (straight line through the origin). From the graph, determine the resistance of the wire.
(b)
Using the resistance obtained in part (a), calculate the resistivity (ρ) of the copper wire. Express your answer in scientific notation to two significant figures (Ω·m).
(c)
If the temperature of the wire rises to 50 °C, estimate the new resistance of the wire.
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Question 5 View Details
In the Materials laboratory a student carries out a tensile test on a cylindrical brass rod of unknown grade. The rod has a measured length of 200 mm. Its diameter is measured at three equally spaced points along the length giving 12.1 mm, 11.9 mm and 12.0 mm. The average diameter is to be used for all calculations. The specimen is loaded in a universal testing machine and the following load (N) and corresponding extension (mm) are recorded: | Load (N) | Extension (mm) | |----------|----------------| | 0 | 0.00 | | 2000 | 0.15 | | 4000 | 0.30 | | 6000 | 0.46 | | 8000 | 0.63 | |10000 | 0.82 | |12000 | 1.05 | |14000 | 1.35 | |16000 | 1.78 | |18000 | 2.40 | Using the data above, answer the following: a) Determine the cross‑sectional area of the rod (expressed to two decimal places in mm²). b) From the linear portion of the load‑extension curve (the first five readings), calculate the stress and strain for each of those points, and determine the Young’s modulus (E) of the material in GPa. Show the method used and give the final value to two decimal places. c) Find the ultimate tensile strength (UTS) of the rod using the maximum load recorded. Express the UTS in MPa to one decimal place. d) Identify two possible sources of systematic error in this experiment and suggest one practical way to minimise each error.
Question Parts
(a)
Determine the cross‑sectional area of the rod (expressed to two decimal places in mm²).
(b)
From the linear portion of the load‑extension curve (the first five readings), calculate the stress and strain for each of those points, and determine the Young’s modulus (E) of the material in GPa. Show the method used and give the final value to two decimal places.
(c)
Find the ultimate tensile strength (UTS) of the rod using the maximum load recorded. Express the UTS in MPa to one decimal place.
(d)
Identify two possible sources of systematic error in this experiment and suggest one practical way to minimise each error.
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