city guilds model questions vol1 2017 engineering | Practical

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Question 1 View Details
A steel rod of length 2.00 m and cross‑sectional area 1.5 × 10⁻⁴ m² is subjected to axial loads. The following data were recorded using a dial gauge: | Load (kN) | Extension (mm) | |-----------|----------------| | 10 | 0.45 | | 20 | 0.92 | | 30 | 1.38 | | 40 | 1.85 | | 50 | 2.31 | Using the method of least squares, determine: a) The mean load and the mean extension. b) The slope of the best‑fit straight line (extension versus load) and write the equation of the line. c) The modulus of elasticity (E) of the steel rod. Comment briefly on the linearity of the data.
Question Parts
(a)
Calculate the mean load (in N) and the mean extension (in m).
(b)
Determine the slope (Δextension/Δload) of the regression line using the least‑squares formula and write the line equation in the form y = mx + c.
(c)
Calculate the modulus of elasticity E (in Pa) and state whether the data support a linear relationship.
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Question 2 View Details
A calorimetry experiment is carried out to determine the specific heat capacity of water. The apparatus consists of a 200 g sample of water placed in an insulated container. The initial temperature of the water is 20.0 °C. An electric heater (voltage 12.0 V, current 2.0 A) is immersed in the water and operated for 300 s. After heating, the water temperature rises to 45.0 °C. Assuming that all electrical energy supplied is absorbed by the water, determine: a) The heat gained by the water (in joules). b) The experimental specific heat capacity (c) of water in J kg⁻¹ K⁻¹. c) Identify two likely sources of error in the experiment and suggest a practical method to minimise each error.
Question Parts
(a)
Calculate the heat absorbed by the water using the temperature change.
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Question 3 View Details
A smooth wooden board 1.20 m long is placed on a rough horizontal surface. A 2.00 kg wooden block is placed at one end of the board. The block is pulled down the board by a string attached to the block and passing over a frictionless pulley at the opposite end of the board. The string is attached to a hanging mass that provides a constant pulling force. The experiment is to determine the coefficient of kinetic friction (µk) between the board and the surface. The following data are recorded during the experiment: - Mass of the hanging weight (M) = 0.80 kg - Acceleration of the system measured with a stop‑watch over 5 s after release = 0.45 m s⁻² - Length of the board that moves during the measurement = 0.60 m - The board is level (no incline).
Question Parts
(a)
State the free‑body diagram for each of the two bodies (the block on the board and the hanging mass) and list all the forces acting on them.
(b)
Derive an expression for the coefficient of kinetic friction µk in terms of the given quantities and calculate its numerical value.
(c)
Identify two possible sources of systematic error that could affect the value of µk obtained and suggest a method to reduce each error.
(d)
Explain why it is important to keep the board level during the experiment and how you would verify its levelness.
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Question 4 View Details
You are required to investigate the behaviour of a series‑parallel resistive circuit. The circuit consists of three resistors: R1 = 12 Ω, R2 = 18 Ω and R3 = 30 Ω. R1 and R2 are connected in parallel, and this parallel combination is then connected in series with R3 across a 6.00 V DC power supply. Using a digital multimeter, you are to measure the voltage across each resistor and the total current drawn from the supply.
Question Parts
(a)
Draw a clear schematic diagram of the described circuit, labeling all resistors, the power supply and the points where voltage measurements are to be taken.
(b)
Calculate the theoretical equivalent resistance (R_eq) of the whole circuit and the expected total current (I_total) supplied by the 6 V source.
(c)
Using the measured values (recorded in the table below), determine the experimental equivalent resistance and compare it with the theoretical value. State the percentage discrepancy. | Quantity | Measured Value | |------------------------|----------------| | Voltage across R1 (V1) | 2.10 V | | Voltage across R2 (V2) | 2.10 V | | Voltage across R3 (V3) | 3.90 V | | Total current (I) | 0.158 A |
(d)
Discuss two possible sources of error that could affect the voltage and current measurements and propose a practical way to minimise each error.
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Question 5 View Details
A student is carrying out a tensile test on a cylindrical steel specimen using a universal testing machine. The specimen has a gauge length of 100 mm and an original diameter of 10 mm. The machine records the applied load (N) against the extension (mm) at intervals of 0.5 mm up to fracture. The recorded data are shown below. | Extension (mm) | Load (N) | |----------------|----------| | 0.0 | 0 | | 0.5 | 1500 | | 1.0 | 3000 | | 1.5 | 4400 | | 2.0 | 5600 | | 2.5 | 6600 | | 3.0 | 7200 | | 3.5 | 7500 | | 4.0 | 7700 | | 4.5 | 7800 | | 5.0 | 7850 (fracture) | Using the data above, answer the following: a) Determine the load at the proportional limit of the specimen by applying the 0.2 % offset method. Show clearly how the offset line is constructed and identify the corresponding load. b) Using the load obtained in (a), calculate: i) the engineering stress (in MPa) at the proportional limit, ii) the engineering strain at the proportional limit, iii) the Young’s modulus (in GPa) assuming the stress–strain relationship is linear up to the proportional limit. c) After fracture the final diameter of the broken specimen is measured as 8.0 mm. Calculate the percentage reduction in area. d) Identify two possible sources of systematic error in this tensile test and suggest one practical way to minimise each error.
Question Parts
(a)
Determine the load at the proportional limit of the specimen by applying the 0.2 % offset method. Show clearly how the offset line is constructed and identify the corresponding load.
(b)
Using the load obtained in (a), calculate: i) the engineering stress (in MPa) at the proportional limit, ii) the engineering strain at the proportional limit, iii) the Young’s modulus (in GPa) assuming the stress–strain relationship is linear up to the proportional limit.
(c)
After fracture the final diameter of the broken specimen is measured as 8.0 mm. Calculate the percentage reduction in area.
(d)
Identify two possible sources of systematic error in this tensile test and suggest one practical way to minimise each error.
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