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ENGINEERING, CS 2025 HSC 20 MC

A cable with an initial length of 15 m and a cross-sectional area of \(300 \times 10^{-6} \ \text{m}^2\) is subjected to a tensile force of \(75\,000\ \text{N}\), causing an elongation of \(\text{0.01 m}\) and a decrease in cross-sectional area to \(280 \times 10^{-6}\ \text{m}^2\).

Assuming the deformation occurs within the elastic region, what is the Young's Modulus of the cable?

  1. \(\text{402 GPa}\)
  2. \(\text{375 GPa}\)
  3. \(\text{268 MPa}\)
  4. \(\text{250 MPa}\)
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\(B\)

Show Worked Solution

\(\sigma=\dfrac{F}{A}=\dfrac{75\ 000}{300\times10^{-6}}=250\times10^{6}\ \text{Pa}\)

\(\varepsilon=\dfrac{\Delta L}{L}=\dfrac{0.01}{15}=6.667\times10^{-4}\)

\(E=\dfrac{\sigma}{\varepsilon}=\dfrac{250\times10^{6}}{6.667\times10^{-4}}=375\times10^{9}\ \text{Pa}=375\ \text{GPa}\)

\(\Rightarrow B\)


♦ Mean mark 47%.

ENGINEERING, CS 2023 HSC 13 MC

Which mechanical property describes an object that is under load and follows Hooke's Law?

  1. Ductility
  2. Elasticity
  3. Malleability
  4. Plasticity
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\(  B \)

Show Worked Solution
  • Hooke’s law states that for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load.
  • Hooke’s law is a fundamental principle in understanding the behaviour of elastic materials.

\(\Rightarrow  B \)

ENGINEERING, CS 2018 HSC 23b

The steel used in the chassis members was tested.

The load–extension graph represents the data collected during the testing of a specimen of the steel.
 

Before testing, the specimen was 1020 mm long with a cross-sectional area of 100 mm².

  1. Calculate Young's modulus for this steel.   (4 marks)
  1. Describe the physical changes that occur in the specimen tested in part (i) when a 20 kN load is applied and then removed, compared to when a 30 kN load is applied and then removed.   (2 marks)
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i.   Young’s modulus

`F = 20 xx 10^3\ text{N}, l = 1020\ text{mm},  e = 1\ text{mm},  text{A} = 100\ text{mm}^2`

`E` `=(Fl)/(eA)`  
  `=(20 xx 10^3 xx1020)/(1 xx 100)`  
  `=204 xx 10^3`  
  `=204\ text{GPa}`  

ii.   

  • Elastic deformation is produced by the 20 kN load.
  • After initial stretching the specimen returns to its original length.
  • Plastic deformation is produced by the 30 kN load.
  • The specimen stays deformed subsequent to release.
Show Worked Solution

i.   Young’s modulus

`F = 20 xx 10^3\ text{N}, l = 1020\ text{mm},  e = 1\ text{mm},  text{A} = 100\ text{mm}^2`

`E` `=(Fl)/(eA)`  
  `=(20 xx 10^3 xx1020)/(1 xx 100)`  
  `=204 xx 10^3`  
  `=204\ text{GPa}`  

♦ Mean mark (i) 51%.

ii.     Elastic deformation is produced by the 20 kN load.

  • After initial stretching the specimen returns to its original length.
  • Plastic deformation is produced by the 30 kN load.
  • The specimen stays deformed subsequent to release.

ENGINEERING, CS 2016 HSC 21aiii

The reinforced concrete modules shown are designed for public seating. A typical use would be as a bus shelter.
 

A 12 mm diameter steel reinforcing bar was used in this seating module. During a proof test, a load of 26 kN extended a 0.9 m length of this reinforcing bar by 1 mm.

Calculate the value of Young's Modulus (E) for this bar.   (3 marks)

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`206.9\ text{GPa}`

Show Worked Solution

`sigma=F/A=(26\ 000)/(pixx6^2)229.9\ text{MPa}`

`epsilon=e/L=1/900=1.1111 xx 10^-3`

`E` `=sigma/epsilon`  
  `=229.9/(1.1111 xx 10^-3)\  text{MPa}`  
  `=206.9 xx 10^3\ text{MPa}`  
  `=206.9\ text{GPa}`  

 

Mean mark 56%.