SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

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
Show Answers Only

\(  B \)

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)
Show Answers Only

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)

Show Answers Only

`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%.