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Confirm that iron is stronger than wood, and briefly give the primary reason for the difference in their material properties.

Physics

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ITEM 3: Material Properties and Construction

Part a· 3 steps

Confirm that iron is stronger than wood.

  1. Compare the forces withstood and extensions.

    Iron: Withstands 6000 N6000 \text{ N} for an extension of 2.0 cm2.0 \text{ cm}.
    Wood: Withstands 4000 N4000 \text{ N} for an extension of 2.5 cm2.5 \text{ cm}.
    Both pieces have the same diameter (0.7 mm0.7 \text{ mm}) and length (10 m10 \text{ m}), meaning their cross-sectional area (AA) and original length (LL) are identical.

  2. Calculate Young's Modulus (EE) for both materials.

    Young's Modulus is a measure of stiffness and strength, defined as E=StressStrain=F/AΔL/LE = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L}.
    Since AA and LL are the same for both, we can compare the ratio FΔL\frac{F}{\Delta L}. A higher FΔL\frac{F}{\Delta L} indicates a higher Young's Modulus and thus greater strength.

    For iron:

    Eiron∝FironΔLiron=6000 N0.02 m=300,000 N/mE_{iron} \propto \frac{F_{iron}}{\Delta L_{iron}} = \frac{6000 \text{ N}}{0.02 \text{ m}} = 300,000 \text{ N/m}

    For wood:

    Ewood∝FwoodΔLwood=4000 N0.025 m=160,000 N/mE_{wood} \propto \frac{F_{wood}}{\Delta L_{wood}} = \frac{4000 \text{ N}}{0.025 \text{ m}} = 160,000 \text{ N/m}

  3. Compare the values.

    Since 300,000 N/m>160,000 N/m300,000 \text{ N/m} > 160,000 \text{ N/m}, the Young's Modulus for iron is greater than that for wood. This confirms that iron is stronger than wood.

Part b

Briefly give the properties that make any three of the listed materials ideal for construction.

  • Bricks: Bricks are ideal because they are durable, fire-resistant, and provide good thermal insulation. They are also readily available and relatively inexpensive.
  • Iron bars: Iron bars are ideal due to their high tensile strength and ductility, making them excellent for reinforcing concrete (rebar) to withstand tension and bending forces.
  • Tiles: Tiles are ideal for roofing or flooring because they are waterproof, durable, and can be aesthetically pleasing. They also offer good protection against weather elements.

Part c

Give the justification for the choice of the colour and nature of the roof materials.

The students argued the wall should be painted white and the roof made of glass.

  • White walls: White is chosen for walls because it is a poor absorber of heat and a good reflector of heat. This helps to keep the interior of the house cool, especially in hot climates, by reflecting sunlight away.
  • Glass roof: A glass roof is chosen because glass is transparent to visible light, allowing natural light to enter the house, reducing the need for artificial lighting during the day. It also allows for solar heating during cooler periods, though this might be a disadvantage in very hot climates.
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