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Toys and engineering materials
Toys and engineering materials

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1.3.2 Building a tower

To gain an understanding of the strength of a LEGO® brick made out of a polymer called acrylonitrile butadiene styrene (ABS), consider how high a tower made of 2 × 2 LEGO® bricks could theoretically reach.

When designing a tower, there is a theoretical limit to the height that can be achieved before it is crushed under its own weight. Plastic is an excellent choice of material for toy manufacture because of its toughness and its high strength-to-weight ratio, but is it really strong enough to build a skyscraper with?

Activity 2 How tall can you build a LEGO® tower?

Timing: Allow about 15 minutes

Engineers have determined that a 2 × 2 LEGO® brick could withstand a force of just under 4220 N before failing. A single 2 × 2 LEGO® brick has a mass of 1.15 g and a height of 9.6 mm (excluding the connecting dimples on the top side).

Assuming g = 9.81 m s−2, calculate the following:

  • a.What mass of LEGO® would provide a force of 4220 N?
  • b.To the nearest brick, how many 2 × 2 LEGO® bricks would constitute the mass of LEGO® calculated in part (a)?
  • c.How high would the tower reach before exceeding the structural strength of a 2 × 2 LEGO® brick?


  • a.The mass required to create a force of 4220 N is

    4220 cap n divided by 9.81 cap n kg super negative one equals 430.173 horizontal ellipsis kg full stop
  • b.The number of LEGO® bricks in 430.173… kg of LEGO® is therefore

    430 173 times horizontal ellipsis g divided by 1.15 g equals 374 063.73 times horizontal ellipsis

    so there are 374 064 bricks to the nearest brick.

  • c.The height of the LEGO® tower is

    374 064 multiplication 9.6 mm equals three 591 014.4 mm equation left hand side equals right hand side 3.591 times horizontal ellipsis multiplication 10 super six mm equals 3.6 km left parenthesis to two s full stop f full stop right parenthesis full stop

Further developments in material performance allowed the introduction of the first sustainable LEGO® bricks in 2018. You can read about these developments in this article [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

To sum up, plastics are an incredibly versatile and often very cheap material that is put to a vast array of uses in toy manufacture. But, like many other synthetic materials, plastics are not really sustainable, and are the cause of significant environmental harm if not correctly disposed of.