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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?

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?