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A catapult consists of two parallel rubber strings, each of lengths 10 cm and cross-sectional area 10 mm2. When stretched by 5 cm, it can throw a stone of mass 100 gm to a vertical height of 25 m. Determine Young's modulus of elasticity of rubber.

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Solution

A stretched catapult has elastic potential energy stored in it (Strain energy stored in both the rubber strings) U=(12YAL2L)×2 This energy, when imparted to the stone, it flies off a height 20 m. Energy possessed by the Stone = mgh. Now, U=mghYAl2L=mgh Y = mghLAl2=1×101×10×25×10110×106×(5×102)2 Y = 10×108N/m2

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