# Results: Measurement of Young's modulus

A set of results for the steel strip are given below.

load, m (kg) |
deflection, δ (10^{-3} m) |

0 | 0 |

0.05 | 3 |

0.10 | 6.5 |

0.15 | 9 |

0.20 | 13 |

0.25 | 16 |

A graph of these results gives:

The gradient of this graph is

\[{\rm{gradient}} = \frac{{16 \times {{10}^{ - 3}}}}{{0.25}} = 6.4 \times {10^{ - 2}}{\rm{mk}}{{\rm{g}}^{ - 1}}\]

In addition

width of strip (w) = | 0.01 m |

thickness of strip (h) = | 0.001 m |

length of strip (L) = | 0.15 m |

So, using equation (2)

\[{\rm{gradient}} = \frac{{0.01 \times {{0.001}^3}}}{{12}} = 8.3 \times {10^{ - 13}}{{\rm{m}}^3}\]

From equation (1) with *P* = *mg*, a graph of *δ *
against *m* will have a gradient

\[{\rm{gradient}} = \frac{1}{3}\frac{{g{L^3}}}{{EI}}\]

and hence

\[E = \frac{1}{3}\frac{{g{L^3}}}{{{\rm{gradient}} \times I}} = \frac{{9.8 \times {{0.15}^3}}}{{3 \times 6.4 \times {{10}^{ - 2}} \times 8.3 \times {{10}^{ - 13}}}} = 2.1 \times {10^{11}}{\rm{Pa(2s}}{\rm{.f}}{\rm{.)}}\]

So the steel from which the strip is made has a Young's modulus of 210 GPa (close to the figure given in the properties table).

Repeating the experiment for the aluminium and polycarbonate strips gives Young's moduli of 70 GPa and 5.5 GPa respectively. These results will be used later in the TLP.