In this TLP we have:

1. Learned how the Young's modulus of a material may be determined using the relationship between the deflection of a cantilever beam δ and the load P applied to it, given by

   

   where L is the distance from support to point of load application, I is the second moment of area of the beam's cross section, and E is the Young's modulus of the beam's material.

2. Used measurements of the deflection and load of a steel cantilever beam to determine the Young's modulus of steel as 210 GPa.

3. Looked at how the asymmetry in the energy-separation graph for atoms in a solid gives rise to an increase in the average interatomic spacing of vibrations as the temperature is increased, the origin of thermal expansion.

4. Derived a formula relating curvature κ to the length x and deflection δ of a bi-material strip:

   

5. Defined the misfit strain Δε for the two components of a bi-material strip as

   Δε = (α_A - α_B)ΔT

   and quoted a formula relating the curvature κ to the misfit strain, the thickness of the strips h (of equal thickness) and the ratio of the Young's moduli E_*

   

6. Used measurements of the change in shape of a steel-aluminium bi-material strip immersed in liquid nitrogen to estimate the boiling temperature of nitrogen as -193ºC.

7. Used measurements of the change in shape of an aluminium-polycarbonate bi-material strip immersed in liquid nitrogen to estimate the thermal expansivity of the polycarbonate as 4.5 x 10^-5 K^-1.

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