Respuesta :
Answer:
[tex]\Delta x=2.304\times 10^{-2}\ m=2.304\ cm[/tex] is the minimum gap between the slabs
Explanation:
Given:
- length of the concrete highway, [tex]l=12\ m[/tex]
- coefficient of thermal expansion, [tex]\alpha=12\times 10^{-6}\ ^{\circ}C^{-1}[/tex]
- range of temperature variation, [tex](-30^{\circ}C\ to\ 50^{\circ}C) \Rightarrow \Delta T=80^{\circ}C[/tex]
Now form the equation of thermal expansion:
[tex]\Delta l=l\times \alpha\times \Delta T[/tex]
[tex]\Delta l=12\times (12\times 10^{-6})\times 80[/tex]
[tex]\Delta l=1.152\times 10^{-2}\ m[/tex]
Since each slab of the highway expands by the above length so the minimum gap between the slabs to prevent buckling:
[tex]\Delta x=2\times \Delta l[/tex]
[tex]\Delta x=2\times( 1.152\times 10^{-2})[/tex]
[tex]\Delta x=2.304\times 10^{-2}\ m=2.304\ cm[/tex] is the minimum gap between the slabs
