Spanning, rek-diagram

Spanning, rek-diagram

Rek is een maat voor de verandering in lengte van een materiaal wanneer er een kracht op wordt uitgeoefend. Als een lift naar beneden gaat, zakt deze en rekt de liftkabels uit. Deze trekkracht veroorzaakt een lengteverandering. Rek bereken je met de formule: \varepsilon=\frac{\Delta L}{L_0}\epsilon=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}\eps=\frac{\Delta L}{L_0}\eps i=\frac{\Delta L}{L_0}\eps=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}\epsi=\frac{\Delta L}{L_0}\epsi l=\frac{\Delta L}{L_0}\epsi lo=\frac{\Delta L}{L_0}\epsi lon=\frac{\Delta L}{L_0}\epsi lo=\frac{\Delta L}{L_0}\epsi l=\frac{\Delta L}{L_0}\epsi=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0}=\frac{\Delta L}{L_0} waarbij de toename in lengte is en de oorspronkelijke lengte. Rek is een dimensieloos getal, maar kan uitgedrukt worden in procenten.

Wat is spanning?

Spanning () is de kracht per oppervlakte-eenheid die op een materiaal wordt uitgeoefend. Het wordt berekend met: waarbij F de kracht is en A het oppervlak van de dwarsdoorsnede. De eenheid van spanning is Newton per vierkante meter (), ook bekend als Pascal (Pa)

Elasticiteitsmodulus

De elasticiteitsmodulus (E) vertelt hoe elastisch een materiaal is. Het is de verhouding van spanning tot rek: E=\frac{\sigma}{\varepsilon}E=\frac{\sigma}{\epsilon\varepsilon} Een hoge E betekent dat het materiaal stijf is, terwijl een laag E betekent dat het materiaal elastisch is.

Spanning-rek-diagram

Een spanning-rek-diagram laat zien hoe een materiaal reageert op een uitgeoefende kracht.

Elastische Vervorming: Dit is het eerste deel van het diagram (stuk 1), waar de vervorming tijdelijk is.

Lineaire fase (1a): Hier is de grafiek een rechte lijn en de spanning is evenredig met de rek \frac{\sigma}{\varepsilon}=\text{constant}

Niet-lineaire fase (1b): Hier begint het materiaal permanent te vervormen. Afbeelding van de elastische fase met aanduiding van rechte en niet-rechte delen.

Plastische Vervorming: In dit gedeelte (stuk 2) blijft het materiaal vervormen, zelf als de spanning niet verandert, een proces dat vloeien wordt genoemd.

Vloeigrens: De spanning waarbij een materiaal blijvend vervormt.

Insnoering en Breuk: In stuk 3 rekt het materiaal verder uit tot het breekt.

Voorbeeld met Nylon

Een nylon draad van 0,33 mm dik en 50 cm lang hangt een gewicht van 650 gram. We willen weten hoeveel langer de draad wordt door het gewicht. Nylon heeft een elasticiteitsmodulus van 2,0 · 10⁹ Pa.

Bereken de Spanning (): F=m\cdot g=0{,}65\cdot9{,}81=6{,}37F=m\cdot g=0{,}65\cdot9{,}81=6{,}37NF=m\cdot g=0{,}65\cdot9{,}81=6{,}37F=m\cdot g=0{,}65\cdot9{,}81=6{,}37,F=m\cdot g=0{,}65\cdot9{,}81=6{,}37,\text{N}F=m\cdot g=0{,}65\cdot9{,}81\text{ }=6{,}37,\text{N}F=m\cdot g=0{,}65\cdot9{,}81\text{ m}=6{,}37,\text{N}F=m\cdot g=0{,}65\cdot9{,}81\text{ m/}=6{,}37,\text{N}F=m\cdot g=0{,}65\cdot9{,}81\text{ m/s}=6{,}37,\text{N}F=m\cdot g=0{,}65\cdot9{,}81\text{ m/s}^{}=6{,}37,\text{N}F=m\cdot g=0{,}65\cdot9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}659{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65b9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}659{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ k }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg= }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \$\$ \textbackslash cdot \$\$ }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \$\$ \textbackslash cdot \$\$ }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash c }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cd }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cdo }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cdot }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cdot }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cdot }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cdot }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cdo }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cd }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash c }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash c }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cd }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cdo }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg \textbackslash cdot }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash cdot }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash cdot }9{,}81\text{ m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash cdot }9{,}81\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash cdot }9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash cdot}9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash cdot}9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash cdo}9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash cd}9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash c}9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg\textbackslash}9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg}9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{ kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65\text{kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=m\cdot g=0{,}65,\text{kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=mg=0{,}65,\text{kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=mg=0{,}65,\text{kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=mg=0{,}65,\text{kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=mg=0{,}65,\text{kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=mg=0{,}65,\text{kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}F=mg=0{,}65,\text{kg}\times9{,}81,\text{m/s}^2=6{,}37,\text{N}N A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0\cdot10^{-8}\text{ m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0\cdot10^{-8}\text{ m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0\cdot10^{-8}\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0\cdot10^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}010^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}010^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}010^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}010^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}010^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}010^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}010^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}010^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0710^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}07\cdo10^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}07\cdo t10^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}07\cdo10^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0710^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0710^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0710^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0710^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}0710^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033)^2}{4}=7{,}07\times10^{-8},\text{m}^2A=\frac{\pi d^2}{4}=\frac{\pi(0{,}00033,)^2}{4}=7{,}07\times10^{-8},\text{m}^2 \sigma=\frac{F}{A}=\frac{6{,}37}{7{,}07\cdot10^{-8}}=9{,}0\cdot10^7\sigma=\frac{F}{A}=\frac{6{,}37}{7{,}07\cdot10^{-8}}=9{,}010^7\sigma=\frac{F}{A}=\frac{6{,}37}{7{,}07\cdot10^{-8}}=9{,}010^7\sigma=\frac{F}{A}=\frac{6{,}37}{7{,}07\cdot10^{-8}}=9{,}010^7\sigma=\frac{F}{A}=\frac{6{,}37}{7{,}07\cdot10^{-8}}=9{,}010^7\sigma=\frac{F}{A}=\frac{6{,}37}{7{,}07\cdot10^{-8}}=9{,}010^7\sigma=\frac{F}{A}=\frac{6{,}37}{7{,}07\cdot10^{-8}}=9{,}010^7\sigma=\frac{F}{A}=\frac{6{,}37}{7{,}07\cdot10^{-8}}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,}{7{,}07\cdot10^{-8}}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}07\cdot10^{-8}}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}07\cdot10^{-8},}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}07\cdot10^{-8},\text{m}}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}07\cdot10^{-8},\text{m}^{}}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}07\cdot10^{-8},\text{m}^2}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}0710^{-8},\text{m}^2}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}0710^{-8},\text{m}^2}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}0710^{-8},\text{m}^2}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}0710^{-8},\text{m}^2}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}0710^{-8},\text{m}^2}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}0710^{-8},\text{m}^2}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}0710^{-8},\text{m}^2}=9{,}0\times10^7\sigma=\frac{F}{A}=\frac{6{,}37,\text{N}}{7{,}0710^{-8},\text{m}^2}=9{,}0\times10^7Pa

Bereken de rek (ε): \varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}0\cdot10^9}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}010^9}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}010^9}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}010^9}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}010^9}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}010^9}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}010^9}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}0\times10^9}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}0\times10^9,}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}0\times10^9,\text{P}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7,}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7,\text{P}}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0\cdot10^7,\text{Pa}}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}010^7,\text{Pa}}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}010^7,\text{Pa}}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}010^7,\text{Pa}}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}010^7,\text{Pa}}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}010^7,\text{Pa}}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}010^7,\text{Pa}}{2{,}0\times10^9,\text{Pa}}=0{,}045\varepsilon=\frac{\sigma}{E}=\frac{9{,}0 \times10^7 , \text{Pa}}{2{,}0 \times10^9 , \text{Pa}}=0{,}045\epsilon\varepsilon=\frac{\sigma}{E}=\frac{9{,}0 \times10^7 , \text{Pa}}{2{,}0 \times10^9 , \text{Pa}}=0{,}045

Nieuwe lengte (): \Delta L=\varepsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023\Delta L=\varepsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}02\Delta L=\varepsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023\Delta L=\varepsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023=\Delta L=\varepsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2\Delta L=\varepsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}\Delta L=\varepsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon\varepsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\sqrt{\placeholder{}}\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\sqrt{\placeholder{}}\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\sqrt{\placeholder{}}\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon\cdot L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}045\cdot]0{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}045\cdot0{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}0450{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}0450{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}0450{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}0450{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}0450{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}0450{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}045\times0{,}5=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}045\times0{,}5,=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}045\times0{,}5,\text{m}=0{,}023=2{,}3\Delta L=\epsilon\times L_0=0{,}045\times0{,}5,\text{m}=0{,}023,=2{,}3\Delta L=\epsilon\times L_0=0{,}045\times0{,}5,\text{m}=0{,}023,\text{m}=2{,}3\Delta L=\epsilon\times L_0=0{,}045\times0{,}5,\text{m}=0{,}023,\text{m}=2{,}3,\Delta L=\epsilon\times L_0=0{,}045\times0{,}5,\text{m}=0{,}023,\text{m}=2{,}3,\text{c}m = 2,3 cm