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Question Number 18666 by tawa tawa last updated on 26/Jul/17

$$\mathrm{An}\mathrm{elastic}\mathrm{material}\mathrm{has}\mathrm{a}\mathrm{length}\mathrm{of}36\mathrm{cm}\mathrm{when}\mathrm{a}\mathrm{load}\mathrm{of}40\mathrm{N}\mathrm{is}\mathrm{hung}\mathrm{on}\mathrm{it}\mathrm{and}$$$$\mathrm{a}\mathrm{length}\mathrm{of}45\mathrm{cm}\mathrm{when}\mathrm{a}\mathrm{load}\mathrm{of}60\mathrm{N}\mathrm{is}\mathrm{hung}\mathrm{on}\mathrm{it}.\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{Original}$$$$\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{string}?$$

Answered by mrW1 last updated on 27/Jul/17

$$36-\frac{45-36}{60-40}\times 40=18\mathrm{cm}$$

Commented by tawa tawa last updated on 27/Jul/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by tawa tawa last updated on 27/Jul/17

$$\mathrm{Any}\mathrm{formular}\mathrm{sir}?$$

Commented by mrW1 last updated on 27/Jul/17

$$\mathrm{x}=\mathrm{length}\mathrm{without}\mathrm{load}$$$$\mathrm{k}=\mathrm{elongation}\mathrm{for}\mathrm{unit}\mathrm{load}$$$$36-\mathrm{x}=40\mathrm{k}...\left(\mathrm{i}\right)$$$$45-\mathrm{x}=60\mathrm{k}...\left(\mathrm{ii}\right)$$$$\left(\mathrm{i}\right)/\left(\mathrm{ii}\right):$$$$\frac{36-\mathrm{x}}{45-\mathrm{x}}=\frac{40}{60}$$$$36\times 60-60\mathrm{x}=45\times 40-40\mathrm{x}$$$$(60-40)\mathrm{x}=36\times 60-45\times 40$$$$\mathrm{x}=\frac{36\times 60-45\times 40}{60-40}=18$$

Commented by mrW1 last updated on 27/Jul/17

$$\mathrm{or}\mathrm{solution}\mathrm{without}\mathrm{equation}:$$$$\mathrm{load}\mathrm{from}40\mathrm{to}60:$$$$\mathrm{length}\mathrm{from}36\mathrm{to}45.$$$$\Rightarrow \mathrm{elongation}\mathrm{for}\mathrm{unit}\mathrm{load}:$$$$\frac{45-36}{60-40}$$$$$$$$\Rightarrow \mathrm{elongation}\mathrm{for}\mathrm{load}=40\mathrm{is}$$$$\frac{45-36}{60-40}\times 40$$$$$$$$\Rightarrow \mathrm{length}\mathrm{at}\mathrm{load}=0\mathrm{is}$$$$36-\frac{45-36}{60-40}\times 40=18\mathrm{cm}$$

Commented by tawa tawa last updated on 27/Jul/17

$$\mathrm{Wow},\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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