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Earlier discussion
2 older comments kept for context.
Emmanuel Oshin
F1= 40, F2=60, e1= 36-Lo, e2= 46-Lo
Lo= Original length
Formula= F1/e1 = F2/e2
40/36 - Lo = 60/45 - Lo: cross multiply
60(36-Lo) = 40(45-Lo)
2160-6Lo = 1800-40Lo
Collect Like terms
2160-1800 = 60Lo-40Lo
360=20Lo
360÷20 = 18cm ✅
60
Oluwaseun Adeyemi
For Hooke's law F = Ke
\( \implies F/e = K \\
f1/e1=f2/e2 \\
\text{Let the original length} = t_0 \\
\text{therefore} e1 = (36 - t_0)cm ; e2 = (46 - t_0)cm \\
\text{if f1} = 40N \text{f2} = 60N \\
\text{Then } \frac{40}{36 - t_0} = \frac{60}{45 - t_0} \\
\implies 40(45 - t_0) = 60(36 - t_0) \\
\text{therefore } 1800 - 40t_0 \\
2160 - 60t_0 \\
60t_0 - 40t_0 = 2160 - 1800 \\
20t_0 = 360 \\
t_0 = 18cm \)