Question
Suppose the ceiling in the previous problem is that of an elevator which is going up with an acceleration of $2.0m/s^2.$ Find the elongations.
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Answer
$a = 2m/s^2 kl - (2g + 2a) = 0$
$\Rightarrow kl = 2g + 2a = 2 \times 9.8 + 2 \times 2 = 19.6 + 4 = 23.6$
$\Rightarrow\text{I}=\frac{23.6}{100}=0.236\text{m}=0.24\text{m}$
When 1kg body is added total mass $(2 + 1)kg = 3kg.$
elongation be $l_1\ kl_1 = 3g + 3a = 3 \times 9.8 + 6 = 33.4$
$\Rightarrow\text{I}_1=\frac{33.4}{100}=0.0334=0.36$
Further elongation $= l_1 - l = 0.36 - 0.24 = 0.12m.$
$\Rightarrow kl = 2g + 2a = 2 \times 9.8 + 2 \times 2 = 19.6 + 4 = 23.6$
$\Rightarrow\text{I}=\frac{23.6}{100}=0.236\text{m}=0.24\text{m}$
When 1kg body is added total mass $(2 + 1)kg = 3kg.$
elongation be $l_1\ kl_1 = 3g + 3a = 3 \times 9.8 + 6 = 33.4$
$\Rightarrow\text{I}_1=\frac{33.4}{100}=0.0334=0.36$
Further elongation $= l_1 - l = 0.36 - 0.24 = 0.12m.$
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