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Stress-Strain Graph

A steel wire ...

Question

A steel wire with cross section $3 c m^{2}$ has elastic limit $2.4 \times 10^{8} P a$ . Find the maximum upward acceleration that can be given to a $1200 k g$ elevator supported by this cable if the stress is not to exceed $1 / 3 r d$ of the elastic limit.

9 m s^{- 2}

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10 m s^{- 2}

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11 m s^{- 2}

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12 m s^{- 2}

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Solution

The correct option is B $10 m s^{- 2}$
If the upward acceleration is $a$ ,
Force on the cable is $= 1200 (g + a)$
This force should be equal to one-third the maximum elastic limit
$1200 (g + a) = \frac{1}{3} \times 2.4 \times 10^{8} \times 3 \times 10^{- 4}$
$g + a = 20$
$a = 20 - 10 = 10 m s^{- 2}$
Option B.

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