Question

A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the
rod to prevent it from contracting when it is cooled from 120°C to 10°C?
Ans: 3.78 * 10 N​

Answer 1

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Answer 2

Answer:$= 4 * 10^{4} N$ force is required for brass rod to prevent it from contracting when it is cooled from 120°C to 10°C.

Explanation:

Length of brass = $185cm$

Diameter of rod = $1.60cm$

$T_{1} = 120$°$C$,  $T_{2} = 10$°$C$, $Y = 0.9 * 10^{11} Pa$, $\alpha = 2* 10^{-5}$ °$C^{-1}$,

$A = 3.14r^{2}$ where r is the radius of brass rod.  $r = \frac{1.60}{2} = 0.8cm$

$T = T_{2} - T_{1}$ $= (10 -120) = -110C$

we know that,

$\frac{F}{A} = -Y*\alpha *T_{}$

by solving for F,

$F = -Y * \alpha *T*A$

$F = - 3.14 * 0.8^{2} * 0.9 * 10^{11} Pa*2* 10^{-5}$°$C^{-1}$$* (10-120)$°$C$

   $= 4 * 10^{4} N$

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