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Standard XII

Physics

Young's Modulus of Elasticity

A steel rod ...

Question

A steel rod $2.0 m$ long has a cross-sectional area of $0.30 {c m}^{2}$ . The rod is now hung by one end from a support structure, and a $550 k g$ milling machine is hung from the rod's lower end. Determine the stress, the strain, and the elongation of the rod.

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Solution

$σ = S t r e s s$ and $ε = s t r a i n$
$σ = \frac{F}{A} = \frac{(550 k g) \times (9.81 m / s^{2})}{3 \times 10^{- 5} m^{2}} = 0.18 ㎬$
$ε = \frac{Δ l}{l_{0}} = \frac{σ}{Υ} = \frac{0.18 \times 10^{9}}{200 \times 10^{9}} = 9 \times 10^{- 4}$
$Δ l = ε l_{0} = (9 \times 10^{- 4}) (2 m) = 0.0018 m = 1.8 m m$

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A steel rod 2.0m long has a cross-sectional area of 0.30cm2. The rod is now hung by one end from a support structure, and a 550kg milling machine is hung from the rod's lower end. Determine the stress, the strain, and the elongation of the rod.

σ=Stress and ε=strainσ=FA=(550kg)×(9.81m/s2)3×10−5m2=0.18㎬ε=Δll0=σΥ=0.18×109200×109=9×10−4Δl=εl0=(9×10−4)(2m)=0.0018m=1.8mm

A steel rod $2.0 m$ long has a cross-sectional area of $0.30 {c m}^{2}$ . The rod is now hung by one end from a support structure, and a $550 k g$ milling machine is hung from the rod's lower end. Determine the stress, the strain, and the elongation of the rod.