Problem 5: Young’s modulus for a particular wood is 1 × 1010 Nm-2. A wooden chair has four legs each of length 42 cm and cross-sectional area 2 × 10-3 m2. Hamza has a mass of 100 kg.
(a) What is the stress on each leg of the chair when Hamza stands on the chair?
(b) By what amount do the chair legs shrinks when Hamza stands on the chair?

Solution

Given

Young’s modulus = 1 × 10^{10} Nm^{-2} Length = 42 cm = 4.2 m

Area = 2 × 10^{-3} m^{2} Mass = 100 kg ⇒ Weight = 100 × 9.8 = 980 N

Required

(a) Stress (b) Δl

(a) Now pressure = F/A = mg/A = 980/0.002 = 490000 = 4.9 × 10^{5} N m^{-2}

(b) Similarly, Δl = (Stress × Length)/Y. Put values,

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