Young's Modulus for a particular wood is 1 x 10¹⁰ N m².  A wooden chair has four legs each of length 42 cm and cross-sectional area of 2x10⁻³ 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 shrink when Hamza stands on the chair? Answer ((a) 510⁵ Nm², (b) 2.110⁻⁵m) 



Given Data:

Young's modulus of particular wood= Y = 1 x10¹⁰ N m⁻²

Length of chair each leg = L =  42 cm = 0.42 m 

Area = A = 2 x10⁻³ m²

Mass of Hamza= m = 100 kg

value of gravitation acceleration = g = 9.81 m s⁻²

To Find:

(a). Tensile stress on each leg = ?

(b)Change in Length in the chair leg = ΔL = ?




Solution:

(a). Tensile stress on each leg = ?

Tensile stress is defined as:

Tensile StressFA

Where F = mg

Tensile Stress = mgA

putting values


Tensile Stress = 100kg9.81ms²210³m²

Tensile Stress = 490.5 x10³ N m⁻²

or 

Tensile Stress = 4.905 x10⁵ N m⁻²  ----------Ans. (1)


(b)Change in Length in the chair leg = ΔL = ?

Young's Modulus is defined as :

Y = StressStrain 


Where Strain = ΔLL So,

thus 


Y = Tensile Stress xLΔL

or

ΔL = Tensile Stress xLY

By putting the corresponding values


ΔL = 4.905 x10⁵ N m⁻² x0.42m110¹Nm²



ΔL = 2.06010110¹ m

ΔL = 2.060 x10⁻⁵ m -----------Ans. (2)





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