Young's Modulus for a particular wood is 1 ｘ 10¹⁰ N m⁻².  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) 5ｘ10⁵ Nm⁻², (b) 2.1ｘ10⁻⁵m) 



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 Stress = `\frac {F}{A}`

Where F = mg

Tensile Stress = `\frac {mg}{A}`

putting values


Tensile Stress = `\frac {100 kg ｘ 9.81 m s⁻²}{2 ｘ10⁻³ m²}`

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 = `\frac {Stress}{Strai n}` 


Where Strain = `\frac {ΔL}{L}` So,

thus 


Y = Tensile Stress ｘ`\frac {L}{ΔL}`

or

ΔL = Tensile Stress ｘ`\frac {L}{Y}`

By putting the corresponding values


ΔL = 4.905 ｘ10⁵ N m⁻² ｘ`\frac {0.42 m}{1 ｘ10¹⁰ N m⁻²}`



ΔL = `\frac {2.060 ｘ10⁵ }{1 ｘ10¹⁰ }` m

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





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