(a) Define Young modulus of elasticity; (b) A spiral spring extends from a length of 10.0 cm to 10.01 cm when a force of 20 N is applied on it. Calculate th...
Question 1 Report
(a) Define Young modulus of elasticity;
(b) A spiral spring extends from a length of 10.0 cm to 10.01 cm when a force of 20 N is applied on it. Calculate the force constant of the spring.
Answer Details
(a) Young modulus of elasticity is the ratio of the tensile stress to the tensile strain of a material, provided the elastic limit is not exceeded.
\[ E = \dfrac{\text{tensile stress}}{\text{tensile strain}} = \dfrac{F/A}{e/l} = \dfrac{F l}{A e}. \]
(b) The force constant is \( k = \dfrac{F}{e} \), where e is the extension.
Extension: \[ e = 10.01 - 10.00 = 0.01\,\text{cm} = 1.0 \times 10^{-4}\,\text{m}. \]
\[ k = \dfrac{F}{e} = \dfrac{20}{1.0 \times 10^{-4}} = 2.0 \times 10^{5}\,\text{N m}^{-1}. \]
The force constant of the spring is \( 2.0 \times 10^{5}\,\text{N m}^{-1} \).
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