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Young's Modulus of Elasticity

Two springs a...

Question

Two springs a and b having spring constants Ka and KB with Ka=2kb are stretched by applying a force of equal magnitude .If energy stored in spring A is Ea what is the energy stored in spring B

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Solution

$L e t t h e s a m e f o r c e t h a t w a s a p p l i e d b e F S o w e k n o w t h a t K_{a} = 2 K_{b} F o r s p r i n g a F = K_{a} x_{a} F = 2 K_{b} x_{a} x_{a} = F / 2 K_{b} . . . . . . . . . . . . . . . . (1) F o r s p r i n g b F = K_{b} x_{b} F = K_{b} x_{b} x_{b} = F / K_{b} . . . . . . . . (2) E_{a} = 1 / 2 (K_{a}) (x_{a})^{2} = 1 / 2 (2 K_{b}) (F / 2 K_{b})^{2} = 1 / 2 {1 / 2 (K_{b}) (F / K_{b})^{2}} E_{b} = 1 / 2 (K_{b}) (x_{b})^{2} = 1 / 2 (K_{b}) (F / K_{b})^{2} = 2 E_{a}$

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