First slide

Work done by Diff type of forces

Question

An elastic spring of unstretched length L and force constant K is stretched by amount x. It is further stretched by another length y. The work done in the second stretching is

Easy

A

$\frac{1}{2} {Ky}^{2}$
B

$\frac{1}{2} K (x^{2} + y^{2})$
C

$\frac{1}{2} K {(x + y)}^{2}$
D

$\frac{1}{2} Ky (2 x + y)$

Solution

Work done to stretch to length x = $\frac{1}{2} K X^{2}$ = $W_{1}$
Work done to stretch to length y = $\frac{1}{2} K {(X + Y)}^{2}$ = $W_{2}$
W = $W_{2} - W_{1}$
W = $\frac{1}{2} k {(y + x)}^{2} - x^{2})$

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