First slide

Work

Question

When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, the stored energy will be increased by (in J)

Moderate

Solution

$100 = \frac{1}{2} {kx}^{2}$ (given)
$W = \frac{1}{2} k (x_{2}^{2} - x_{1}^{2}) = \frac{1}{2} k [{(2 x)}^{2} - x^{2}]$
$= 3 \times (\frac{1}{2} {kx}^{2}) = 3 \times 100 = 300 J$

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