Functions, 2ADV EQ-Bank 7

Energy \((E)\) stored in a spring, measured in joules, varies directly with the square of its compression distance \(d\), measured in centimetres.

When a spring is compressed by 4 cm, it stores 48 joules of energy.

How much energy is stored when the spring is compressed by 7 cm? (3 marks)

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\(\text{147 joules}\)

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\(E \propto d^2 \ \Rightarrow \ E=k d^2\)

\(\text{Find \(k\) given \(\ E=48 \ \) when \(\ d=4\):}\)

\(48\)	\(=k \times 4^2\)
\(k\)	\(=3\)

\(\text{Find \(E\) when \(\ d=7\):}\)

\(E=3 \times 7^2=147 \ \text{joules}\)