Suppose 4 J of work are needed to stretch a spring 14 cm from its natural position. How much work is needed to stretch it 20 cm from its natural position

8.16 J

Explanation:

Applying,

W = ke²/2 Equation 1

Where W = work done in stretching the spring, k = spring constant, e = extension

make k the subject of the equation

k = 2W/e² Equation 2

From the question,

Given: W = 4 J, e = 14 cm = 0.14 m

Substitute these values into equation 2

k = 2(4)/0.14²

k = 8/0.0196

k = 408.16 N/m

If stretchd 20 cm from its natural length,

Therefore,

e = 20 cm = 0.2 m

W = 408.16(0.2²)/2

W = 8.16 J

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resonant frequency