In one position the extension of the spring is 8.0 cm. The elastic potential energy stored by the spring is 4.0 J. Calculate the spring constant of the spring. Use the Physics Equations Sheet. add step Spring co

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In one position the extension of the spring is 8.0 cm. The elastic potential energy stored by the spring is 4.0 J. Calculate the spring constant of the spring. Use the Physics Equations Sheet. add step Spring co

Answer 1

The spring constant of the spring is \(1250 \, \text{N/m}\).

Answer 2

## Step 1: The elastic potential energy stored in a spring can be calculated using the formula: ### \(PE_{spring} = \frac{1}{2}kx^2\) where: - \(PE_{spring}\) is the elastic potential energy, - \(k\) is the spring constant, - \(x\) is the displacement of the spring from its equilibrium position. ## Step 2: In this problem, the elastic potential energy \(PE_{spring}\) is given as \(4.0 \, \text{J}\), and the displacement \(x\) is given as \(8.0 \, \text{cm}\). Convert the displacement to meters: ### \(x = 8.0 \, \text{cm} = 0.08 \, \text{m}\) ## Step 3: Rearrange the formula to solve for the spring constant \(k\): ### \(k = \frac{2 \cdot PE_{spring}}{x^2}\) ## Step 4: Substitute the given values into the rearranged formula: ### \(k = \frac{2 \cdot 4.0 \, \text{J}}{(0.08 \, \text{m})^2}\) ## Step 5: Calculate the spring constant \(k\): ### \(k = \frac{8.0 \, \text{J}}{0.0064 \, \text{m}^2} = 1250 \, \text{N/m}\)

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In one position the extension of the spring is 8.0 cm. The elastic potential energy stored by the spring is 4.0 J. Calculate the spring constant of the spring. Use the Physics Equations Sheet. add step Spring co

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