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0.090 J of energy is transferred when stretching a spring - OCR Gateway - GCSE Physics - Question 13 - 2023 - Paper 4

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0.090 J of energy is transferred when stretching a spring. The spring constant of the spring is 50 N/m. What is the extension of the spring? Use the Equation Shee... show full transcript

Worked Solution & Example Answer:0.090 J of energy is transferred when stretching a spring - OCR Gateway - GCSE Physics - Question 13 - 2023 - Paper 4

Step 1

What is the extension of the spring?

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Answer

To determine the extension of the spring, we can use the formula for the potential energy stored in a spring, which is given by:

E=12kx2E = \frac{1}{2} k x^2

where:

  • EE is the energy stored in the spring (in joules),
  • kk is the spring constant (in N/m), and
  • xx is the extension of the spring (in meters).

Given:

  • E=0.090E = 0.090 J
  • k=50k = 50 N/m

We can rearrange the formula to solve for xx:

x2=2Ekx^2 = \frac{2E}{k}

Substituting the values:

x2=2×0.09050x^2 = \frac{2 \times 0.090}{50}

Calculating:

x2=0.1850=0.0036x^2 = \frac{0.18}{50} = 0.0036

Now, take the square root to find xx:

x=0.0036=0.06 mx = \sqrt{0.0036} = 0.06 \, \text{m}

Thus, the extension of the spring is 0.060 m. The correct answer is (C).

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