Another student suggests that an elastic band could be used instead of a spring in a newton-meter. Look at the force-extension graph for an elastic band. Explain why the elastic band would not make a good replacement for a spring. A spring has a spring constant of 30 N/m. Calculate the energy transferred when the spring is extended by 4.0 cm.

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Another student suggests that an elastic band could be used instead of a spring in a newton-meter - OCR Gateway - GCSE Physics - Question 19 - 2021 - Paper 1

Question 19

Another student suggests that an elastic band could be used instead of a spring in a newton-meter. Look at the force-extension graph for an elastic band. Explain ... show full transcript

Worked Solution & Example Answer:Another student suggests that an elastic band could be used instead of a spring in a newton-meter - OCR Gateway - GCSE Physics - Question 19 - 2021 - Paper 1

Step 1

Explain why the elastic band would not make a good replacement for a spring.

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Answer

The elastic band does not follow Hooke's Law over its entire range of extension, which means it does not provide a linear relationship between force and extension. In contrast, springs exhibit a consistent spring constant for extensions within their elastic limits, ensuring predictable and reliable behavior. Additionally, the hysteresis effect observed in the force-extension graph of the elastic band indicates energy loss during unloading, which can lead to inefficiencies in a newton-meter setup.

Step 2

Calculate the energy transferred when the spring is extended by 4.0 cm.

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Answer

To calculate the energy transferred to the spring, we use the formula for elastic potential energy:

$E = \frac{1}{2} k x^2$

where:

$E$ is the elastic potential energy,
$k$ is the spring constant (30 N/m), and
$x$ is the extension in meters.

First, convert the extension from centimeters to meters: 4.0 cm = 0.04 m

Now substituting the values into the formula:

$E = \frac{1}{2} \times 30 \times (0.04)^2$

Calculating:

$E = \frac{1}{2} \times 30 \times 0.0016 = 0.024 \text{ J}$

Thus, the energy transferred when the spring is extended by 4.0 cm is 0.024 joules.

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Another student suggests that an elastic band could be used instead of a spring in a newton-meter - OCR Gateway - GCSE Physics - Question 19 - 2021 - Paper 1

Worked Solution & Example Answer:Another student suggests that an elastic band could be used instead of a spring in a newton-meter - OCR Gateway - GCSE Physics - Question 19 - 2021 - Paper 1

Explain why the elastic band would not make a good replacement for a spring.

Calculate the energy transferred when the spring is extended by 4.0 cm.

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