Video: Mechanics and Dynamics

An elastic string of natural length 4 m and modulus of elasticity 8 N is stretched to a length of 4.5 m. How much energy is stored in the stretched string?

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Video Transcript

An elastic string of natural length four metres and modulus of elasticity eight newtons is stretched to a length of 4.5 metres. How much energy is stored in the stretched string?

In order to answer this question, we need to recall our formula to calculate the elastic potential energy or E.P.E. This is equal to 𝜆 multiplied by 𝑥 squared divided by two 𝑙. 𝜆 is the modulus of elasticity, in this question, eight newtons. 𝑙 is the natural length. This is equal to four metres. 𝑥 is the extension in the stretched string. As the stretched length in this case was 4.5 metres, we can calculate 𝑥 by subtracting four, the natural length, from 4.5. This is equal to 0.5 metres.

We now have values for 𝜆, 𝑥, and 𝑙. Substituting in these values gives us an elastic potential energy of eight multiplied by 0.5 squared divided by two multiplied by four. We could type this straight into the calculator. However, we might notice that on the denominator or bottom, we have two multiplied by four. This is equal to eight. We can then cancel the eights, leaving us with an E.P.E. of 0.5 squared. 0.5 multiplied by 0.5 is 0.25. The energy that is stored in the stretched string is 0.25 joules.

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