Elastic strings and springs and elastic energy questions

Questions to attempt

6 questions on Elastic strings and springs and elastic energy, each with its mark scheme and worked method. Reveal the answer when you have had a go.

1. FM1-3.1 · Elastic strings and springs. Hooke's law.

   Q1

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   1.

   An elastic string has natural length $1.5\,\text{m}$ and modulus $120\,\text{N}$. It is stretched to length $1.8\,\text{m}$. Calculate its tension.

   (3)

   (Total for Question 1 is 3 marks)

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2. FM1-3.1 · Elastic strings and springs. Hooke's law.

   Q2

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   2.

   A light spring has spring constant $80\,\text{N m}^{-1}$ and is extended by $0.06\,\text{m}$. Find its tension.

   (2)

   (Total for Question 2 is 2 marks)

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3. FM1-3.1 · Elastic strings and springs. Hooke's law.

   Q3

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   3.

   A $1.5\,\text{kg}$ particle hangs in equilibrium from a vertical elastic string of natural length $0.8\,\text{m}$ and modulus $49\,\text{N}$. Taking $g=9.8\,\text{m s}^{-2}$, determine the extension and the equilibrium length of the string.

   (4)

   (Total for Question 3 is 4 marks)

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4. FM1-3.2 · Energy stored in an elastic string or spring.

   Q4

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   4.

   An elastic string has natural length $1.2\,\text{m}$ and modulus $60\,\text{N}$. Find the energy stored when its length is $1.5\,\text{m}$.

   (3)

   (Total for Question 4 is 3 marks)

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5. FM1-3.2 · Energy stored in an elastic string or spring.

   Q5

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   5.

   A spring of constant $200\,\text{N m}^{-1}$ is compressed by $0.08\,\text{m}$. Calculate the elastic energy stored.

   (2)

   (Total for Question 5 is 2 marks)

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6. FM1-3.2 · Energy stored in an elastic string or spring.

   Q6

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   6.

   A $2\,\text{kg}$ particle is attached to the lower end of a vertical elastic string with natural length $1\,\text{m}$ and modulus $49\,\text{N}$. It is released from rest when the string is at natural length. Taking $g=9.8\,\text{m s}^{-2}$, find its speed after descending $0.6\,\text{m}$.

   (5)

   (Total for Question 6 is 5 marks)

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FM1-3 Elastic strings and springs and elastic energy revision notes