3C.3.1 Elastic strings and springs Quiz: Pearson Edexcel Further Maths, Unit 27

The 20 questions

1. What is Hooke's law for an elastic string of natural length L, modulus lambda and extension x?

   • T = L / (lambda x)
   • T = lambda x / L
   • T = lambda + x / L
   • T = lambda x L

2. What does the modulus of elasticity lambda of a string represent?

   • The extension produced by unit tension
   • The energy stored per unit extension
   • The tension needed to double the length of the string
   • The natural length of the string

3. What is the elastic energy stored in a string of natural length L, modulus lambda and extension x?

   • lambda x^2 / L
   • (1/2) lambda L x
   • lambda x / (2L)
   • lambda x^2 / (2L)

4. What is the natural length of an elastic string?

   • Its length when stretched to its modulus
   • Its length including the extension
   • Its average length during oscillation
   • Its length when no tension acts on it

5. In an elastic string, what does the extension x measure?

   • The modulus divided by the natural length
   • The total length of the string
   • The increase in length beyond the natural length
   • The decrease in length below the natural length only

6. Does Hooke's law apply to a spring under compression?

   • No, springs under compression never store energy
   • No, Hooke's law applies only to extensions
   • Yes, a spring under compression exerts a thrust proportional to the compression, within its elastic limit
   • Yes, but the thrust is proportional to the square of the compression

7. What form of energy is stored in a stretched elastic string?

   • Chemical energy
   • Kinetic energy
   • Thermal energy
   • Elastic potential energy

8. An elastic string has modulus 40 N, natural length 2 m and extension 0.5 m. What is the tension?

   • 20 N
   • 40 N
   • 2.5 N
   • 10 N

9. For the string in the previous setting, what is the elastic energy stored?

   • 1.25 J
   • 10 J
   • 5 J
   • 2.5 J

10. A particle of mass 4 kg hangs in equilibrium from an elastic string of modulus 60 N and natural length 1.5 m, with g = 9.8 m/s^2. What is the extension, to 2 decimal places?

    • 0.98 m
    • 0.65 m
    • 1.47 m
    • 39.2 m

11. For the equilibrium string in the previous setting (extension 0.98 m), what is the elastic energy stored, to 1 decimal place?

    • 19.2 J
    • 39.2 J
    • 9.6 J
    • 58.8 J

12. A particle of mass 2 kg is attached to an elastic string of natural length 1 m and modulus 20 N. It is released from rest at the point where the string is at its natural length, with g = 9.8 m/s^2. What is the extension at the lowest point, to 2 decimal places?

    • 3.92 m
    • 1.96 m
    • 0.98 m
    • 1.00 m

13. A spring with stiffness 80 N/m is compressed by 0.05 m. What thrust does it exert?

    • 4 N
    • 80 N
    • 1.6 N
    • 0.4 N

14. A spring with stiffness 200 N/m is compressed by 0.1 m. How much elastic energy is stored?

    • 2 J
    • 10 J
    • 0.1 J
    • 1 J

15. An elastic string has modulus 30 N and natural length 1.2 m. What is the tension when its length is 1.5 m?

    • 5 N
    • 25 N
    • 7.5 N
    • 30 N

16. A particle of mass 3 kg is attached to an elastic string of natural length 1.5 m and modulus 30 N, released from rest at natural length, with g = 9.8 m/s^2. What is its extension at the lowest point, to 2 decimal places?

    • 4.41 m
    • 2.94 m
    • 1.96 m
    • 1.47 m

17. A string of modulus 20 N and natural length 1 m is stretched from an extension of 0.5 m to 1.5 m. What is the work done?

    • 20 J
    • 10 J
    • 22.5 J
    • 2.5 J

18. A particle hangs in equilibrium from a string with modulus 50 N, natural length 1 m and extension 0.2 m, with g = 9.8 m/s^2. What is its mass, to 2 decimal places?

    • 0.98 kg
    • 1.02 kg
    • 2.00 kg
    • 10.2 kg

19. Why must the elastic energy term be included when applying conservation of energy to a particle attached to an elastic string?

    • Because the tension in the string is constant during the extension
    • Because gravity does no work on a particle attached to a string
    • Because the string does negative work as it stretches, so energy is stored in the string
    • Because the particle gains kinetic energy as the string stretches

20. A student says that doubling the extension of an elastic string doubles the energy stored. Which evaluation is correct?

    • False, since the energy is independent of the extension
    • True, provided the modulus is also doubled
    • False: energy depends on the square of the extension, so doubling the extension quadruples the energy
    • True: energy is proportional to the extension

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