Elastic potential energy
Stretching or compressing a spring requires work. For a Hookean spring, the stored elastic energy is half the final force multiplied by the deformation: E = ½kx². The factor of one half accounts for the force increasing from zero.
Specification outcomes (2)
- 3.4.2(a) Interpret force–extension (or compression) graphs; calculate work done as area under graph.
- 3.4.2(b) Calculate elastic potential energy using E = ½Fx or E = ½kx².
H156 v2.0 · May 2026
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OCR A AS · June 2018 · H156/01
Question 22(d), using the tension from 22(c) · 2 marks
Use the spring tension established in the preceding equilibrium calculation and the spring constant to calculate stored elastic energy.
Question paper p. 13 · Mark scheme p. 7
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A spring obeys Hooke's law and has a spring constant of 25 N m⁻¹. (a) Calculate the extension produced by a force of 5.0 N. (2) (b) Calculate the elastic potential energy stored in the spring at this extension. (2)
Matched by specification tags · 4 marks
Try this question now →A technician calibrates the spring bumper of a small instrument trolley. Figure 1 shows the force F needed to compress the spring by x from its natural length. The graph is a straight line through (0, 0), (0.020 m, 1.2 N), (0.040 m, 2.4 N) and (0.060 m, 3.6 N). The trolley has mass 0.60 kg. It is released from rest against the spring at compression 0.060 m on a horizontal track. A constant resistive force of 0.60 N opposes the motion as soon as the trolley moves. The spring's mass is negligible and its deformation is elastic. The trolley loses contact with the spring at its natural length. There are no other energy losses. (a) Use the gradient of the force-compression graph to determine the spring constant. [2] (b) Use the graph to calculate the work needed to compress the spring from its natural length to 0.060 m. [2] (c) Calculate the acceleration just after release, stating its direction relative to the bumper. [3] (d) Calculate the speed when the trolley loses contact with the spring. Account for the work done against resistance. [3] (e) Explain why a single constant-acceleration equation cannot describe the whole interval while the trolley is in contact with the spring. [2] (f) Calculate the distance travelled after losing contact before the trolley stops. Use a constant-acceleration equation for this part. [3]
Matched by specification tags · 15 marks
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