Springs and graph interpretation
One graph can describe both stiffness and work. Its gradient measures force per unit extension; its area measures force multiplied by extension.
Follow the reasoning
- Check force is on the vertical axis and extension on the horizontal axis.
- Convert extension to metres before calculating the gradient.
- Use a large triangle on the best-fit straight line for k.
- Find area under the curve to calculate work, dividing it into shapes if needed.
Specification outcomes (4)
- 3.4.1(b) State and apply Hooke’s law.
- 3.4.1(c) Define the force constant k of a spring or wire using F = kx.
- 3.4.1(d)(i) Interpret force–extension or compression graphs for springs and wires.
- 3.4.2(a) Interpret force–extension (or compression) graphs; calculate work done as area under graph.
H156 v2.0 · May 2026
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PhysicsUK practice
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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]
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