CAIE A-Level Physics 6.2.3 Elastic Potential Energy

Practise interpreting force–extension graph area as stored elastic energy, applying ½Fx within proportional limits and distinguishing losses.

Exam points

determine elastic potential energy from the area under a force–extension graph for deformation within the limit of proportionality
use the triangular area 1/2Fx when the force–extension relationship is proportional and include correct units
interpret the graph area as stored elastic energy and distinguish loading energy from other work or losses

[Maximum number: 2]

A spring is fixed at one end and is compressed by applying a force to the other end. The variation of the force F acting on the spring with its compression x is shown in Fig. 3.1.

Fig. 3.1

A compression of 0.045 m is produced when a force $F_{1}$ acts on the spring. The spring has a spring constant of $800 \mathrm{Nm}^{-1}$ .

Use Fig. 3.1 to show that, for a compression of 0.045 m , the elastic potential energy of the spring is 0.81 J .

$(E=) \frac{1}{2} k x^{2}$ or $\frac{1}{2} F x$ or area under graph

C1

$\frac{1}{2} \times 800 \times(0.045)^{2}$ or $\frac{1}{2} \times 36 \times 0.045=0.81$ (J)

A1

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6.2.3—The elastic potential energy of a material deformed within its limit of question 1