CAIE A-Level Physics AS 6.2.4 Ep 1 2 Fx 1 2 Kx2 for a Material Deformed Within Its Limit of Questions

Interpret the area under a force–extension graph as elastic potential energy stored.

Exam points

Interpret the area under a force–extension graph as elastic potential energy stored.

[Maximum number: 3]

Fig. 4.1 shows the variation with extension x of the tensile force F for two wires, G and H, made from the same material.

Fig. 4.1

The elastic limit has not been exceeded for G or H.

Wires G and H are joined together end-to-end to form a composite wire of negligible weight. The composite wire hangs vertically from a fixed support.

A block of weight of 2.0 N is attached to the end of the wire, as shown in Fig. 4.2.

Fig. 4.2

Calculate the total elastic potential energy $E_{\mathrm{P}}$ of the composite wire due to the weight of the block.

E_{P}=

E=1 / 2 F x

or

$E=1 / 2 k x^{2}$ and F=k x

or

E= area under graph
$\begin{aligned} \text { for } \mathrm{G}: E=1 / 2 \times 2.0 \times\left(0.39 \times 10^{-3}\right) \text { or } 1 / 2 \times 5.1 \times 10^{3} \times\left(0.39 \times 10^{-3}\right)^{2} \text { for } \mathrm{H}: E=1 / 2 \times 2.0 \times\left(0.29 \times 10^{-3}\right) \text { or } 1 / 2 \times 6.9 \times 10^{3} \times\left(0.29 \times 10^{-3}\right)^{2} \begin{aligned} E_{\mathrm{P}}= 3.9 \times 10^{-4}+2.9 \times 10^{-4} =6.8 \times 10^{-4} \mathrm{~J} \end{aligned} \end{aligned}$

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CAIE A-Level Physics AS 6.2.4 Ep 1 2 Fx 1 2 Kx2 for a Material Deformed Within Its Limit of Questions question 1