Home / CIE AS & A Level Physics : 6.2 Elastic and plastic behaviour – Exam style question – Paper 1
The graph shows the variation in extension with force for a sample of rubber.
The top line shows the variation in extension as a force is applied.
The bottom line shows the variation in extension as the force is removed.
What is represented by the area between the two lines?
Correct Answer: \( \boxed{\mathrm{B}} \)
The area under a force-extension graph represents the work done.
The area between the loading and unloading curves is the difference between the work done during loading and the work recovered during unloading.
This is the energy dissipated as heat due to hysteresis.
Therefore, the correct answer is (B).
Two identical springs have the same spring constant \(k\). The springs are connected in parallel. The length of the unstretched springs is \(x\).
A force \(F\) is applied to the spring combination. The length of the springs is now \(y\).
Both springs are deformed within their limits of proportionality.
Which expression gives the elastic potential energy stored in one of the springs?
Correct Answer: \( \boxed{\mathrm{A}} \)
The extension of each spring is \(y-x\).
Since the springs are identical and connected in parallel, each carries a force of \(F/2\).
The elastic potential energy in one spring is
\(E=\dfrac{1}{2}\times\dfrac{F}{2}\times(y-x)=\dfrac{1}{4}F(y-x)\).
Therefore, the correct answer is (A).
The graph shows how the extension of a spring varies with the force used to stretch it.
What is the elastic potential energy of the spring when the extension is \(4.0\,\mathrm{cm}\)?
Correct Answer: \( \boxed{\mathrm{C}} \)
The elastic potential energy equals the area under the force-extension graph.
At an extension of \(4.0\,\mathrm{cm}=0.040\,\mathrm{m}\), the force is \(30\,\mathrm{kN}=3.0\times10^{4}\,\mathrm{N}\).
\(E=\dfrac{1}{2}Fx=\dfrac{1}{2}\times3.0\times10^{4}\times0.040=600\,\mathrm{J}\).
Therefore, the correct answer is (C).