A metal wire is attached at one end to a fixed point and a load is hung from the other end so that the wire hangs vertically.

Question 3

A metal wire is attached at one end to a fixed point and a load is hung from the other end so that the wire hangs vertically. The load is increased from zero to 20 N. This causes the wire to extend elastically by 5.0 mm. The load is then reduced to 12 N and the extension decreases to 3.0 mm.

How much strain energy is released during the unloading process?

A 0.8×10^-2 J             B 1.8×10^-2 J               C 2.4×10^-2 J             D 3.2×10^-2 J

Reference: Past Exam Paper – June 2016 Paper 12 Q21

Solution:

Answer: D.

Strain energy released under the unloading process is obtained by the area under the load-extension graph between 3.0 mm and 5.0 mm.

Strain energy   = area under graph

                        = area of trapezium

                        = ½ × (12+20) × (5.0 – 3.0) × 10^-3

                        = 0.032 J = 3.2×10^–2 J

 
Alternatively, the area under the graph could be split into the area of a triangle and that of a rectangle instead of calculating the area of a trapezium.