Find out the final extension and the work done:
(i) A spring of stiffness 4 N/cm of extension is extended steadily yet the force of 20 N is reached. Find out the final extension and the work done to cause this extension.
(ii) If the extension is further to be enhanced by 20%, how much additional work is necessary. What is the ultimate magnitude of force needed to achieve this.
Stiffness (K) of a spring is described as force required to cause unit deflection. Therefore, if s1 is the deflection under a force F1
∴ Stiffness = F1/ s1 = tan θ
∴ 4 = 20 /s1
s1 = 20 /4= 5 cm
(i) W. D. on spring to cause extension s1 = Area of Δ Os1 A
= (20 × 5) /2 = 50 N-cm.
Further 20% extension beyond s1 = 0.2 × 5 = 1 cm
s1 s2 = 1 cm
s2 = Total Extension = Os2 = 6 cm
∴ F2 = Stiffness × 6 = 24 N.
(ii) Additional WD from s1 to s2 = Area of trapezium As1 s2 B
=( (F1 + F2 )/2 ) × s1 s2
= ((20 + 24)/2) × 1= 22 N-cm.