The diagram below represents the graph of the force applied in stretching a spiral spring against the corresponding extension produced within its elastic limit.
Using the notations on the graph, determine the:
(a) force constant of the spring;
(b) work done in stretching the spring from 10 x 10(^{-2})m to 20 x 10(^{-2})m.
Explanation
a) Force constant of the spring = slope of the graph = (frac{Delta force}{Delta Extension})
= (frac{60 — 0}{20 – 0 times 10^{-2}} = frac{60}{20 times 10^{-2}})
= 300Nm(^{-2})
(b) Work done = Area under the trapezium ABCD
= 1/2 (30 + 60) x (20 — 10) x 10(^{-2}) = 4.5J