Answer to Question #91258 in Mechanics | Relativity for Umar

Question

If a force of 100N stretches a spring by 0.1cm, find
a) the elastic constant
b) the work done in stretching the spring 0.3cm if the elastic limit is not exceeded

Answer 1

(a) The Hooke's law states

$$F=kx$$

So, the elastic constant

$$k=\frac{F}{x}=\frac{100\:\rm{N}}{0.001\:\rm{m}}=100000\:\rm{N/m}$$

(b) The work done

$$W=\frac{1}{2}kx^2$$

$$=\frac{1}{2}\times 100000\;\rm{N/m}\times (0.003\;\rm{m})^2=0.45\:\rm{J}$$