Question

To compress a spring 5.0 cm from its unstretched length, 18.0 J of work must be done. (a) What is

the magnitude of the force needed to stretch it to 7.5 cm? (b) How much work must be done in stretching this spring 7.5 cm from its unstretched length?

Answer 1

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

$$k=2W/x^2=2*18.0/0.05^2=14400\;\rm N/m$$

(a)

$$F=kx\\ =14400*0.075=1080\:\rm N$$

(b)

$$W=\frac{kx^2}{2}=\frac{14400*0.075^2}{2}=40.5\:\rm J$$