Answer to Question #189269 in Physics for Emmanuel

Question

A spring in a hanging scale increases it’s length by 16.5 cm from it’s normal length when an object with a mass of 2.2 kg is hung from the spring.  Determine: (a) the spring constant, (b) the elastic potential energy stored in the spring by hanging this mass from it, and (c) the mass of an object that increases the spring length by 30 cm from it’s normal length when it is hanging from the spring.

Answer 1

(a)

$$F=kx,$$ $$mg=kx,$$ $$k=\dfrac{mg}{x}=\dfrac{2.2\ kg\cdot9.8\ \dfrac{m}{s^2}}{0.165\ m}=131\ \dfrac{N}{m}.$$

(b)

$$PE=\dfrac{1}{2}kx^2,$$ $$PE=\dfrac{1}{2}\cdot131\ \dfrac{N}{m}\cdot(0.165\ m)^2=1.78\ J.$$

(c)

$$m=\dfrac{kx}{g},$$ $$m=\dfrac{131\ \dfrac{N}{m}\cdot0.3\ m}{9.8\ \dfrac{m}{s^2}}=4.0\ kg.$$