Answer to Question #121538 in Mechanics | Relativity for isaac

Question

What mass should be hung on an elastic material of stiffness 100N/m to produce an extension of 20cm.

Answer 1

By the definition of the Hooke's Law, we get:

$$F = kx,$$

here, $F$ is the force acting on the elastic material, $k$ is the stiffness of the material, $x$ is the extension of the material.

From the other hand, $F = mg$ (when the mass is attached), and substituting it into the first equation we get :

$$mg = kx,$$ $$m = \dfrac{kx}{g},$$ $$m = \dfrac{100 \ \dfrac{N}{m} \cdot 0.2 \ m}{9.8 \ \dfrac{m}{s^2}} = 2.04 kg.$$

Answer:

$m = 2.04 kg.$