Work Energy and Power
3.0 Spring Force
3.0 Spring Force
Consider a situation when one end of a spring is attached to a fixed wall and other ends to a block, which is free to move on a horizontal table. The force due to spring is known as tension. Tensional force is always opposite to the displacement. The natural length of the spring is $L$ and the spring constant is $k$.
According to Hooke’s law, the tension in a spring is proportional to the extension or compression. $$\begin{equation} \begin{aligned} {F_T} \propto x \\ {F_T} = - kx \\\end{aligned} \end{equation} $$
The negative sign states that the displacement and tensional force are in opposite direction.
Mechanism of spring
Spring in its natural length, therefore $x=0$ As, ${F_T}=-kx=0$ So, external force ${F_{Ext}}=0$ |   |
Here, the spring has enlongation $x$. Therefore, ${F_T}=-kx$ (-ve sign indicates that the tensional force is towards left and the displacement is towards the right. So, force and displacement are in opposite direction. External force, ${F_{Ext}}=kx$ |   During elongation of the spring, the tension force is towards the spring |
Here, the spring has compression $x$. Therefore, ${F_T}=-kx$ (-ve sign indicates that the tensional force is towards the right and the displacement is towards left. So, force and displacement are in opposite direction. External force, ${F_{Ext}}=kx$ |   During compression of the spring, the tension force is away from the spring |
