Hooke’s Law

Hooke’s Law                                  

• $F = -k \Delta x$
• States that within the limit of proportionality, the extension produced in a material is directly proportional to the load applied
• SI unit of k: Nm^-1
• $\uparrow$ k( Higher stiffness), $\downarrow$ extension
• Applies to springs, elastic springs and metals in form of wires

Springs connected in parallel

$k_{eff} \, = \, k_{1} + k_{2} + \, …$

Springs connected in series

$\frac{1}{k_{eff}} = \frac{1}{k_{1}} + \frac{1}{k_{2}} + \, …$

• Same load, less extension compared to series

Elastic potential energy stored in wire or spring (Amount of work stored)

$W = \frac{1}{2} k_{eff} X^{2}$