Hooke's Law Calculator
Hooke's Law Formula
F = k × x
Where:
F = Force applied (N)
k = Spring constant (N/m)
x = Displacement (m)
Theory
Hooke's Law Explained
Hooke's Law states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance. The law is named after 17th-century British physicist Robert Hooke.
Mathematically, Hooke's Law is expressed as: F = -k × x, where:
- F is the force applied to the spring (in Newtons, N)
- k is the spring constant or stiffness (in Newtons per meter, N/m)
- x is the displacement of the spring from its equilibrium position (in meters, m)
The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement (restoring force).
Example Calculations
Calculate Force
Given: k = 200 N/m, x = 0.1 m
F = k × x = 200 × 0.1 = 20 N
Calculate Spring Constant
Given: F = 50 N, x = 0.25 m
k = F / x = 50 / 0.25 = 200 N/m
Calculate Displacement
Given: F = 100 N, k = 500 N/m
x = F / k = 100 / 500 = 0.2 m
Applications
Real-World Applications of Hooke's Law
Vehicle Suspension
Springs in car suspensions use Hooke's Law to absorb shocks and provide a smooth ride.
Spring-Loaded Doors
Mechanisms that automatically close doors use springs working within Hooke's Law limits.
Spring Scales
Traditional weighing scales use springs where displacement is proportional to the weight.
Trampolines
The bounce of a trampoline is governed by Hooke's Law as the mat stretches downward.