Question

Determine the equation of the relationship between the force and the extension. Hooke's Equation: Fs = -k(delta)x

Answer 1

Let , A block is attached to a spring having spring constant .A force " "is applied and spring has got an elongation of units .

now,

Hooke's Law states that the force needed to extend or compress a spring by some distance is proportional to that distance or we can say that ,that restoring force is equal to the negative of the displacement (deformation) times a constant.

Mathematical representation of HOOK'S law is :

where:

There is a negative sign on the right hand side of the equation because the restoring force always acts in the opposite direction of the displacement (for example, when a spring is stretched to the left, it pulls back to the right).

• = displacement of the spring’s end from its equilibrium position (a distance, in SI units: meters);
• = restoring force exerted by the spring on that end (in SI units: N or kg·m/s2); and
• = spring constant (in SI units: N/m or kg/s2). When this holds, the behavior is said to be linear. If shown on a graph, the line should show a direct variation. (as shown in figure).