Restoring Force and Work Done by A Spring

Restoring Force

Force that restores a system to an equilibrium position. (Is opposite of the displacement)

Elastic

Objects that exert restoring forces.

Equilibrium length

Length of the spring when it is neither pushing or pulling

L0 (0 is the subscript)

Symbol of the Equilibrium length

Farther the push/pull = larger the force

The force of the spring is proportional to the displacement from equilibrium.

Fsp (sp is the subscript)

Symbol of the Force of the spring

Sign of Fsp

The thing which is always opposite to the sign of the delta of displacement.

Fsp = -kΔs

Mathematical representation of the Hooke’s Law

k

Symbol for the spring constant. Which is the absolute value of the slope of the spring force vs displacement graph.

-ve integer of k

A Mathematical indication of a restoring force

Robert Hooke

Person who discovered the relationship between the force and displacement of spring.

Hooke’s Law

1) Not a true nature’s law like Newton’s law

2) Just a model of a resisting force

3) Works only for small displacement from equilibrium

4) Will fail if compressed or stretched way too far.

Ideal spring

Hypothetical massless spring for which Hooke’s Law is true at all displacements.

Larger k

A large pull will be required to cause a significant stretch. (Stiff spring)

Smaller k

A very little force is required to stretch a spring (Soft spring)

Stick-slip motion

Once the object slips; it will shoot forward some distance; then stop and stick again; with a recurring sequence.

Earthquake

An example of a stick-slip motion.

W = 1/2(k)(x²)

Formula for the work done by spring