obsidianvault/physics/Force and Translational Dynamics/Spring Force.md

Force and Translational Dynamics

Spring force uses Hooke's law: \vec F_s=-k\Delta \vec x k = stiffness of spring \Delta x = displacement from measured from a relaxed length negative sign means force points back towards equilibrium

Vertical spring stretched the spring until k\Delta x = mg at equilibrium.

Hooke's law in magnitude is |\vec F_s|=k|\Delta x| Spring constant k measures in N/m. Bigger k means more stiff (obviously). Spring force is a restoring force that points towards equilibrium position of object spring relationship. For a vertical spring with hanging mass, relaxed length is not equilibrium because gravity stretches spring

Ideal Spring:

The mass of an ideal spring is treated as negligible compared to the objects attached to it.

• You can ignore the spring's own weight in calculations.
• You focus only on the interaction between the spring and the attached object.

An ideal spring follows a linear force-displacement relationship.

• The force is directly proportional to how far the spring is stretched or compressed.
• Stretch it twice as far and it pulls back with twice the force.
• This behavior stays consistent each time you use the spring.

Direction of Spring Force

When a string is stretched:

• \Delta x is positive
• Spring force is negative, pulling back When a string is compressed:
• \Delta x is negative
• Spring force is positive, pushing forward

WHEN CALCULATING THE \Delta x OF A VERTICAL SPRING WITH A HANGING MASS, USE THE RELAXED POSITION NOT THE EQUILIBRIUM POSITION.