2026-08-16 10:00:57: Spring Force

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physics/Force and Translational Dynamics/Spring Force.md

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+[[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.

root.md

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-# the big **R**
+"Excess is easy, anyone can do it. What's beyond most… is making it succinct—the art of abbreviation."