<p align="right">Last Update: <font color="#4f81bd">November, 26, 2024</font></p> ## BIG IDEAS - A change in shape due to the application of a force is deformation. - The size of the deformation is known as Hooke's law. - The restoring force is directly proportional to the displacement of the mass. --- The [[Force|force]] exerted by a spring is a <font color="#f79646">restoring force</font>. [[Robert Hooke]] (1678) determined that the restoring force is directly proportional to the [[Displacement|displacement]] of the [[Mass|mass]]. ![[Springs Hanging Vertically.png]] ### SI Unit - The [[SI units]] for the spring constant is $N/m$ ### Formula $\vec{F}_s = -kx \tag{1}$, where $\vec{F}_s$ is the spring force, $k$ is the spring constant, and $x$ is the displacement of the spring. - The negative sign is due to the restoring force being opposite the direction of the mass’s motion. - The spring constant is a measure of the stiffness of a spring. A stiffer spring has a greater _k_ value. ### Background - In the 1650s, Robert Hooke was working in Robert Boyle’s laboratory and studying elasticity. - The law with his name states that a force is proportional (linear) to the distance stretching or compressing for certain elastic materials. - The distance is the amount of deformation. $\vec{F} \propto x$ - Adding a spring constant to the proportion changes this proportion to a simple equation: $\vec{F} = -k x$ - where the $k$ is the spring constant, $x$ is the distance the material moves, and $\vec{F}$ is the restoring force. - The minus sign designates the force acting in the direction opposite to the displacement. - A force is a push or pull during an interaction between at least two objects. - A newton is $kg \frac{m}{s^2}$ - Weight ($W$) is a force, where $W = m \cdot g$. - The symbol $g$ represents the gravitational field strength. - The numerical value of $g$ is based on the location of the object. - Mass remains the same regardless of its location. --- ==Simple Harmonic Motion== (SHM) is periodic motion from a _restoring force_ proportional to displacement. > [!important] > Simple harmonic motion describes the vibration of atoms, the variability of giant stars, and countless other systems from musical instruments to swaying. Demonstration 1: Vibrating Spring Demonstration 2: Equilibrium Position The motion of Earth orbiting the sun is periodic. Is it simple harmonic motion? Why or why not? #### Example Problem What is the spring constant if a mass of 0.45 kg attached to a vertical spring stretches the spring 1.5 cm from its original equilibrium position? #### Example Problem What is the spring constant if a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from the equilibrium position? #### Example Problem How much force is required to pull a spring 3.5 cm from its equilibrium position if the spring constant is 2.7 x10<sup>3</sup> N/m? ### Slide Deck <div style="position: relative; width: 100%; height: 0; padding-top: 56.2500%; padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden; border-radius: 8px; will-change: transform;"> <iframe loading="lazy" style="position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;" src="https://www.canva.com/design/DAGPwPTLleU/bQxt6IPtrv8a8yYNBcjNiQ/view?embed" allowfullscreen="allowfullscreen" allow="fullscreen"> </iframe> </div> ### Video <div class="sp-embed-player" data-id="c0QroNVCsEc"><script src="https://go.screenpal.com/player/appearance/c0QroNVCsEc"></script><iframe width="100%" height="480px" style="border:0;" scrolling="no" src="https://go.screenpal.com/player/c0QroNVCsEc?width=100%&height=480px&ff=1&title=0" allowfullscreen="true"></iframe></div> ### Related Topics --- [[Home|Home]] | [[Oscillations]] | [[Periodic Motion]] | [[Simple Harmonic Motion]] | [[Waves]] | [[Module 0 Sound]] | [[Electromagnetic radiation]]