# Year 11 Physics, Applied.

Combining my passion for physics and computer science, **Year 11 Physics, Applied** is a collection of interactive demonstrations and simulations designed to visualise and help myself and my peers understand the physics concepts taught in **my Year 11 Physics class.**

This website and demos are maintained by me, *l-m*.

I use the C programming language to create these demos, which are compiled to WebAssembly using Emscripten. My demos also use supporting libraries like sokol and Dear ImGui, which abstract away the complexities of the web, allowing me to focus on creating engaging and effective demos.

All of the code in my repository yr11-physics-applied on GitHub is licensed under the MIT open source license, so you can use it however you like.

Want something else to read? Check out my blog at *l-m.dev.*

Mar 25, 2023

To sum two vectors, use trigonometry to find the $x$ and $y$ components of each vector.

$$
\begin{align*}
\vec{s} + \vec{p} &= \vec{r} \\
x_{s} \cos \theta_s + x_{p} \cos \theta_p &= x_{r} \\
y_{s} \sin \theta_s + y_{p} \sin \theta_p &= y_{r} \\
\end{align*}
$$
Mar 26, 2023

The static friction coefficient $\mu_{s}$ and the kinematic friction coefficent $\mu_{k}$. Static friction keeps objects at rest staying at rest, and the kinematic friction slows down objects in already in motion.

An objects friction is in direct relationship with the force applied from another object contacting against it, the normal force $F_n$.

$$
\begin{align*}
F_{N} &= mg \\
F_{f_{s}} &\leq \mu_{s} F_{N} \\
F_{f_{k}} &= \mu_{k} F_{N} \\
\end{align*}
$$
May 19, 2023

The *amplitude* $A$ of a transverse wave determines the height or intensity of the wave, measured in metres $m$. The *wavelength* $\lambda$ corresponds to the distance between two adjacent crests or troughs, also measured in metres $m$. The *wave velocity* $v$ refers to the rate at which the wave energy travels through the medium, measured in $ms^{-1}$.

Wave period $T$ and frequency $f$ are closely related. Frequency $f$ measures the number of cycles per second in the SI unit hertz $\text{Hz}$. The wave period $T$ is the time taken in seconds $s$ for one wave cycle.

$$
\begin{align*}
f = \frac{v}{\lambda} &&
\lambda = \frac{v}{f} &&
v = f\lambda
\end{align*}
$$
$$
\begin{align*}
f = \frac{1}{T} &&
T = \frac{1}{f}
\end{align*}
$$
Graphing a sinusoidal wave requires the wavelength $\lambda$ and amplitude $A$.
$$
f(x) = A \sin \frac{2\pi}{\lambda} x
$$
May 21, 2023

The *Ideal Gas Law* is the equation for a hypothetical ideal gas.

The product of pressure $P$ and volume $V$ is equal to the products of the number of substance $n$, the *Ideal Gas Constant* $R$, and temperature in kelvin $T$. This is one arrangement of the *Ideal Gas Law*.

$$
PV = nRT
$$
Pressure $P$ is force $F$ applied over area $A$. Pressure $P$ can also be derived from rearranging the previous equation.

$$
\begin{align*}
P = \frac{F}{A} &&
P = \frac{nRT}{V}
\end{align*}
$$
Force $F$ can then be derived from the pressure and area $A$.

$$
F = \frac{nRT}{V} \cdot A
$$
The Force $F$ exerted by the softbodies internal pressure $P$ can now be used to 'inflate' the softbody by applying pressure along a normal vector.

May 24, 2023

Gravitational potential energy is a form of potential energy associated with the position of an object in a gravitational field. It represents the energy that an object possesses due to its vertical height above a reference point, often taken as the ground.

Energy is measured in the SI unit Joule $J$.

Potential energy $U$ is the products of the mass $m$ of the object in kilograms, the acceleration $g$, and the height of the object $h$ above the reference point.

$$
U = mgh
$$
As an object is lifted or raised against the force of gravity, work is done and energy is stored in the form of potential energy.

As the object falls, gravitational potential energy $U$ is gradually converted into gravitational kinetic energy $K$. When the object reaches the bottom of the drop, its potential energy becomes zero, and all the potential energy has been transformed into kinetic energy.

$$
K = \frac{1}{2}mv^2
$$
According to the principle of conservation of energy, the total energy of the system remains constant.

$$
\Delta U = \Delta K
$$