2026-08-17 08:24:01: Work

This commit is contained in:
2026-08-17 08:24:02 -04:00
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commit 0b7baaa446
9 changed files with 79 additions and 53 deletions
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@@ -19,3 +19,4 @@ hale - to compel to go / (archaic) to pull draw drag or hoist
incongruence - out of place/absurd
olfactory - part of sensory system used for smells
nebulous - misty/foggy/mysterious
umbra - shadowy part
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[[Work Energy and Power]]
# Summary
* Work transfers energy in or out of a system. It's a scalar.
* $W=fd\cos \theta$ for constant forces.
* Work equals $F_{||}$ versus displacement integral.
* Conservative forces do path independent work that is zero in a full loop and stays the same no matter what path is taken to the endpoint (e.g. gravity) while non-conservative forces care about the path taken (e.g. air resistance).
* Net work = $\Delta K = \Sigma W_i$
## Conservative vs Non Conservative
* Potential energy is conservative only
* examples of conservative are gravity and spring
* Conservative essentially means the work done only changes mechanical energy
* Non conservatives do work that convert mechanical energy into things like thermal energy (e.g. friction)
* Usually converted to sound or thermal energy
Work by a constant force formula: $$W=F_{||}d=Fd\cos \theta$$
$W$ is in joules
$F$ is force in newtons
$d$ is displacement
$\theta$ is the angle between the force and displacement vector
Net work is the sum of work done by each force: $W_{net}=\Sigma F_{||,i}d$
Parallel component: $F_{||}=F\cos \theta$
Parallel component: $F_{\perp}=F\sin \theta$
Work-Energy Theorem:
$$\Delta K=\Sigma_iW_i=\frac{1}{2}mv^2_f-\frac{1}{2}mv^2_i$$
Net work = change in kinetic energy
For friction the mechanical energy lost to friction is modelled as: $$\Delta E_{mech}=F_fd\cos\theta$$
When friction acts in the opposite direction to the motion (it usually is) the equation is modelled as: $$\Delta E_{mech}=-F_fd$$
Work equals integral of the parallel force component $F_{||}$ versus d
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[[kinesmatics]]
a vector quantity that describes a change in velocity, denoted as $a$ or $\vec a$
accel is to velocity as velocity is to position
second derivative of position
$\vec a_{avg}= \frac{\Delta v}{\Delta t}$
$\vec v_{avg}=\frac{\Delta d}{\Delta t}$
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[[kinesmatics]]
$v_{{avg}}=\Delta d / \Delta t$
$a_{{avg}}= \Delta v / \Delta t$
$d=d_2-d_1$
$d=v_1t+\frac{1}{2}at^2$
$d=v_2t-\frac{1}{2}at^2$
$d=\frac{1}{2}(v_1+v_2)*t$
$v_2=v_1+at$
$v_2^2=v_1^2+2ad$
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[[physics]]
stuff like velocity vectors yadiyadiyada
@@ -1 +0,0 @@
[[physics]]
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[[quantum mechanics]]
time independent equation:
$$\hat{H}\psi = E\psi$$