[[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