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

physics/Work Energy and Power/Work.md

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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