37 lines
1.6 KiB
Markdown
37 lines
1.6 KiB
Markdown
[[Work Energy and Power]]
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# Summary
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* Work transfers energy in or out of a system. It's a scalar.
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* $W=fd\cos \theta$ for constant forces.
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* Work equals $F_{||}$ versus displacement integral.
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* 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).
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* Net work = $\Delta K = \Sigma W_i$
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# Conservative vs Non Conservative
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* Potential energy is conservative only
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* examples of conservative are gravity and spring
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* Conservative essentially means the work done only changes mechanical energy
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* Non conservatives do work that convert mechanical energy into things like thermal energy (e.g. friction)
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* Usually converted to sound or thermal energy
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Work by a constant force formula: $$W=F_{||}d=Fd\cos \theta$$
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$W$ is in joules
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$F$ is force in newtons
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$d$ is displacement
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$\theta$ is the angle between the force and displacement vector
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Net work is the sum of work done by each force: $W_{net}=\Sigma F_{||,i}d$
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Parallel component: $F_{||}=F\cos \theta$
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Parallel component: $F_{\perp}=F\sin \theta$
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Work-Energy Theorem:
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$$\Delta K=\Sigma_iW_i=\frac{1}{2}mv^2_f-\frac{1}{2}mv^2_i$$
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Net work = change in kinetic energy
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For friction the mechanical energy lost to friction is modelled as: $$\Delta E_{mech}=F_fd\cos\theta$$
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When friction acts in the opposite direction to the motion (it usually is) the equation is modelled as: $$\Delta E_{mech}=-F_fd$$
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Work equals integral of the parallel force component $F_{||}$ versus d
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