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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 \thetafor 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
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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
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