vault backup: 2026-08-17 09:49:11
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[[Work Energy and Power]]
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megumi energy
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# SUMMARY
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# Summary
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* potential energy refers to multiple objects in a system affecting each other with conservative forces
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* In MY words, potential energy is j stored kinetic energy that something has due to its surroundings, and it cashes it out and converts the PE to KE.
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* Scalar
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* Gravitational potential energy between 2 spherical masses: $U_g=-G\frac{m_1m_2}{r}$. Near surface approximation: $\Delta U_g=mg\Delta y$
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* For a system with more than 2 objects, potential energy is sum of energy of every pair.
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## Zero Potential Energy Definition
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# Zero Potential Energy Definition
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* Can define zero PE as any convenient reference point
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* For gravitational PE, a common ref point is ground level.
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* Springs equilibrium is the natural zero PE point.
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[[Work Energy and Power]]
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Power is how fast energy moves or changes form.
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# Summary
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* SI Unit is Watts (W), where 1 W = 1J/s
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* Average power is energy change over time: $P_{avg}=\frac{\Delta E}{\Delta t}$. Work changes energy so $P_{avg}=\frac{W}{\Delta t}$
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* Instantaneous power for a constant force: $P_{inst}=F_{||}v=Fv\cos \theta$ using only force component parallel to velocity.
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* Sign of power tells direction, positive means energy added negative means energy removed.
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* When an object moves at a constant speed, energy is zero.
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# Average Power Calculation
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$$P_{avg}=\frac{\Delta E}{\Delta t}$$
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Examples:
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* 60 watt light bulb transfers 60 joules into light and heat.
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* 1500 watt hair drier running for 5 minutes transfers 1500 * 300 watts.
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* Solar panel generating 500 watts per second stores 500 joules to be used later.
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# Power as Work Rate
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$$P_{avg}=\frac{W}{\Delta t}$$
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Power can be calculated by dividing work by time taken.
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# Instantaneous Force from Power
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$$P_{inst}=F_{||}v=Fv\cos \theta$$
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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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# 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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