vault backup: 2026-08-17 09:49:11

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