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# Physics MidTerm 2 Cheat Sheet by brandenz1229

Goes over... Chapter 6: Work and Kinetic Energy Chapter 7: Potential Energy, Energy Conservation Chapter 8: Momentum, Impulse, Collision

### Chapter 6: Work and Kinetic Energy

 m = mass g = 9.8 m/s F = Weight (N) F = m ⋅ g s = distance K``E`` = Kinetic Energy W = Workdone Power = P (Watts) x = cos y = sin 1 km = 1000m 1kg = 1000g ΔK = K``f`` - K``i`` Friction = always negative g = -9.8 (decre­asing) g = 9.8 (normal) a = g (gravi­tat­ional accele­ration) Θ = Angle between F and s || = Component of F parallel to dl v = velocity W = (∫P``2`` to P``1``) F⋅dl W = F``||`` dl W = (∫P``2`` to P``1``) F⋅cosΘ⋅dl W = F ⋅ s (Joules) P``av`` = ΔW / Δt P = lim Δt > 0 (ΔW / Δt) = dW / dt V``f`` = V``i``2 + 2 ⋅ a ⋅ s P = (W/t) Constant Speed : (a = 0) F = force P = F ⋅ v Friction (opposite) = cos(180o) W``x`` = F (cosΘ)⋅s || W``y`` = F (sinΘ)⋅s a = (V``f``2 - V``i``2) / (2⋅ s) F``s`` = (1/2)⋅m⋅V``f``2 - (1/2)⋅m⋅V``i``2 W``grav`` = m⋅g⋅h P = (W/t) K``E`` = (1/2)⋅m⋅V2 P``E`` = m⋅g⋅h

### Chapter 7: Potential Energy, Energy Conser­vation

 Potential Energy = U, P``E`` ΔK = -ΔU``grav`` K = Kinetic Energy R = Radius s = y``f`` - y``i`` U``grav`` = m ⋅ g ⋅ y Δs = Δxî + Δyĵ ``cm`` = circular motion k = constant of spring P``E`` = (1/2)⋅k⋅x2 W``grav`` = w-vector ⋅ Δs-vector Diameter = 2 ⋅ Radius W``f`` = Work Done by Friction if elastic... K``E`` = P``E`` W``grav`` = F × s W``grav`` = m ⋅ g ⋅ y``i`` - m ⋅ g ⋅ y``f`` K``i`` + U``i`` = K``f`` + U``f`` (1/2)⋅m⋅V``i``2 + m⋅g⋅y``i`` = (1/2)⋅m⋅V``f``2 + m⋅g⋅y``f`` if gravity does work.... E = K + U``grav`` W``total`` = K``f`` - K ``i`` W``total`` = W``grav`` + W``el`` + W``other`` W``other`` + U``i`` - U``f`` = K``f`` - K``i`` arrange to.... K``i`` + U``i`` + W``other`` = K``f`` + U``f`` Work done on a spring W = (1/2)K``E``⋅X``f``2 - (1/2)K``E``⋅X``i``2 Work done by a spring W = (1/2)K``E``⋅X``i``2 - (1/2)K``E``⋅X``f``2 U``cm`` = m ⋅ g ⋅ R Elastic Potential Energy U``el`` = (1/2)⋅K``E``⋅x2 Work Done by Elastic Force W``el`` = (1/2)⋅K``E``⋅x``i``2 - (1/2)⋅K``E``⋅x``f``2 if elastic force does work, and mechanical energy is conserved K``i`` + U``el``, ``i`` = K``f`` + U``el``, ``f`` Work Done by Friction: W``f`` = -W``fric`` W``f`` = -(-f``k``⋅ s) W``f`` = μ``k``⋅m⋅g⋅s Law of Conser­vation of Energy ΔK + ΔU + ΔU``int`` = 0 F = F``x`` + F``y`` + F``z`` F``x``(x) = -m⋅g F``y``(y) = -m⋅g F``z``(z) = -m⋅g F``x`` = (1/2)⋅K⋅x2

### Chapter 8: Momentum, Impulse, Collisions

 p = momentum J = Impulse m = mass v = velocity P = m ⋅ v (kg ⋅ m/s) F = d``p`` / d``t`` J``y`` = (∫t``f`` to t``i``) ΣFy dt J``y``= (F``av``)``y`` (t``f`` - t``i``) J``y`` = P``fy`` - P``iy`` J``y`` = (m⋅V``fy``) - (m⋅V``iy``) J = ΣF (t``f`` - t``i``) J = ΣF⋅Δt J = (∫t``f`` to t``i``) ΣF dt J``x`` = (∫t``f`` to t``i``) ΣFx dt J``x``= (F``av``)``x`` (t``f`` - t``i``) J``x`` = P``fx`` - P``ix`` J``x`` = (m⋅V``fx``) - (m⋅V``ix``) ΣF = (P``f`` - P``i``) / (t``f`` - t``i``) J = F``av``(t``f``- t``i``) J = (P``f`` - P``i``) = {F} : Change in Momentum P = P``A`` + P``B`` = |P``A`` + P``B``| Assuming m``1`` and m``2`` don't change m``1``⋅v``1``+m``2``⋅v``2`` = constant (P``1``+P``2``)``i`` = (P``1``+P``2``)``f`` P``1``+P``2`` = constant P``i`` = P``f`` V``f`` = (m``1``⋅v``1``+m``2``⋅v``2``) / (m``1``++m``2``)

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