Download Kinematics Vf = vi + at D = vit + ½ a t = vi + 2ad V = d/t Speed versus

Kinematics Vf = vi + at D = vit + ½ a t 2 Vf 2 = vi 2 + 2ad V = d/t Speed versus velocity???? ∆H = Hf ­ Hi Vectors ­ has magnitude and direction Velocity displacement Acceleration Force Momentum Electric field Magnetic field Scalars ­ has magnitude only Speed Distance Time Inertia Area Volume Temperature Mass Resultant = sum of component vectors Interia – resistance to change Newton’s 1 st Law a) A body at rest tends to stay at rest tends to stay at rest, unless acted upon by an outside force b) a body in motion tends to stay in motion, in a straight line at constant speed, unless acted upon by an outside force Newton’s 2 nd Law F=ma Newton’s 3 rd Law For every action there is an equal and opposite reaction Projectile: an object which is thrown or launched and continues its motion under the influence of its own inertia and gravity 1 N of Force Accelarates a single kilogram of mass at 1 m/sec 2 1N = 1 kgm/sec 2 μ= friction force / Normal force f= μN
μ=coefficient of friction (constant for each material/surface) Work, Power, Energy, etc. Work = (Force) (Distance) Joules = (Newtons) (meters) Power = W’ = rate at which work is done Power = work / time = (Fd)/t = Fv Watt = joules/sec = (newtons ∙ meters)/sec = newtons ∙ (meters/sec) 1 horsepower = 746 watts Potential energy: stored energy PE = U = mgh PE = U = (kilograms) (m/sec) (meters) = (Newtons) (meters) = joules Kinetic Energy KE = ½ ∙ m ∙ v 2 KE = (.5)(kg)(m/sec) 2 = joules (kg)(m/sec) 2 (meters) (Newtons)(meters) (joules) KE + U = KE + U ß always ????????? or only always for momentum SPRINGS Hookes Law = springs or other stretchy bendy things F=­kx K = Elastic constant X= change in distance F=­kx K=F/x K = (newtons)/(meters) Us = ½ kx 2 f = 1/(2π)•√(k/m) T = 2π•√(m/k) Do we need to know springs in vertical oscillation???? Pendulums f = 1/(2π)• √(g/L) T=2π•√(L/g)
Momentum P=mv P = kg (m/sec) Impulse = F∆T Joules = (newtons) (sec) ∆mv = F∆T m∆v = F∆t m (∆v/∆t) = F ma=F Elastic collision: no permanent change of shape – NO ENERGY LOSS Inelastic Collision – permanent change of shape, loss of energy MV + MV = MV + MV ß Always (inelastic or elastic doesn’t matter) Elastic (See pic below); V1= [(m1­m2)/(m1+m2)] (v1i) V2 = [(2m1)/(m1+m2)] (v1i) Centrifugal Force – not a real force Centripetal Force – a force that maintains an object goin in a circular path at constant speed (real) Centripetal Acceleration Ac = v 2 /r Fc = mv 2 /r
Universal Gravitation: F=G (m1 ∙ m2)/r 2 G=6.67 ∙ 10 ­11 Nm 2 /kg 2 mg = G (m1 ∙ m2)/r 2 g=GM/r 2 Torque – twisting effect of a force acting of a perpendicular distance Torque = Fd τ = FdsinΘ PE = U = Fr = ­(GmM)/r Fluid Continuity FB = pVg p = density V = volume displace F/A = p L/T = V V = Area • Length Flow Rate = (density) Area (L/t) = (density) Area (volume) (density1)A1V1 = (density2)A2V2 AV = AV Pressure = Force/Area PAir = 1.01 • 10 5 Pa = 14.7 psi = 1 atm 1 N/m 2 = 1 Pa Volume Flow = Volume/t Hydrostatic Pressure Pressure = F/A = (density)gh N/m 2 = Pascal Densitywater = 1000 kg/m 3 FBouyancy = FB = (density)(volume)(g)
Bournoulli’s: V=√(2g•∆y) Volume/Time = A(length)/time = A(l/t) = AV E = 1 – Qc/QH E = 1 – Tc/TH E = Wnet/QH = (QH­QC)/QH = 1 – Qc/QH QH = Heat in • ­1 Qc = Heat Out Wn = QH­QC Isobaric = Same Pressure Isometric – same volume Isothermal – Same Temperature Adiabatic – Same Q (heat) W= ­p ∆V ∆U = 3/2 nRT R = 8.31 T = Temperature in Kelvin N = # of molecules (in moles) ∆U = W + Q W = Fd = F/A (d) (A) (P) (volume) = Joules if Temp doesn’t change then ∆U = 0 work done on gas = compression: W = (­) work done by gas = expansion: W = (+) Q = heat energy (joules) U = Internal energy of system (joules) Adiabatic: Q = 0 Heat into: +q Heat exit: ­q
Thermal Expanision ∆l = l α ∆T l is original length α is linear thermal expansion coefficient ∆T is temp. change in o C or Kelvin Energy = Woutput/Winput Electric Field 1 electron = ­ 1.6 • 10 ­19 colombs 1 proton = + 1.6 • 10 ­19 colombs Induction = rearrangement of charge without contact Conduction – by physical contact Discharge – excess charge drains off Colombs Law F = K (q1q2)/r 2 K = 9 • 10 9 Nm 2 /C 2 1 nanometer = 1 • 10 ­9 m E=Force/charge = F/q = Newtons/coloumbs = kq/r 2 E= potential (voltage)/distance = V/d = volts/meters Work = (Force) (Distance) = V•q Fluid Viscosity – the resistance to flow or resistance to shear forces Voltage – “pressure” which “pushes” electrical charge through a conductor Current – the rate at which fluid flows (gal/min) Resistance – works against/inhibits flow, viscosity Ohm’s Law Voltage = Current • Resistance V=IR Volts = Amperes • Ohms I= Q/T Current = Amps = Colombs/sec Electrical Power Power = work/time = energy/time P = IV = I (IR) = I 2 R = V 2 /R
Energy = Power • Time R= p (L/A) Series Voltage Add up to Total Current All Same Resistance RE = R + R Capacitors 1 /CE = 1 /C1 + 1 /C2 Parallel All Same Add up to Total 1/RE = 1/R + 1/R CE = C1 + C2 Capacitor – a device that stores charge Capacitance = charge/voltage = q/V = coloumb/volts 1 Coloumb/ 1 volt = 1 Faraday ½ VQ = ½ V(CV) = ½ C V 2 Q = CV V= Q/C ½ (a/c)(Q) = ½ Q 2 /C C = εo • (A/d) εo = Epilsoon “naught” εo is permittivity of free space εo = 8.85 • 10 ­12 C 2 /(Nm 2 ) 1 μF = 1 • 10 ­6 F Capacitors in Series 1 /CE = 1 /C1 + 1 /C2 Capacitors in Parallel CE = C1 + C2 Dielectric Constant K = C/Co = with dielectric /without dielectric K > 1.00 ß no units Magnetic Fields 1. Magnet has polarity 2. Unlikes attract, likes repel 3. Materials that are easily magnetic , like iron, are called ferromagnetic a. Domain Theory – magnetic domains – regions that have the same M.F. direction. Magnetic domains are randomly arranged.
4. A comparison is a small magnet that is free to rotate – imaginary lines of force around a magnet are called Magnetic Flux (φ) measured in Webers Magnetic flux density is the number of Flux lines per unit area: B= φ/A = webers/m 2 = newtons/Amperes = Teslas Stronger magnets = more flux lines B = F /IL Magnetic flux lines come out of North pole and go into south pole F=BIL Newtons = Teslas • Amps • Length (meters) F=qVB Newtons = coloumbs • velocity in m/sec • Teslas F=qVB = BIL Electromagnetic Induction Current goes positive to Negative Right hand Rule for proton Left hand rule for e­ Other right hand rule for wire?? Solenoid B = (μo • I • N) / L = μo•n•I μo = 4π • 10 ­7 T/(mA) = magnetic Permiability ß Solenoid?? n = loops / meter N = loops in solenoid L = length (meters) B Field near a Wire B = (μo • I) / (2 π d) Electronvolt (eV) Unit of Energy 1 e ­ accelerated through a potential diff of 1 Volt U = qV = (1.6 • 10 ­19 C) (1 Volt) = 1.6 • 10 ­19 = 1 eV Θ = Normal (Perpendicular or 90 o ) – Flux Lines
Induced EMF – electromotive force ε = ­[N (∆φ)] / ∆T ε = B • l • V φ = BA cosΘ Lenz’s Law – an induced current will flow in such a direction that the magnetic field it produces will oppose the magnetic field whose motion produced it. φ = B(∆A)cosΘ ∆A = L(velocity) (∆t) ∆φ =Bl (velocity) (∆t) cosΘ ε = N(∆φ) / (∆t) = N•B•l•v•cosΘ Electron: Mass = 9.11 • 10 ­31 kg q = ­1.6 • 10 ­19 C Snell’s Law n1sinΘ1 = n2sinΘ2 n = index of refraction = c/v = 3 • 10 8 / velocity n > 1 Θ is angle from the normal Less Dense to more Dense – Towards Normal More Dense to less dense = Away from normal Reflection ΘI = ΘR As velocity decreases, frequency is constant and λ decreases V= f λ T = 1/f f = 1/T T = period (sec) f = frequency = sec ­1 = Hz Transverse vs. Longitudal Mechanical waves – vibration Electromagnetic waves – do not require a vibrating mass, moves more efficiently through vaccuum C = 3.0 • 10 8 m/sec Resonance for closed pipe is at ¼ λ
Resonance: when frequency of vibration matches the natural frequency of the object and dramatic increase in amplitude results V = √(t/μ) nλ = dsinΘ Not as good: x/L = nλ/d tmin = λ/4n1 m= ­di/do = hi/ho 1/f = 1/do + 1/di If do > f Then real If do < f then virtual Mirror Outside focal length – real If inside one focal length then virtual and inverted Parallel goes through 1 F Through radius reflects parallel Draw line top of object through 2F (normal reflection) Lens Parallel then through 1F Through center is straight line Through 1F then parallel E=hf
h = planck’s constant = 6.63 • 10 ­34 Joules/sec = 4.14 • 10 ­15 eV/sec Takes more energy to remove e­ from inner shell 1 eV = 1.6 • 10 ­19 VC hf = KE + φ hf is incident of photon energy KE is kinetic energy of freed electron φ is work function = minimum energy needed to free an e­ from a surface p=mv =mc p=h/λ λ = h/p = h/mv U = atomic mass of units (AMU) Proton 1.007276 u Neutron 1.008665 u H atom 1.007825 u Electron 5.4857 • 10 ­4 u 1 amu = 1.66054 • 10 ­27 kg E=mc 2 931.5 MeV = 1 amu We have to know that the area under which curves means wut??? Electric Potential: ∆UE = ­WE capacitance = B/V = Flux / voltage = Q/V = Charge/Voltage Faraday = Coulombs / Volt