#20

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Components of a Vector if V = 34 m/sec ∠48°

then

Vi = 34 m/sec•(cos 48°); and VJ = 34 m/sec•(sin 48°) #4 Weight = m•g g = 9.81m/sec² near the surface of the Earth = 9.795 m/sec² in Fort Worth, TX Density = mass / volume

#21

Heating a Solid, Liquid or Gas Q = m•c•∆T (no phase changes!) Q = the heat added c = specific heat. ∆T = temperature change, K Linear Momentum momentum = p = m•v = mass • velocity momentum is conserved in collisions Center of Mass – point masses on a line xcm = Σ(mx) / Mtotal Angular Speed vs. Linear Speed Linear speed = v = r•ω = r • angular speed Pressure under Water P = ρ•g•h h = depth of water ρ = density of water

#23

ρ=

#7

m unit : kg / m 3 V

(

)

#25

Ave speed = distance / time = v = d/t Ave velocity = displacement / time = v = d/t Ave acceleration = change in velocity / time Friction Force FF = µ•FN If the object is not moving, you are dealing with static friction and it can have any value from zero up to µs FN If the object is sliding, then you are dealing with kinetic friction and it will be constant and equal to µK FN

#26

#8

#28

Universal Gravitation

F =G

m1 m2 r2

G = 6.67 E-11 N m² / kg²

#9

τ = F•L•sin θ Where θ is the angle between F and L; unit: Nm Newton's Second Law Fnet = ΣFExt = m•a Work = F•D•cos θ Where D is the distance moved and θ is the angle between F and the direction of motion, unit : J Power = rate of work done #30

Torque

#29

Mechanical Energy PEGrav = P = m•g•h KELinear = K = ½•m•v² Impulse = Change in Momentum F•∆t = ∆(m•v) Snell's Law n1•sin θ1 = n2•sin θ2 Index of Refraction n=c/v c = speed of light = 3 E+8 m/s Ideal Gas Law P•V = n•R•T n = # of moles of gas R = gas law constant = 8.31 J / K mole.

#11

#31

#12

#32

#16

Power =

Work time

unit : watt #34 Periodic Waves v = f •λ f=1/T

Efficiency = Workout / Energyin Mechanical Advantage = force out / force in M.A. = Fout / Fin #19 Constant-Acceleration Linear Motion v = vο + a•t x (x-xο) = vο•t + ½•a•t² v v ² = vο² + 2•a• (x - xο) t (x-xο) = ½•( vο + v) •t a (x-xο) = v•t - ½•a•t² vο

T = period of wave

#35

Constant-Acceleration Circular Motion ω = ωο + α•t θ θ−θο= ωο•t + ½•α•t² ω 2 2 ω = ωο + 2•α•(θ−θο) t θ−θο = ½•(ωο + ω)•t α θ−θο = ω•t - ½•α•t² ωο

Version 5/12/2005

#36

Reference Guide & Formula Sheet for Physics

#53 Resistor Combinations SERIES Req = R1 + R2+ R3+. . . PARALLEL 1 1 1 1 = + +K + = R eq R1 R 2 Rn

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Buoyant Force - Buoyancy FB = ρ•V•g = mDisplaced fluid•g = weightDisplaced fluid ρ = density of the fluid V = volume of fluid displaced Ohm's Law V = I•R V = voltage applied I = current R = resistance Resistance of a Wire R = ρ•L / Ax ρ = resistivity of wire material L = length of the wire Ax = cross-sectional area of the wire #54

∑R

i =1

n

1

i

#37

Newton's Second Law and Rotational Inertia τ = torque = I•α I = moment of inertia = m•r² (for a point mass) (See table in Lesson 58 for I of 3D shapes.) Circular Unbanked Tracks

#55

mv 2 = µmg r

#56 #58 Continuity of Fluid Flow Ain•vin = Aout•vout Moment of Inertia I cylindrical hoop m•r2 solid cylinder or disk ½ m•r2 2 solid sphere /5 m•r2 hollow sphere ⅔ m•r2 1 thin rod (center) /12 m•L2 thin rod (end) ⅓ m•L2 Capacitors Q = C•V Q = charge on the capacitor C = capacitance of the capacitor V = voltage applied to the capacitor RC Circuits (Discharging) Vc = Vo•e Vc − I•R = 0 #60 − t/RC

#39

Heat of a Phase Change Q = m•L L = Latent Heat of phase change Hooke's Law F = k•x Potential Energy of a spring W = ½•k•x² = Work done on spring

A= Area v = velocity

#41

#42 #44

Electric Power P = I²•R = V ² / R = I•V Speed of a Wave on a String

#59

T=

mv 2 L

T = tension in string m = mass of string L = length of string

#45

Projectile Motion Horizontal: x-xο= vο•t + 0 Vertical: y-yο = vο•t + ½•a•t² Centripetal Force

Thermal Expansion...