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Physics Equations Terms : Speed Distance traveled Time Displacement Initial Velocity Acceleration Final Velocity Physics Equations Formulas : Average Speed (straight line motion) Displacement Average Velocity Average Acceleration All formulas deal with finding average values over a period of time. The motion over this period of time does not have to be constant to use these formulas. 1 Physics Equations for uniform acceleration When a body is undergoing uniform acceleration for a time interval, the average velocity will not change. Because of that, there are formulas that can be used to calculate the displacement, the initial velocity, the final velocity and the acceleration given the correct information. Formulas : For bodies in freefall, they are in uniform acceleration. The precise value for the acceleration due to gravity is g = 9.8 m/s2. Formulas : Formulas are similar to those for uniform acceleration but have g as the constant acceleration. Remember, Δy is the vertical displacement 2 Projectile motion : Projectile motion includes vertical motion and horizontal motion. The motion in the vertical or y direction must include acceleration. The motion in the horizontal direction has an acceleration of zero. Horizontal motion : Vertical Motion : Newton's Second Law The formula for the 2nd law is: Fnet = manet Fnet : is the net force for the system m : mass of the body or connected bodies anet : net acceleration for the body or system the net force is acting on The Net force is the sum of all the forces acting on a body. 3 Possible forces that act on a body that should be included in a Free Body Diagram if present. Applied Force Force of Gravity Weight Fgrav = mg Normal Force Frictional Force Tension Force Spring Force Air Resistance Force Uniform Circular Motion T : Period : Time to complete one revolution : Frequency : number of revolutions that occur per second. v : linear speed : how fast the body is moving along the circular path. ac : centripetal acceleration C : Circumference : distance around the edge of a circular path 4 Uniform Circular Motion Formulas : Period T = Frequency Circumference C = 2πr Linear Speed Centripetal Acceleration Centripetal Force Universal Law of Gravitation m1m2 Fg =G d2 Fg ≡ Force of Gravitational Attraction G = 6.67 x1011 N Universal Constant of Gravitation m1 ≡ mass of body 1 m2 ≡ mass of body 2 d ≡ distance between bodies as measured from center to center 5 Kepler's Third Law of Planetary Motion T2 3 =k R Where : T = period of orbit R = semimajor axis or orbital radius k = kepler's constant Momentum p = mv Where: p = momentum m = mass v = velocity 6 Change in momentum Δp = mΔv = m(vf vi) Where : Δp = change inmomentum m = mass vi = initial velocity vf = final velocity Impulse J = F*Δt Where : J = Impulse F = Force Δt = time interval 7 Impulse Momentum theorem Impulse experienced is equal to the change in momentum for a body. J = F*Δt mΔv = Δp J = F*Δt mΔv = Δp F*Δt mΔv Conservation of Momentum The sum of the momenta before a collision will be equal to the sum of the momenta after the collision as long as the net external force is zero. Σpi = Σpf p1i + p2i = p1f + p2f m1v1i + m2v2i = m1v1f + m2v2f 8 Work • Work is the measure of the change in energy for a body because of a force. W=F d W = Work done by the force F = Force d = displacement Power Power is the rate at which work is done. W P= t P = power produced by a force W = Work done by the force t = time work was done in. 9 Law of Work Win = Wout Expanding the equation ~ Fede = Frdr Fe = effort force – force you apply de = effort distance – distance applied force acts over Fr = resistance force – force machine gives dr = resistance distance – distance machines force acts over The reduction is determined by Mechanical Advantage – ratio of effort to resistance force MA = Fr Fe Fe = effort force - force you apply Fr = resistance force 10 Ideal Mechanical Advantage : ratio of effort distance to resistance distance. de IMA = dr dr = resistance distance de = effort distance Efficiency = (work out divided by work in) Wout Eff = Win Percent efficient is just efficiency as a percentage. % Eff = Eff * 100% 11 Potential NRG : PE Gravitational Potential NRG can be calculated. PE = mgh PE = Potential Energy m = mass in kilograms g = 10 m/s/s h = height of the object above the ground. Kinetic Energy Equation KE = ½ mv2 Where KE = kinetic energy in J m = mass of the object in kg v = speed of the object in m/s The units of Kinetic Energy are Joules 12 Work - NRG Theorem Work done equals the change in kinetic NRG for a body. Wnet = ∆KE Wnet = KEf - KEi Work done by gravity Wg = -∆PE = -(PEf - PEi) Wg = PEi - PEf Law of Conservation of NRG The total mechanical NRG of a closed system stays constant TME = KE + PE and PEi + KEi = PEf + KEf for a closed system When friction is involved : PEi + KEi = PEf + KEf + Wother 13 Coulomb's Law F=k F = electric force in Newtons k = constant (just a #) = 9.0x109 Nm2/C2 q1 = charge of object #1 in Coulombs (C) q2 = charge of object #2 in Coulombs (C) d = distance between two charges in meters Ohm's Law R= V Where: V : voltage : Volts : V I V = IR I : current : Ampere: A R : Resistance : Ohms: Ω P : Power : Watt : W P = VI 2 V P = I 2R = R 14 Equivalent resistance : Series Req = R1 + R2 + R3 +..... Parallel 1 1 + 1 + 1 = Req R1 R2 R 3 Wave Equation v = λf where : v ≡ Wave speed in m/s λ ≡ wavelength in meters f ≡ frequency in Hz 15