Formulas & Constants

Transcription

1 Formulas & Constants Net Force F = Fnet The sum of all forces acting on an object is called the net force on the object. The direction of each force must be taken into consideration when summing forces (e.g. forces acting in the same direction add, forces acting in opposite directions subtract). Units: The SI (metric) unit of force, the newton N, is named in honor of Issac Newton. Equilibrium Rule F = 0 When the sum of all forces acting on an object is zero (the net force on the object = 0), the object is in equilibrium. An object in equilibrium is stationary (not moving) or is moving at a constant speed in an unchanging direction. The Equilibrim Rule is basically a restatement of Newton s First Law of Motion. Speed and Velocity speed = distance covered time interval velocity is speed and direction. Units: The SI (metric) unit for speed (and velocity) is a combination of the standard units of distance and time, meters per second, m/s. 1

2 Acceleration acceleration = a = v t = v final v initial t change of velocity time interval Acceleration is a change in velocity during a time interval. Remember that velocity is speed and direction. This means that an object undergoes acceleration anytime its speed or direction changes. Units: The SI (metric) unit for acceleration is a combination of the units of velocity and time, meters per second squared, m/s 2 Newton s 2 nd Law N et F orce = (mass)(acceleration) F net = m a If the net force on an object is not zero, the object will accelerate. This means that the object s speed, direction, or both, will change. How much and object will accelerate depends on its mass - the greater the mass the smaller the acceleration. Units: the SI (metric) unit of mass is the kilogram, kg. Note that 1 kg = 1000 g. Weight and Force F weight = m g where g = 9.8 m s 2 Weight is the attractive force due to gravity on a mass. Your weight is a measure of the force between you and the Earth. The acceleration due to gravity near the Earth s surface is g. Units: Weight is a force and therefore weight is measured in newtons, N.

3 Momentum F t = P = P f P i = m v f m v i where F = force, t = contact time, P = change in momentum, P f = final momentum, P i = initial momentum, v f = final velocity, and v i = initial velocity. This formula is often called the impluse formula. Note that this relationship is useful if you know any three of the following four: force, time, initial momentum, or final momentum. Note that it is important to use the correct SI (metric) units for force, mass, velocity, and time. P f = P i Conservation of Momentum where P f = final momentum of the system, and P i = initial momentum of the system. This relationship is useful when you can determine either the initial or final momentum of a system of objects. Note that it is important to use the correct SI (metric) units for mass and velocity. Energy KE = 1 2 m v2 Kinetic Energy where KE = kinetic energy, m = mass, and v = velocity. Kinetic energy is the energy of motiom. Anything moving has kinetic energy. Units: The SI (metric) unit for energy is the joule, J. Note that it is important to use the correct SI (metric) units for mass and velocity. P E = m g h Potential Energy where P E = potential energy due to Earth s gravity, m = mass, g = acceleration due to gravity, and h = height above the ground. Potential energy is the energy an object has due to its position. Gravitational potential energy is the energy a massive object has due to its position relative to a location on Earth. Units: The SI (metric) unit for energy is the joule, J. Note that it is important to use the correct SI (metric) units for mass, acceleration, and distance.

4 Energy continued... E = KE + P E Total Energy where E = total energy, KE = kinetic energy, and P E = potential energy. E f = E i Conservation of Energy where E f = final energy of the system, and E i = initial energy of the system. This relationship is useful when you can determine either the initial or final energy of a object (or a system of objects). Note that it is important to use the correct SI (metric) units for mass, velocity, acceleration, distance, and energy. Work W = F d where W = work, F = force, and d = distance. Units: The unit of work is the same as the unit of energy, the joule, J. This formula is useful if you know two of the following three quanitities: force, distance, and work. Note that it is important to use the correct SI (metric) units for work, force, and distance. W = KE = (KE f KE i ) where W = work, KE = change in kinetic energy, KE f = final kinetic energy, and KE i = initial kinetic energy. This formula is useful if you know two of the following: work, inital, or final, kinetic energy. Note that it is important to use the correct SI (metric) units for energy, mass, and velocity. Power P = W t Power is work per unit time. Units: Typically, power is measured in watt. One watt is one joule of work performed in one second.

5 Heat Q T = c m T = c m (T f T i ) where Q T = heat transfer needed to change temperature, c = specific heat capacity, m = mass, T = change in temperature, T f = final temperature, and T i = initial temperature. Units: Heat is energy. This fact was not known when heat was first studied, and so now we are stuck with two units in common usage: joules and calories. One calorie is equilivant to Joules. Note that there is another bit of confusing notation: 1 Calorie = 1000 calories = 1 kilocalorie = 1 kcal. Additionally, the unit for specific heat may be specified in joules or calories, and mass is typically specified in grams (or kg). Q v = m L v where Q v = heat transfer needed to change phase between a liquid and a gas, m = mass, and L v = heat of vaporization. To convert a liquid into a gas an amount of heat Q v must be added to the liquid. To convert a gas into a liquid an amount of heat Q v must be removed from the gas. Note: the unit for heat of vaporization may be specified in joules or calories. Q f = m L f where Q f = heat transfer needed to change phase between a liquid and a solid, m = mass, and L f = heat of fusion. To convert a solid into a liquid an amount of heat Q f must be added to the solid. To convert a liquid into a solid an amount of heat Q f must be removed from the liquid. Note: the unit for heat of fusion may be specified in joules or calories. Heat Properties of Water specific heat c = cal/ o C/g = J/ o C/g heat of fusion L f = 334 J/g heat of vaporization L v = 2256 J/g

6 Electric Force F = k Q 1 Q 2 d 2 where k = 9 x 10 9 N m 2 /C 2. Units: Force is in newtons, N, charge is in coulombs, C, and distance in meters, m. This formula allows you to calculate the force between two electric charges. Note that opposite sign charges attract, and same-sign charges repel. Electric Work and Energy voltage = Ohm s Law V = I R electric energy or work amount of charge where V = voltage, I = electric current, and R = resistance. Units: voltage is in volt, V, electric current in ampere, A, and resistance in ohm, Ω Electric Power P = I V where P = power, V = voltage, and I = electric current. Units: Power is in watt. Transformers V 1 = V 2 N 1 N 2 V 1 I 1 = V 2 I 2 V 1 = voltage in primary V 2 = voltage in secondary N 1 = turns in primary N 2 = turns in secondary

7 I 1 = current in primary I 2 = current in secondary Note: be careful to use the correct units for voltage and current. Waves f = 1 T where f = frequency, and T = period. v = λ f where v = wave speed, λ = wavelength, and f = frequency. distance = (speed)(time) speed of sound = 343 m/s speed of light = 300,000 km/s speed of light = 300,000,000 m/s Atomic Mass atomic mass = M isotope ( percent of isotope 100 Percentage of total amount ) % of total amount = 100 (partial amount) total amount Half Life Half life is the amount of time for 1 2 of a substance to undergo nuclear decay. Balancing Chemical Equations The number of atoms of each type must be the same on both sides of a chemical equation.

8 Acids and Bases [H 3 O + ][OH ] = 1.0 x ph = log[h 3 O + ] where [H 3 O + ] = hydronium ion concentration and [OH ] = hydroxide ion concentration. Moles 1 mole of substance = Atomic Mass in grams of substance Examples: 1 mole of C = grams of C 1 mole of H 2 O = grams of H 2 O convert grams to moles: #ofmoles = # of grams # of grams in 1 mole convert moles to grams: # of grams = (# of moles) (# of grams in 1 mole) Mixtures & Solutions concentration in grams/liter concentration in g/l = grams of substance Liters of solution

9 concentration in moles/liter concentration in moles/l = moles of substance Liters of solution