Physics 1010Comprehensive ReviewPart-1Extra Credit Grades Will be posted on website by Tuesday for thecurrent EC assignment EC credits for the surveys will be postedafter all surveys have been completed,probably next Thursday Last EC assignment will post tonight, duenext ThursdayGeneral Test Information Final is worth 80 points, as much as all yourmid-terms put together Equivalent to ~16% of your final grade;that’s more than a letter grade Will do comprehensive reviews from now on Most review questions will be graded forclicker credit, BUT last week of reviews willNOT be gradedGeneral Test Information All material is eligible for the final That includes Extra Credit Assignments (eg.aeropllanes, greenhouse effect, friction) Bring questions to classSkill and Concept Overview Concepts – velocity, acceleration, force, Newton’slaws, gravity, springs;work, momentum, energy, power, conservation laws;pressure;oscillators, waves (sound and EM);black bady radiation, temperature scales;electric charge, magnetic dipoles, Coulomb force;voltage, current, resitance, circuits Skills – read and interpret graphs, linear equations,quadratic equations (squares or square roots).Velocity Velocity is the changeof an object’s positionwith respect to time. x is position, v isvelocity.txv!!=Velocity is the slope!Acceleration Acceleration is the change of anobject’s velocity with respect totime. v is velocity, a is acceleration.tva!!=Acceleration is the slope!Kinematic Equations of Motion Rearranging equation from previous slide:Similarly for position:v = vi + atx = xi + vit + (1/2) at2Newton’s First Law An object that is not subject to any outsideforces moves at a constant velocity. When an object is not accelerating, it can stillbe subject to external forces, but the net forceis zero.Newton’s Second Law Fundamental equation of dynamics:F = m a Acceleration is in the same direction as netforce.Newton’s Third Law For every force that one objects exerts on asecond object, there is an equal and oppositeforce that the second object exerts on the first. This does not apply to two forces acting onthe same object.Gravity Objects of different masses fall at the samerate. The gravitational force on an object must beproportional to its mass.2/ 8.9 smgmgFgravity!=Friction Frictional forces oppose motion. Two types: static and sliding. Sliding friction force is generally smaller thannormal force. Friction force is related to the force that isnormal to the contact surface.Springs Hooke’s law:kxFspring!= The spring force is a restoring forceproportional to the displacement of theobject. Spring constant k depends on the type ofspring.Momentum & Impluse Momentum is a body-specific quantity that is conservedduring collisions. Its unit is kg m/s. Impulse is the change in an object’s momentum over sometime interval, and is equal to the force applied to the objecttimes the duration of that force. Its unit is kg m/s = N smvp !ptFI !=!"Work Work is defined as the displacement of an objectmultiplied by the force on that object in thedirection of the displacement. Its unit is N m = J. Net work is the net force on the object in thedirection of the displacement multiplied by thedisplacement.xFW !"Power Power is the work done per unit time. Itsunit is J/s = W.tW!"#Pressure and Density Pressure is defined as the force applied to a surfacedivided by the area of that surface. Its unit is N/m2= Pa. Mass density is defined as the mass of an objectdivided by the volume of the object. Its unit iskg/m3.AFP =Vm=!Energy Energy comes in a variety of forms: kinetic,thermal, spring potential, gravitational potential,etc. Energy always has the unit J. The forms we discussed in class:221mvEk=mghEg=221kxEsp=Conservation of Momentum As previously mentioned, momentum isconserved during collisions. This is not themomentum of the individual objects – onlythe total momentum of the system isconserved.ffiivmvmvmvm2121+=+Conservation of Energy The total mechanical energy of a system isconstant in time. This allows us to compare the energyquantities at different times.K++++=thspgkEEEEEffiimghmvmghmvE +=+=222121The Work-Energy Relation If net work is done on an object, energy istransferred to that object. That energy isequal to the work done (notice the same unitsfor each). The energy can be in any form whatsoever.EWnet!=The energy change can be kinetic,potential, spring, or thermal.Bouyancy ForcesArchimedes’ Principle:The buoyancy force on an object is equal to the weight of the fluid displaced by the object.Fb = Wf = ρ V gWhere ρ is the density of the displaced fluidOscillators A harmonic oscillator is something thatexhibits periodic motion where the period isindependent of the amplitude of the motion.kmTsp!2=glTpendulum!2= The frequency of an oscillator is the inverseof the period.Tf1=Sound waves Sound waves are compression (longitudinal) wavesthat travel through the air (or water, or other fluids orsolids). The pitch of a sound is directly related to itsfrequency. The speed, frequency, and wavelength of a soundwave exhibit a simple relationship:!fvs=Useful Formulae Kinematics: v=v0+at, x=x0+v0t+(1/2)at2 Newton’s II: F = ma Gravity: Fw= mg (g=9.8 m/s2) Friction: Ff = µFN (µ ~0.3 if not otherwisegiven) Hook’s Law: Fs= -kx Momentum: p = mvUseful Formulae Work: W=F L (L is length along which F isapplied) Torque: T=F d (d is perpendicular distanceto the line of force) Rotational Newton’s II: T=Iα (I=moment of inertia, α=angualacceleration)Useful Formulae Power: P=E/t Pressure: P=F/A (careful, confusing notation) Density: ρ=m/V Bernoulli: P+ρgh+(1/2)ρv2=const. Energy: Ek=(1/2)mv2, Eg=mgh, Es=(1/2)kx2 Buoyancy: Fb = Ffluid weight = ρfluidVfluidgUseful Formulae Spring oscillator: Pendulum: Period-Frequency: f=1/T Waves: v= λ /T=λfkmTsp!2=glTpendulum!2=Useful Formulae Black Body Radiation: P=σT4 Coulomb Force: F = k (q1 q2)/R2 Ohm’s Law: V=IR EPE = qV Circuits: P=IV; parallel: same voltage,currents add upseries: same current, voltages add upUseful Formulae Transformers: Right hand rule:currentNorth poleUnit Conversions k (kilo) = 1000 (1km=1000m) M (mega) = 1,000,000 (1MW=1,000,000W) c (centi) = 1/100 (1m=100cm) m (milli) = 1/1000 (1m=1000mm) µ (mirco)