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linear motion--free fall - when the ball is at the max height, the velocity v is 0. The max height the ball reaches above the ground is found by using: vf^2=vi^2+2ay projectile motion - obj has a velocity and position in both vertical and horizontal directions. no acceleration in the x direction, so particle moves with constant horizontal speed Force - Vector quantity. Units: N (kg*m/s^2) F=ma mass and weight - mass (m)-scalar weight (w)-force vector W=mg unit: N Newton's laws of motion - 1. A body in motion will stay in motion
- A net force applied to a body of mass m will result in that body undergoing acceleration. F=ma
- For every action there is an equal and opposite re-action
moment of force/torque τ - τ=rFsin(θ) minimum torque occurs when theta= centripetal acceleration--does not change the speed of obj - a=v^2/r centripetal force--magnitude of the centripetal force on a particle - F=ma=mv^2/r elevator probs - while elevator is accelerating upward, the tension in the cable must be greater than the maximum weight so that the difference produces a nonzero acceleration. while elevator is moving at a constant speed, its acceleration is zero, so net force on the elevator is also zero, so the tension and weight are equal. frictional force - Obj sliding down--the normal force decreases as the angle of the incline increases. frictional force decreases as the angle of the incline increases relationship of velocity and time of revolution - v=2πr/T Box up an incline: solving for perpendicular force - F=mg*cosθ
Total mechanical energy - E=K+U -mechanical energy is conserved when the sum of the potential and KE remains constant -mechanical energy is not always conserved though. when friction is present, ME is drained away in heat work-energy theorem - W=ΔK=Kf-Ki PULLEY efficiency: the measure of the amt of work a person puts into a machine that comes out - Efficiency=W out/W in W out=(loadxload distance) W in=(effortxeffort distance) load=mass of objgravity effort distance=the effort for the load to move through the distance by all pulleys (ex: if there are 6 pulleys and load must move a distance of 4 m...6 pulleys m=24 (load distance) momentum - p=mv
vector quantity--for two of more obj, the total momentum is the vector sum of the individual momentums impulse (J) - J=Ft=mv-mv0=delta P Internal forces - Forces that one part of a system exerts on another part external forces - forces that are exerted on any part of system from the outside of the system conservation of momentum - pinitial=pfinal collisions - total momentum before the collision equals the total momentum after the collision mavai+mbvbi=mavaf+mbvbf completely inelastic collision - colliding bodies stick together after the collision with a combined mass of ma+mb. ONLY ONE unknown final velocity mavai+mbvbi=(ma+mb)vf
Thermal expansion of liquids when heated - ΔV=βV0ΔT β=3α Heat - A bodys temp is related to the internal energy of that body. At constant volume, an increase in temp indicates an inc in internal energy and a decrease in temperature indicates a dec in internal energy Conversion factors among the heat units are - 1 Cal=10^3 cal=3.97 Btu=4,184 J convection - transfer of heat via physical motion of the heated material. it can only take place in FLUIDS (liquids and gases) during convection, heated portions of fluid rise from the source of heat, while colder portions sink radiation - Transfer of energy by EM waves and is the only method that allows transfer of heat thru a vacuum Specific heat (Q) - Q=mCΔT this applies to any formula that does not undergo a phase change Specific heat of water - c=1 cal/gK=1 cal/g of degrees C=4.184 J/gK
Heat of transformation (L) - during a phase change, the temp remains the same and the heat gained or lost is related to the amt of material that changes phase Q=mL First law of thermodynamics:pressure - Gas particles hitting a wall. As more particles hit the wall, the net force on the wall increases. Force per unit area is the pressure of the gas: P=F/A Unit: Pa (Newton/m^2) Work - -A gas contained in a cylinder with a piston that is able to move up and down -When piston moves up=work is done BY the system (POSITIVE WORK) -When piston is compressed=work is done ON the system (NEGATIVE WORK) work depends on pressure and volume -The process in which the pressure (isobaric) remains constant W=PΔV
-the state of motion for an obj at rest vs. one moving linerarly w/constant vel is the same -a net force is requires to change the present state of motion for an obj angular velocity (ω) - w=w0+at w0=initial angular vel a=angular acceleration (rad/s2) t=duration of angular acceleration max acceleration for SHM - amax=ω^2*A ω=angular freq ω=(k/m)^0. A=maximum stretch (amplitude) speed of waves - v=fλ λ=v/f =v/T where T=period of oscillation=1/f f=frequence of waves
thermal conduction (Q) - Q=kA(Thot-Tcold)t/d k=coefficient of thermal conductivity A=cross sectional area of material Thot-Tcold=temp difference d=thickness t=duration of heat transfer resistance of a wire in circuit - R=ρl/A ρ=resistivity of wire l=length of wire A= cross-sectional area of wire Electric force - qE=Bqv q=charge of particle E=electric intensity (units: V/m) B=magnetic induction (units: T) v=speed of particle
de broglie's wavelength - λ=h/p=h/mv wavelength in relation to momentum Speed of light in a solution - v=c/n c=3x10^8 m/s n=refractive index of medium frequency of light doesnt change from medium to medium Electromagnetic Spectrum in order of lowest to highest wavelength - Gamma rays X-rays UV VIS (VIBGYOR) IR Microwaves
Radio waves Electromagnetic Spectrum in order of lowest to highest frequency (and Energy) - Radio waves Microwaves IR VIS (ROYGBIV) UV X-rays Gamma rays "Roman men invented very unusual x-ray guns" wavelength of violet and red - violet 400nm red 700nm Law of reflection - angle of incidence = angle of reflection Snell's Law of Refraction -
m=mass of block x=stretch Wave on a string equation - y=Asin(kx-ωt) A=amplitude of wave k=wave number ω=angular freq t=time kx=2π when x=λ=wavelength of wave λ=2π/k Calculate work in a P vs V graph - If isobaric process: W=pΔV Electric field (E) - E=kq/r^ q=magnitude of charge r=distance from point charge k=910^9 Nm^2/C^
Emf force (Faraday's Law of Induction) - ε=vBL = ∆phi/∆T, where phi = BAcosθ = magnetic flux unit: volts v=speed of wire B=magnetic field l=length of wire *current generated will flow in direction that opposes the change that has induces emf Energy in relation to voltage, current, time - E=VIt bc P=E/T=IV Ohm's Law - I=V/R UNITS: Amps green light+red light= - yellow light
m=ρV W=ρVg Density of water - 10^3 kg/m^ Specific gravity - ratio of density of a substance to the density of water Pressure (P) - scalar quantity P=F/A SI Unit: 1 Pa (N/m^2) 1 atm - 1.013*10^5 Pa Absolute pressure in a fluid due to gravity on an obj somewhere below the surface
- P=P0+ρgh P0=pressure at the surface (usually 1.013*10^5 Pa) ρ=density of fluid
g=gravity h=depth below the surface Gauge Pressure (Pg) - Pg=P-Patm Pascals Princple - A change in the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. F1d1=F2d2=Work Archimedes Principle (Buoyant force) - Fb=ρfluidgVsubmerged Bernoulli Equation - Viscosity - Measure of internal friction of a fluid, because of viscosity, a force must be exerted to cause one layer of fluid to slide past another. Fluids and gases have viscosity, but viscosity of gases tends to be lower. SI Unit: (N*s/m^2)
