| Question | Answer |
| 1 eV | 1.60x10^-19J |
| h | 6.626 x 10^-34 J*s |
| Rh | 2.18x10^-18 J/e- |
| c | 3.0x10^8m/s |
| √2 | 1.4 |
| √3 | 1.7 |
| 1 mole; ideal gas; STP | 22.4L |
| 1 mole | 6.022 x 10^23 particles |
| SOH-CAH-TOA | 3-4-5
5-12-13
8-15-17 |
| log(AB) | log A +logB |
| log(A/B) | logA-logB |
| log(A^B) | B*logA |
| log(1/A) | -logA |
| logx | ln(x)/2.3 |
| log(n x 10^m) | m+0.n |
| x^0 | 1 |
| x^1 | x |
| (x^a)(x^b) | x^(a+b) |
| (x^a)/(x^b) | x^(a-b) |
| (x^a)^b | x^(ab) |
| (xy)^a | (x^a)(y^a) |
| (x/y)^a | (x^a)/(y^a) |
| x^(-1) | 1/x |
| x^(1/n) | n√x |
| x^(m/n) | n√(x^m)=(n√x)^m
ex: x^(9/2)=√x^9=(√x)^9 |
| Angle chart | Sin(0)=0
Sin(30=π/6)=1/2
Sin(45=π/4)=√2/2
sin(60=π/3)= √3/2
sin(90=π/2)=1
sin(180=π)=0
sin(270=3π/2)=-1
cos(0)=1
cos(30=π/6)=√3/2
cos(45=π/4)=√2/2
cos(60=π/3)= 1/2
cos(90=π/2)=0
cos(180=π)=-1
cos(270=3π/2)=0 |
| vector | physical quantity w/both magnitude & direction |
| scalar | physical quantity w/magnitude but no direction |
| Vector adding & subtracting
* when given angle use SOHCAHTOA to find vector X&Y components | Add: Head of 1st vector must meet tail of 2nd vector & draw arrow from tail of 1st to head of 2nd
Subtract: place head of two vectors together & draw arrow from tail to tail
For 3 or more: break into x&y components
Y& Xtot=R=√(x^2tot +y^2tot) |
| Linear Motion Eqns | (tax) ▲x=Vi*t + 1/2a*t^2
(vat) Vf=Vi + a*t
(vax) (Vf)^2=(Vi)^2+2a*▲x
Vavg=1/2(V+V1)
X=v*t=((V+Vi)/2)T
*Find max height Vel. vertical=o at highest point of path
v=√(2gh) |
| Center of mass | -point where single force can be applied in any direction & cause all points to accelerate equally
-if uniformly dense it will consider with geometric center but if not it will shift to heavier side
X=(m1x1+m2x2+..)/(m1+m2+..) |
| Hooke Law (spring) | F=-k▲x
yield point: deformed to point it can't gain it's original shape
fracture point: deformed to breaking point |
| Displacement vs time | slope=Vinstanteneous (v=▲d/t)
upward slop=+ vel
downward slope=- vel
straight line=constant vel
straight horizontal slope= m=0 v=0
curved line= m=changing v=changing |
| velocity vs time | slope=a instanteneous (a=▲v/t)
upward slop=+ a
downward slope=- a
straight line=constant a
straight horizontal slope= a=0
curved line=a=changing
(-) a could be slowing down or going in reverse direction |
| Total displacement | (area above x-axis & below curve)-(area below x-axis&above curve) |
| Total distance | sum of areas b/w curve & x-axis |
| Types of Forces | Fnet=sum of all forces Fnet=o when equal in magnitude & opposite in direction
Gravitational: mg
Electromagnetic: require magnet/charge object
Contact: Normal (Fn) & Friction (Fk or Fs)
Univ Gravitation: GM1M2/r^2 |
| Projectile Motion | Peak height found by v=√(2gh). to find max height of projectile launched from ground V=Visin(angle) due to vx=0 so final vel. can be found due projectile dropped from certain h |
| How to draw free body diagram | 1) Draw it in simple terms
2)Find center of mass
3) Define system & draw only forces acting on system
4)know if Fnet exist or net |
| First Law of Newton | (law of inertia)
any object in a state of rest or motion stays in that state unless a force is applied |
| Second Law of Newton | (F=ma)
m↑a↓if F is constant but F↑a↑ if m=constant |
| Third Law of Newton | (-Fa=Fb)
for every action there's an equa; & opposite rxn |
| Uniform circular motion | Fc=M(v^2)/r=ma
a=(v^2)/r |
| Universal Gravitation | F=GM1M2/r^2 (m*kg/s^2)
G=6067x10^-11(m^3/kg*s^2)
determines how quickly two objects w/slightly different masses accelerate toward each other |
| Inclined Planes | Fn=mgcos(angle)=Fy
Fx=mgsin(angle)
Look at diagram |
| Friction static | fs≤µkFn when surfaces don't slide |
| Friction kinetic | fk=µkFn when surfaces slide |
| Torque | =F*r*sinΘ
r=distance b/w point of rotation & F is applied
-could be CCW or CW
↑τ ↑rotation of accel ↑F ↑r
-Fg always middle of all forces(stick has mass)
-mboard found by picking midpoint as τboard & point of rotation no longer at end of board |
| Equilibrium | Fnet=o
τnet=0
so a=o v=constant
static equi: velocities=0
dynamic equi: velocities=nonzero but constant
Fup+Fnet=Fdown |
| system | area separated from universe(surroundings)
E leaving system=E entering surroundings
E total system= systems sum |
| open system | energy(work&heat) & mass exchanges w/surroundings |
| closed system | energy (work&heat) are exchanged but not mass |
| isolated system | energy (work &heat) & mass aren't exchanged |
| Energy unit | Joule (J)=1kg*(m^2)/s^2=1N*m |
| Mechanical energy | Etot=KE+U=1/2mv^2 + mgh or 1/2mv^2 -GM1M2/r |
| Gravitational potential energy | -GM1M2/r=mgh E↓r↓ |
| Elastic potential energy | 1/2k▲x^2 |
| 1st Law of Thermodynamics | ▲Etotal=W+q=KE+U+▲Einternal |
| Work | W=F*d*sin(Θ)=-PV |
| adiabatic | q=0
▲U=W |
| constant vol | W=0
▲U=q |
| Isothermal | ▲U=0
W=q |
| 2nd Law of Thermodynamics | process that moves from one state of equilibrium to another , entropy of system and environment together will increase or remain the same |
| Linear expansion | -increase in length by most solids when heated
▲L=α*L*▲T T↑L↑
mnemonic: (αl▲t) |
| volume expansion | increase in volume of fluid when heated
▲V=ß*V*▲T |
| conduction | direct transfer of energy via molecular collisions (direct contact) |
| convection | transfer of heat by the physical motion of fluid |
| radiation | transfer of energy by electromagnetic waves |
| specific heat (J,calories, Calories (kcal)) | q=mc▲T
-only used when object doesn't change phase
-NO TEMP change during phase change
Q>0 heat gained
Q<0 heat lost |
| heat of transformation | Q=m*L
-quantity of heat required to change the phase of 1g of a substance |
| Work Kinetic Theorem (J, N*m) | -absence of heat; adiabatic U=q so W=▲KE
W=F*d*cos(Θ)=-P▲V
F is (+) when same direction as displacement
F is (-) when in opposite direction
W DONE on system it's (+)
W DONE on surroundings (system doing work) it's (-)
W>0 compression
W<0 expansion |
| Conservation of Energy | K1+U1=K2+U2 so ▲E=0
There are no non-conservative forces (kinetic frictional forces, pushing & pulling forces) |
| Power (J/s) | P=W/▲t=▲E(tot)/t |
| Instantaneous power | Pinst=F*v*cos(Θ) |
| Fluid density (kg/m^3) | p=m/vol |
| density of water | 1000kg/m^3=1g/cm^3 |
| specific gravity | sg=p(substance)/p(water)
sg<1 lighter than water
sg=1 equilibrium as heavy as water
sg>1 heavier than water |
| Fluid pressure(N/m^2) | P=F/A
-pressure experienced by the object as a result of the impulse of collisions |
| Fluids at Rest | P=pgy
p=density g=gravitational constant y=depth of fluid from the top of object to the bottom of fluid
↓y ↓mass ↓pressure
P=F/A=m1g/A1=m2g/A2 |
| Gauge pressure | Pg=P-Patm
measure of the pressure (negative fluid/air sucked in) to atmosphere pressure |
| Absolute pressure | P=pgy+Patm |
| P total fluids | add each Pfluid when fluids are stacked one above the other |
| Pascal's Principle | pressure applied distributed undiminished throughout that fluid
Ex: air pressure on top of mountain is low due to atmosphere acting like sea of air where y↓ m↓ since closer to the top P=mgy↓ |
| Hydraulic lift | W1=W2 since F1d1=F2d2
A2>A1
F2>F1
d1>d2
-look at slide |
| Buoyancy Force | Fb= p(fluid)*V(fluid)*g=M(fluid)*g
Vfluid dissipated=A*y
-▲P,▲y,▲F reach MAXIMUM when object FULLY submerge and values DOESN"T change w/ depth once submerged |
| Archimede's Principle | -Fb exerted by standing fluid on object submerged or sunk
↑P ↑F ↑y since P=pgy=F/A |
| Floating object | (p(obj)/p(fluid))=(Vfluid/Vobj)≤1
Fb=Fg(object)
Mfluid*g=Mobj*g
M(fluid)=M(obj) |
| Submerged object | (p obj/p fluid)=(V fluid/ V obj)=1
Mfluid=Mobj
p fluid=p obj |
| Sunk object | p obj/p fluid≥ 1
Fb + Fn=Fg=M obj * g
Fb Fg
M obj M fluid
Vfluid=Vobj |
| Weight Loss Apparent
*sunk object | Fn< Fg
p fluid/p obj *100=apparent weight loss |
| Characteristics of Ideal Fluid | 1) No viscosity- tendency to resist flow
2) Incompressible- uniform density
3) Lack Turbulence- experience laminar (steady) flow so same velocity in same direction &magnitude
4) Experience irrotational flow- no rotation |
| Volume vs Mass Flow Rate | Vol. Flow rate= Q=A*v
↑A↓v
Mass Flow rate= I=p*Q=p*A*V |
| Characteristics of Non-ideal Fluid | drag, real viscosity, turbulence, compressible
↑velocity in center of pipe
↑resistance flow ↑fluid-obj interface ↓width of pipe ↑drag ↑Length of pipe
*Flow from high to low pressure
▲P=Q*R←resistance
Q=(▲P*π*r^4)/8*R*L
R→viscocity
L→pipelength |
| Bernoulli's Eqn | P1+ 1/2p*(V1)^2 + pgh1= P2+ 1/2p*(V2)^2 + pgh2
↓ ↓
KE U h: measure from bottom to top
*relationship b/w P&V: ↑stay put ↑stung ↑P but if not P↓(↓molecular collision) |
