13. Law of Gravitation: all particles attract other particles with a gravitational force whose magnitude is F= G(m1m2/r^2) (Newton’s law of Gravitation) *m1 and m2 = masses *r = separation *G = (6.67x10^-11 N*m^2/kg^2)

Superposition: if n particles interact, the net force >F1,net on particle 1 is the sum of the forces from other particles: F1,net = Σn,i=2 (>F1i) where sum is vector sum of forces >F1i on particle 1 from 2,3,…n >F1=∫d>F

Gravitational Acceleration: (Ag) F=mAg or Ag = (GM/r^2) Free-Fall Acceleration: >g (free fall acceleration) differs (smaller) near earth from >Ag (gravitational acceleration)

Gravitation Within Spherical Shell: shell exerts no force on particles inside it, if so, it is from mass inside: Mins =pVins=p(4pir^3)/3 *p=density

Gravitional Potential Energy: (U) is the negative work is done by the g force of a particle. U= -GMm/r Potential Energy of a System: If more than one particle U=-(Gm1m2/r12 + Gm1m3/r12 +Gm2m3/r23)

Escape Speed: object will escape g pull of astronomical body if the speed near the body is at least = escape speed (v) v=sqrt(2GM/R) (r=radius)

Kepler’s Laws: motion of satellites: 1. Law of orbits: all planets move in elliptical orbits with the sun at one focus. 2. Law of areas: a line joining any planet to the sun sweeps out equal areas in equal time intervals (cons. Of angular momentum). 3. Law of periods: the square of the period ‘T’ of any planet is

proportional to the cube of the semimajor axis ‘a’ of its orbit, for circular orbits with r: T^2=((4pir^2)/GM)r^3 (a substitutes r for elliptical planetary orbits) *M=mass of attracting body Energy in Planetary Motion: when a planet or sat. with mass ‘m’ moves in circular orbit with radius ‘r’, its pot. (U) and kin. (K)

energy are given by U= -GMm/r K=GMm/2r mech. Energy E=K+U

Emech=-GMm/2r (elliptical sub. ‘a’ with ‘r’)

14. Density: p = change in mass/change in volume or m/V Fluid Pressure: can’t stand shear stress so conforms, exerts perpendicular force to surface. P=change in F/change in A or F/A *F=force *A=area

Force resulting from fluid pressure at a particular pt. has the same magnitude in all directions. Gauge pressure =|abs. pressure – atm. Pressure|

Pressure Variation with Height and Depth: pressure in fluid at rest varies with vertical ‘y’ position. For ‘y’ measured positive upward, P2=P+pg(y1-y2) Pressure in fluid is the same for all points at the same level. If depth ‘h’ is below pressure P0, P=P0+pgh *P = pressure in sample Pascal’s Principle: change in

pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and the walls of the containing vessel.

Archimedes’ Principle: when object is partially or fully submerged in fluid, a buoyant force >Fb from surrounding fluid acts on object. Force is directed upward: Fb=mf(g) *mf=mass of fluid.

Apparent weight of an object on which a buoyant force acts is related to its actual weight by WEIGHTapp=WEIGHT-Fb

Flow of Ideal Fluids: (incompressible and lacks gooeyness) Flow in tube: Rv=A(v)=constant *Rv=volume flow rate *v=speed of fluid Mass Flow Rate: Rm=p(Rv)=p(A)(v)=constant

Bernoulli’s Equation: (cons. Of Emech) P+.5p(v^2)+pgy=constant

15. Frequency: (f, # of oscillations per sec) 1 hertz = 1 Hz = 1 oscil. Per sec = 1 s^-1 Period: (t, time required for one whole oscillation/cycle) T=1/f

Simple Harmonic Motion: displacement X(t) of a particle from its equilibrium pos. is described from: X(t)=Xmcos(Wt+theta) *Xm=amplitude of disp. *Wt+theta=phase of motion *theta=phase constant Angular freq: W=(2pi)T=2(pi)f

Velocity: v = -W(Xm)sin(Wt+theta) Acceleration: a=-(W^2)Xm(cos(Wt+theta)) *pos. quantity W(Xm)=velocity amp ‘Vm’ of motion *pos. quantity (W^2)Xm=acc. Amp ‘Am’ of motion

Linear Oscillator: particle with mass ‘m’ that moves under influence of Hooke’s Law restoring force given by F=-kx gives: W=sqrt(k/m) (angular freq.) and T=2(pi)sqrt(m/k) (period)

Energy: particle in SHM has K=.5m(v^2) and U=.5k(x^2). If no friction, Emech=K+U=constant Pendulums: torsion: T=2(pi)sqrt(I/k) simple: T=2(pi)sqrt(L/g) physical: T=2(pi)sqrt(I/mgh) SMP is projection of UCM onto the diameter of circle in which circular motion occurs. Damped Harmonic Motion: Emech in real

oscillating system decreases during oscillations because external forces inhibit oscillations and transfer Emech to Ethermal. If the damping force is given by >Fd=-b>v *>v=velocity *b=damping constant displacement of oscillator: X(t)=Xm(e^(-bt/2m)cos(W’t+theta) *W’=ang. Freq. of damped oscil. W’=sqrt[(k/m)-

(b^2/(4m^2))] If b<sqrt(km) then W’=W E(t)=.5k(Xm^2)e^(-bt/m)

Force Oscillations and Resonance: if external force with angular frequency ‘Wd’ acts on an oscillating system with natural angular frequency ‘W’, the system oscillates with ‘Wd’. Velocity amplitude Vm of system is greatest when Wd=W (resonance, amp. Xm of system is approx. greatest under same cond.)

18. Zeroth Law of Thermodynamics: if bodies A and B are each in thermal equilibrium with a third body ‘C’ (thermometer) , then A and B are in thermal equilibrium with each other.

Kelvin Temperature Scale: T=(273.16K)(lim gas->0 (P/P3)) *T=kelvins *P3 and P=pressure

Celsius and Fahrenheit Scales: Tc=T-273.15 *Tc=degrees C Tf=((9/5)Tc)+32 *Tf=degrees F

Thermal Expansion: all objects change in size in different tempertatures. Change in L=L(α)(change in T) *L=linear dimension *α=coefficient of linear expansion Change in V=Vβ(change in T) *V=volume *β=3α (coefficient of volume expansion) Heat: (Q) energy transferred because of temp. difference. Units: joules

(J), calories (cal), British thermal units (btu) 1 cal=3.968x(10^-3) Btu=4.1868 J

Heat Capacity and Specific Heat: Q=C(Tf-Ti) *C=heat capacity Q=cm(Tf-Ti) *m=mass if object has a mass *c=specific heat *molar specific heat=heat capacity per mole (6.02x(10^23))

Heat of Transformation: heat absorbed by a material may change the material’s physical state—solid to liquid—the amount of energy required per unit mass to change the state (not temp) of material is its heat of transformation ‘L’ Q=Lm heat of vaporization ‘Lv’ is the amount of energy per unit mass that must

be added to vaporize a liquid or that must be removed to condense a gas. Heat of fusion ‘Lf’ is the amount of energy per mass unit that must be added to melt a solid or must be removed to freeze a liquid.

Work Associated with Volume Change: amount of work ‘W’ done by a gas as it expands or contracts from an initial volume ‘Vi’ to a final ‘Vf’ is given by: W=∫dW=∫P(dV),Vi,Vf *P=pressure

First Law of Thermodynamics: (cons. of energy for thermodynamic process) Change in Eint=Eint,f-Eint,i=Q-W dEint=dQ-dW *Eint=internal energy *Q=energy exchanged as heat (pos. if absorbed, neg. if loses heat) *W=work done (pos. if expands against ext. force, neg. if contracts because of ext.

force)

Applications of the First Law: adiabatic: Q=0, Change in Eint=-W | constant-volume: W=0, Change in Eint=Q | cyclical: Change in Eint=0, Q=W | free expansions: Q=W=Change in Eint=0

Conduction, Convection, and Radiation: the rate ‘Pcond’ at which energy is conducted through a slab for which one face is maintained at the higher temp. Th and the other face is maintained at the lower temp Tc. Pcond=Q/t=kA((Th-Tc)/L) Each face of slab has area A, the length of the slab has area A, the length

of the slab (the distance between the faces) is L, and k is the thermal conductivity of the material.

Convection occurs when temp. differences cause an energy transfer by motion within a fluid.

Radiation is an energy transfer through the emission of electromagnetic energy. The rate ‘Prad’ at which an object emits energy through thermal radiation is: Prad=Ԑσ(A)(T^4) where σ=5.6704x(10^-8) W/m^2*K^4 <= Stefan-Boltzmann constant. Ԑ is the emissivity of the object’s surface. A=surface area and

T=surface temp in kelvins. The rate ‘Pabs’ at which an object absorbs energy through thermal radiation from its environment, which is the uniform temp. ‘Tenv’ (in kelvins), is: Pabs= Prad=Ԑσ(A)(Tenv^4)