Formula Sheet for Physics 1111 Final Exam

Kinematics for motion in 1-D with a=const:

V=Vo+ at;X=Vot+(1/2)at2; V2=V02 + 2aX

Free falling motion:Vy=Voy - gt;Y=Vot - (1/2)gt2; Vy2=V0y2 – 2gY

Projectile motion: in the horizontal direction: Vx=Vo and X=Vox t

in the vertical direction:Vy=Voy - gt; Y=Vot - (1/2)gt2 and Vy2=V0y2 – 2gY

Vox=Vocos and Voy=Vo sin is the angle of the initial velocity)

Newton’s Law:F=ma;fk=kFN;

FN=mg coson an incline plane)

FN=mg +/- Fy=mg +/- Fsin(when the applied force F is not horizontally)

where is the angle of the surface with the horizontal

Uniform circular motion:

Fc=mV2/R; fsmax=sFN; fk=kFN;;FG=Gm1m2/R2

Energy and work:

KE=(1/2) mV2;PEG=mgH;PEel.=kx2/2;E=KE +PE

W=F d cos is the angle between F and d)

Wnet=KEf –KEi;

WC=Ef – EI; If WNC=0, Ei =Ef; WNC is the work done by non-conservative forces

Linear Momentum:

P=mV;Ptotal=m1v1 + m2v2 + …;Pi = Pf (in a collision)

V1 +V1’= V2+V2’ (for an elastic collision); V1’=V2’ (for a perfect inelastic collision)

Torque and Rotation:

=F R sinc.c.w.c.w.;wheremi ri2 or I=0.5MR2 for solid cylinder

Simple harmonic motion:

=(k/m)1/2; E=(1/2)mv2 + (1/2)kx2=(1/2)mvo2=(1/2)kA2

Wave Motion:Speed of wave: v=fnn

Speed of wave in a string: v=(FT/)1/2FT is the tension in the string and =m/L is the linear density of the string

Speed of sound waves in air: v=331 +0.6 T(oC); v=343 m/s at T=20oC

Frequency and standing waves of vibrating string and air-tube:

Wavelength of standing wave: n=2L/n (n=1, 2, 3, ...) (String fixed both ends or air-tube open both ends)

Wavelength of standing wave: n=4L/(2n-1) (n=1, 2, 3, ….) (Air-tube opens at one end)

The resonance frequency of a vibrating string or an air-tube: fn=v/n (n=1, 2, 3, …)

Sound:Intensity of sound: I=Power/Area=P/A (W/m2), for the isotropic sound wave, A=4R2.

Intensity level: =10log(I/Io), whereIo=1x10-12 w/m2 is the hearing threshold intensity

Doppler Effect:f’=fo(Vwave-/+Vobs)/(Vwave+/-Vsource)

where f’ is the Doppler=shifted frequency, fo is originally generated frequency

Vobs is the speed of the observer and Vsource is the speed of the source

Heat:Qlost=Qgained

For temperature change: Qi=mici Tici – specific heat for ith material

For phase change:Qi=miLL – latent heat

cice=2010 J/kg.K; cwater=3186 J/kg.K; for water: Lf=334x103 kJ/kg; Lv=2256x103 kJ/kg

Fluid:Pressure under fluid: P=Pa + gh where Pa =1.013x105 N/m2 is atmosphere pressure and h is the depth and  is the density of fluid.

Bouyangcy: Fbuoyancy=Vdisplacedfluidg

Ideal gas law:PV=nRTwhere R=8.31 J/mole.K=0.0821L.atm/mole.K

If the number of gas is constant, Pi Vi/Ti= PfVf/T