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July 26, 2014

Posts by Elena


Total # Posts: 4,343

physics
0=N-m₁g => N = m₁g 0=T-F(fr) => T=F(fr)=μN= μ•m₁g 0=T-m₂g => T= m₂g -------- μ•m₁g = m₂g μ = m₂g/m₁g= 50/100 =0.5

physics
mv²/R =GmM/R² v² =GM/R M= v²R/G (the gravitational constant G =6.67•10⁻¹¹ N•m²/kg²)

physics
F=ma=mω²R ω↑=> F↑

physics
mv₀²/2= mgh h= v₀²/2g mg(H+h) = mv²/2 mgH +mv₀²/2 = mv²/2 v=sqrt{ v₀² +gH} = = sqrt{1.7²+9.8•3.2} = 5.85 m/s

physics
The 1st ball h=v₀t₁+gt₁²/2 The 2nd ball x=v₀t₂ h = gt₂²/2 t₁<t₂

physics
s=vt=90000•0.5/3600 = 12.5 m

Physics
ℰ = -N•dΦ/dt = -N•d(B₀Scosωt)/dt = = NB₀Sωsinωt, ℰ max= NB₀Sω, Without the figure, I believe that S=πR² => ℰ max= NB₀πR²ω = =100•10⁻⁶•3.14•0.1...

physics
ma=mω²R, ω=sqrt(a/R) = =sqrt(g/R) = =sqrt(9.8/100)=0.313 rad/s

physics
T=2πsqrt(L/g), T₁=2πsqrt(L/g₁), (T/T₁)²=g₁/g, g₁ = g(T/T₁)² =…

physics
f=1/T =1/2πsqrt(L/g)=...

physics
m₁=10 kg, m₂=m₁+62=72 kg, f₁= ω₁/2π = sqrt(k/m₁)/2 π , f₂=ω₂/2π = sqrt(m₂/k)/2 π, f₂ =f₁•sqrt(m₁/ m₂)=3sqrt(10/72)=1.12 Hz.

physics
R=0.04 m t= 0.012 m The solution is correct.May be there is mistake in calculations (or in your answer)...

physics
Newton’s 2nd law vector(ma) = vector(mg ) +vector( N) +vector(Ffr) Projections: ma=F(fr) 0=N-mg mv²/r =μN N=mg mv²/r = kN = μmg μ=v²/gr. tanα =F(fr)/N = μmg/mg = μ = v²/gr. v=sqrt{gr•tanα} T=2πR/v= 2πR/...

physics
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.html η=1-Tc/Th =1- 253.15/323.15 =0.2166, η = W/Qh => Qh= W/ η =3.6•10⁷/0.2166 = 1.66•10⁸ J= =39648.4 kCal 10 kW•h•10 ¢/kW•h= 100 ¢ (1.66...

physics
T=2π•sqrt(m/k) T₁²=4π²m₁/k T₂²=4π²m₂/k T₁²/T₂²=m₁/m₂ m₂=m₁T₂²/T₁² Δm= m₂-m₁ = =m₁(T₂²/T₁²-1)= =0.46[...

physics
T₀=2πsqrt(L/g) = =2πsqrt(0.81/9.8)= =1.8064 s. ΔL=α•L•ΔT=19•10⁻⁶•0.81•18 =2.77•10⁻⁴m L₁=L+ ΔL =0.81+2.77•10⁻⁴= =0.810277 T₁=2πsqrt(L₁/g)= =2πs...

physic
PE=KE=KE(transl) +KE (rot), mgh=mv²/2 + Iω²/2 = =mv²/2 + mR²v²/4R² =3mv²/4, mgh=3mv²/4, gLsinθ=3v²/4, v=sqrt(4gLsinθ/3).

physics
x is the length of unloaded spring F=k•Δx F=mg => m₁g=k(0.19-x) m₂g=k(0.75-x) m₁/m₂=(0.19-x)/(0.75-x) x=[0.19m₂ - 0.75m₁]/(m₂ -m₁) = =[0.19•2.8 – 0.75•0.3]/(2.8-0.3) = 0.1228 m k= m₁g/(0.19-x) = ...

physics
(a) F=k•Δx F=mg => mg=k•Δx k= mg/Δx =165/0.015 = 11000 N/m (b) m₁a=N-m₁g N=m₁(g+a) k•Δx₁= m₁(g+a) Δx₁=m₁(g+a)/k= =94(9.8+1.25)/11000=0.094 m

physics
PE=KE m₁gh =m₁v₁²/2 v₁ =sqrt(2gh) = sqrt(2•0.03•0.05) = =0.055 m/s. m₁v₁ = m₁u₁ + m₂u₂ u₂=2m₁v₁/(m₁+m₂)=2•0.03•0.055/(0.03+0.02) = 0.066 m/s. 0= u₂ -at a= u...

physics
Mg•L=2mg•x 70•0.65 = 2•30x x=70•0.65/60=0.75 m

physics
(a) mv₁²/2=0.22•N₁•Q N₁=mv₁²/2•0.22•Q = =2•10⁵•55²/2•0.22•1.3•10⁸ =10.6 gal (b) 0.22•N₂•Q= mv₂²/2 -mv₁²/2 +mgh, N₂ = m(v₂² -v&...

physics
average SPEED = distance/time taken =(32.5+78)/30•60=0.062 m/s displacement = sqrt(32.5²+78²)=84.5 average VELOCITY = displacement/time taken =84.5/30•60=0.047 m/s

physics
88 km/h =88000/3600= 24.44 m/s ------ average SPEED = distance/time taken =(32.5+78)/30•60=0.062 m/s displacement = sqrt(32.5²+78²)=84.5 average VELOCITY = displacement/time taken =84.5/30•60=0.047 m/s

Physics
You can find the solution in http://www.cabrillo.edu/~cfigueroa/11/11prob_sets/Solutions/11prob_sol_5%20.pdf

MITx: 2.01x
The above answers are correct because I got a green chek and not a red X.

MITx: 2.01x
Q2_1_1 TXC=-t_0*L Q2=1_2 a) 0<=x<L ===>> (2*t_0*L)/(pi*G_0*R4) b)L<=x<=3L =>>(2*t_0*(2*L-))/pi*G_0*R^4) c) x=2*L

Physics Help ASAP
I can’t understand the direction of Observer motion (towards or from the car?). If the car and observer move towards each other, their relative speed is 25-2 =23 m/s, then f=f₀/[1-v/c)] = =520/[1-23/334] = 558.5 Hz If they move in the same direction v =25+2 = 27 m/s...

Physics Help ASAP
http://en.wikipedia.org/wiki/Doppler_effect http://hyperphysics.phy-astr.gsu.edu/hbase/sound/dopp.html

physics
ΔL = αLΔT α =12 •10⁻⁶ °C⁻¹ ΔL = 12 •10⁻⁶•65•( -37-22) = - 0.046 m

physics
ΔL = αLΔT ΔL = 12•10⁻⁶•3•2.4•33 = 2.85•10⁻³ m ΔL/2 = 2.85•10⁻³ /2 = 1.425•10⁻³ m

physics
The volume of liquid that spills over the can is the difference between the increase in the volume of the liquid and that of the aluminum can ΔV=β₁VΔT - β ₂VΔT β₁=(ΔV/VΔT) + β ₂ = =(6.1•10⁻⁶/...

general physics
Q₁=m₁cΔT₁ Q₂=m₂cΔT₂ m₁cΔT₁=m₂cΔT₂ m₁ΔT₁=m₂ΔT₂ m₁ΔT₁=m₂ΔT₂ m (40.8 -30.9)=(190-m)(30.9-11.3) Solve for ‘m’

Physics
R=R1+R2+R3

physics
Q₁=mc₁ΔT₁ Q₂=mc₂ΔT₂ mc₁ΔT₁=mc₂ΔT₂ c₁ΔT₁=c₂ΔT₂ c₁(95-30)=c₂(292-30) c₂=c₁(95-30)/(292-30)= =840•65/262 = 208.4 J/kg•°C.

physics
mL= =m₁c ΔT m₁ = mL/c ΔT = =0.068•3.94•10⁵/4183•30.1= =0.213 kg

physics
mL= =m₁c ΔT m₁ = mL/c ΔT = =0.068•3.94•10⁵/4183•30.1= =0.213 kg

solid mechanics
E=205 kN/mm²= 205•10⁹ N/m². σ=E•ε(longitudinal) F/A = E•ε(longitudinal) ε=ε(longitudinal) = F/A•E= =40000/(20•10⁻³)²•205•10⁹=4.9•10⁻⁴. If a=0.2 m, b=c=0.002 m, &#...

solid mechanics
normal stress σ = F/A = 250000/0.1•0.1 = 2.5•10⁷ N/m² Tangential stress τ = F /(A/cosα) = Fcosα/A = =250000•0.5/0.1•0.1=1.25•10⁷ N/m²

Solid Mechanics
E=205 kN/mm²= 205•10⁹ N/m², μ = 0.3 σ=E•ε(longitudinal) F/A = E•ε(longitudinal) ε=ε(longitudinal) = F/A•E= =40000/(20•10⁻³)²•205•10⁹=4.9•10⁻⁴. If a=0.2 m, b=...

physics
η= 40% =>η =0.4 input heat Q₁=1.05•10¹⁴J waste heat Q₂=0.6 Q₁=6.3•10¹³ J Q₂/W=1.5 work W=0.4 Q₁=4.2•10¹³ J

physics
W=2.05•10⁸ J η= 4.00%=> η = 0,04 Q =W/0.04=5.125•10⁹ J Waste heat = Q - W = 5.125•10⁹-2.05•10⁸ = 4.92•10⁹ J N= 5.125•10⁹/6•10⁹ = 0.85

physics
Heat input Q=W+Q₁ = =8000+8000 = 16000 J η=W/Q =8000/16000=0.5 η =50%

physics
d=0.025 m Δx=0.31 m W=pΔV=p•πd²•Δx/4= =2.4•10⁵•3.14•0.025²•0.31/4 =36.5 J F=W/ Δx = 36.5/0.31 = 117.8 N

physics
0.2kcal/kg•℃=837.36 J/kg•℃ m = ρV=837.36• (a) Q=mcΔT=2.16•10⁴•837.36•10.5=1.9•10⁸ J (b) α = 2.5•10⁻⁶ /℃ ΔL = α•L•ΔT = 2.5•10⁻⁶•8.5...

Physics
mgH-mgh= mv²/2 v=sqrt{2g(H-h)} = …

Physics
s=(v²-v₀²)/2a

Dynamics
c.Velocity vectors before and after the collision.

Physics
λ=c/f => f=c/ λ = 3•10⁸/6•10⁻⁷=5•10¹⁴ Hz

Physics
ω=sqrt(k/m) = sqrt(20/2) = 3.16 rad/s x=Asinωt v=Aωcosωt t=0 => cosωt=1 A=v/ω =4/3.16=1.265 m x=Asinωt sinωt =x/A=1/1.265 =0.79 cos ωt =sqrt{1-sin²ωt} = 0.612 v₁=Aωcosωt =1.265•3.16•0.612 =2.44...

Dynamics
KE=PE+W(fr) m•v²/2 = m•g•h +F•s= =m•g•s•sinα +F•s. F=m(v²/2s - g•sinα)

BTech, Mechanical
For the 1st ball, the time of the upward motion v=v₀-gt v=0 0=v₀-gt t= v₀/g =18/9.8=1.83 s. The height of the 1st ball h= v₀t-gt²/2=18•1.83 - 9.8•(1.83)²/2= =16.53 m The time of the 1st ball downward motion before the 2nd ball begins...

Physics
Ice m₁=200 g = 0.2 kg c₁ = 2060 J/kg•K λ =335000 J/kg Water c₂=4183 J/kg•K m₂=? m₁c₁[0-(-5)] + m₁λ+ m₁c₂(21-0) = m₂c₂(65-21) m₂=m₁(5c₁+λ+21c₂)/44 c₂ = =0.2(...

dynamics
F=P/v=mgsinα v=P/mgsinα=200/80•9.8•0.06 = 4.25 m/s

dynamics
0,06P=Fv=mgv v=0.06P/mg

Physics
m=F/a Weight =mg

physics
Steel ρ₁ =7800 kg/m³ V₁=m₁/ρ₁=2.6/7800 = 3.3•10⁻⁴ m³ Gasoline ρ₂ = 750 kg/m³ m₂=ρ₂V₂=750•15•10⁻³ =11.25 kg ρ(ave) =( m₁+m₂)/(V₁+VS...

physics
V =m /ρ =41/750 = 0.055 m³ =14.53 gallons V=L•W•D= > D=V/L•W = 0.055/0.4•0.9 =0.15 m

physics
a=F/m F1=F/4.5 => a1=a/4.5=12.5/4.5=2.78 m/s^2

earth
Solar eClipse http://en.wikipedia.org/wiki/Solar_eclipse Lunar eClipse https://en.wikipedia.org/wiki/Lunar_eclipse

Physics
Q= mc Δt mc(50-20) = Mc(90-50) m=M•40/30 = 800•40/30 = 1067 kg

physics
cM[t(ini) –t(fin)] = mr cMΔt = mr Δt= mr/cM= 2.5•10⁻³•2260•10³/4183•0.28 = 4.8℃ T(fin) = 90-4.8 = 85.2℃

physics
(a) m=ρ•V= ρ•L•W•H=917•160000•45000•250=1.65•10¹⁵ kg (b) Q=mL=1.65•10¹⁵•334000=5.51•10²º J (c) Q/Q(US) =5.51•10²º/8•10¹⁹=6.89 (d) Q/q= 5.51•10&#...

physics
At 37.0ºC the heat of vaporization Lv for water is 2430 kJ/kg or 580 kcal/kg. Heat of Fusion and vaporization at 0℃ for water(ice) L(f)= 334 kJ/kg. m(cond) •L(v)=ML(f) M= m(cond) •L(v)/ L(f)= =7.4•10⁻³•2430000/334000 =5.38•10̿...

physics
For human body c=3470 J/kg. At 37.0ºC the heat of vaporization Lv for water is 2430 kJ/kg or 580 kcal/kg m•c•Δt= m(cond) •L(v) m(cond) = m•c•Δt/L(v) = =60•3470•0.75/2430000 =6.43•10⁻² kg=64.3 g

physics
(a) Stefan-Boltzmann Law R=σT⁴ R=P/A =P/4πR² σT⁴=P/4πR² T =forthroot{ P/4σπR²} = =forthroot{3.8•10²⁶/4•5.67•10⁻⁸•π•(7•10⁸)²} =5744 K (b) P₀= P/4&...

physics
F(x) = F•cosα

physics
(a) ω=sqrt(k/m) = sqrt(305/0.26) = 34.2 rad/s y=Asin ωt = > y=0.28sin34.2t (meters) (b) y=A (longest) A= Asin ωt sin ωt = 1 ωt= π t= π/ω=3.14/34.2= 0.092 s. T=2π/ ω = 2•3.14/34.2 = 0.183 s The shortest spring after T/2 ...

Physics
(a) Stefan-Boltzmann Law R=σT⁴ R=P/A =P/4πR² σT⁴=P/4πR² T =forthroot{ P/4σπR²} = =forthroot{3.8•10² /4•5.67•10⁻⁸•π•(7•10⁸)²} =5744 K (b) P₀= P/4πR...

general physics
ρ= m/V= 6.3•10²⁸/1.6•10³=3.93 •10²⁵ kg/m³ m= ρV₁=3.93 •10²⁵•2 •10⁻⁷=7.875•10¹⁸ kg=17.4•10¹⁸ lb

general physics
p = 2 atm = 202650 Pa p₀ = mg/a•b = 160/0.4•0.24 =1667 Pa N = p/p₀ =202650/1667=121.6 ≈122

general physics
http://www.phy.ilstu.edu/~holland/phy108/Homework%2015%20solution.pdf http://answers.yahoo.com/question/index?qid=20120322205457AAh2i77

general physics
http://answers.yahoo.com/question/index?qid=20090419164616AAiRaHT

physics
(a) m=ρ•V= ρ•L•W•H=917•160000•45000•250=1.65•10¹⁵ kg (b) Q=mL=1.65•10¹⁵•334000=5.51•10²º J (c) Q/Q(US) =5.51•10²º/8•10¹⁹=6.89 (d) Q/q= 5.51•10&#...

Physics
Q=Mc ΔT =mL(v) m/M = c ΔT/L9v) = =4183•1.6/2430000 = 0.00275 or 0.275%

physics
1.25 kcal = 5233.5 J c(merc) = 139 J/kg•K c(steel) = 470 J/kg•K c(concrete) = 880 J/kg•K c(water) = 4183 J/kg•K ΔT=Q/mc =5233.5/1.25• 139 =30.1º => 50,1º ΔT=Q/mc =5233.5/1.25•470 =8.91º => 28,91º ΔT=Q/mc =5...

Physics
PE₁=k•q₁•q₂/r₁ r₁=∞ =>PE₁ =0 PE₂=k•q₁•q₂/r₂ r₂= 7.07•10⁻¹² m ΔPE= PE₂ - PE₁=PE₂= = 9•10⁹•8e(-8e)/ 7.07•10⁻¹...

Physical Science
A. increasing its thickness R=ρL/A A↑=>R↓

physics
The image size of a distant object is simply its angular size multiplied by the lens focal length. 1/f = 1/f₁+ 1/f₂−d/f₁•f₂. f₁= 20 cm =0.2 m f₂= - 8 cm = - 0.08 m 1/f = 1/0.2 – 1/0.08 - 1/0.2•0.08= =5-12.5-62.5 = - 70 f...

physics
The image size of a distant object is simply its angular size multiplied by the lens focal length. 1/f = 1/f₁+ 1/f₂−d/f₁•f₂. f₁= 20 cm =0.2 m f₂= - 8 cm = - 0.08 m 1/f = 1/0.2 – 1/0.08 - 1/0.2•0.08= =5-12.5-62.5 = - 70 f...

Physics
v =v₀-at t=( v₀-v)/a = s= v₀t - at²/2 =…

Physics
Or it may be 60 s after the first 10 s v₃ = v₀+a(t₁+t₂) = 10+0.6•(10+60)=52 m/s

Physics
v₁=v₀+at₁ a= (v₁-v₀)/t₁ = (16-10)/10 = 0.6 m/s² v₂=v₀+at₂ = 10+0.6•60 = 46 m/s

velocity
http://hyperphysics.phy-astr.gsu.edu/hbase/vel2.html http://en.wikipedia.org/wiki/Velocity

physics
W=KE=mv²/2

Elementary mechanics
the gravitational constant G =6.67•10⁻¹¹ N•m²/kg², M=1.9•10²⁷ kg !!!!!!!!!!!! R=7.15•10⁷ m !!!!!!!! v=sqrt(2GM/R)= =59539 m/s ≈59.5 km/s

physics
No. The plane mirror will give an image of the object that is on the opposite side. It creates an erect, virtual image of the same size as the object where the distance from the object to the mirror equals the distance from the image to the mirror.

Physics
V=A•L A=V/L R=ρL/A = ρL²/V L=sqrt{RV/ρ} = =sqrt{ 0.15•2•10⁻⁶/1.72•10⁻⁸} = 4.17 m

Physics Help
Using Problem 5 page 234 from http://books.google.com.ua/books?id=PQRo3XuHHvYC&pg=PA262&lpg=PA262&dq#v=onepage&q&f=false From steam table at 22.5 bar Hw= 936.48 kJ/kg He = 1865.2 kJ/kg - enthalpy of evaporation (Latent heat) Enthalpy of 1 kg of wet steam is H=Hw+ζ •H...

Physics Help
Another table http://www.chem.mtu.edu/~tbco/cm3230/steamtables.pdf gives more precise values Hs =2801.7 kJ/kg Hw = 936.48 kJ/kg As a result ζ= (Ht-Hw)/ (Hs-Hw)= =(2279.434-936.48)/(2801.7-936.48) = =13.42.954/1865.22=0.7199 => ≈72%

Physics Help
(A)Ht=Hs•ζ+(1-ζ)Hw, where Ht = total (actual) enthalpy (kJ/kg), Hs = enthalpy of steam (kJ/kg), Hw = enthalpy of saturated water or condensate (kJ/kg) Using steam-pressure table http://enpub.fulton.asu.edu/ece340/pdf/steam_tables.PDF we can find the magnitudes f...

Physics
p=F/A= mg/πr²= =0.001/3.14•0.0002²=7958 Pa

Physics
ρ= m/V =0.240/89•10⁻⁶=2696 kg/m³

Physics
PE=KE=KE(transl) + KE(rot) I= mR² mgh = mv²/2 + I ω²/2= = mv²/2 + mR²v²/2R²= = mv²/2+ mv²/2 = mv² v=sqrt(gh)= …

Physics
(a) L=Iω= I•2πn=0.4•2π•6 = 15.08 J•s (b) L₁=L₂ I₁•2 πn₁ =I₂•2 πn₂ I₂=I₁•n₁/n₂= 0.4•6/1.25 = 1.92 kg•m² (c) 2 πn₂= 2 πn₁-...

Physics
PE=KE=KE(transl) + KE(rot). mgh = mv²/2 + I ω²/2= = mv²/2 + I v²/2R². I= (2R²/v²)(mgh- mv²/2)= =mR²(2gh/v² -1) = = mR²(2•9.8•2/36 -1)= =mR²(1.09-1)=0.09 mR²

Physics
τ=FR= 180•0.28 = 50.4 N•m I=mR²/2 = 75•0.28²/2=2.94 N•m² τ=Iε => ε= τ/I = 50.4/2.94 = 17.14 rad/s² τ₁=FR-F(fr)r =180•0.28 - 20•0.015 = 50.4 – 0.3 = 50.1 N•m ε₁= τ...

Physics
v=500000/3600 =138.9 m/s ω=v/R=138.9/30=4.63 rad/s n= ω/2π=4.63/2 π=0.74 rev/s

Physics
F₁+mg=F₂ ….(1) 2•F₁+1•mg=1.5•F₂…(2) From (1) F₁ =F₂ -mg ….(3) Substitute (3) in (2) 2(F₂ -mg) +mg = 1.5•F₂ F₂=2mg=.... F₁=mg= ....

physics
KE=mv²/2

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