Friday
April 18, 2014

Posts by Elena


Total # Posts: 4,303

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

PHYSIC
KE=PE+W(fr) KE=mv²/2 PE= mgh W(fr) =F(fr) •s=µmgcosα•h/sinα mv²/2 =mgh+µmgcosα•h/sinα Solve for ‘v’

physics
s=s₀+vt= =0.2-0.5•20 = - 9.8 m

Physics
F=Δp/Δt=mΔv/Δt= =m[v₂-(-v₁)]/Δt= =m(v₂+v₁)/Δt= =1.2•(6+2)/ Δt=… Check the given data (time of contact!!!!)and substitute it

physic
W = F • d = Fx•rx + Fy•ry = (12 N) (13 m) + (−1 0 N)(+11 m) = 156 -110=46 J

physic
mv²/R=GmM/R ² v= sqrt (GM/R) =… T=2πR/v= …

College Physics
ω₁= √(g/L₁) ω₂=√(g/L₂) 1.8 ω₁=ω₂ 1.8√(g/L₁)=√(g/L₂) 1.8²g/L₁=g/L₂ L₂=L₁/3.24=10/3.24 = =3.086 ≈3.19 m = 309 cm

College Physics
v= 7 moles, T₁=300 K V₁=1000cm³= 10⁻³ m³ V₂=0.316•10⁻³ m³ W= {(vRT₁)/(γ-1)} •[1-(V₁/V₂)^(γ-1)]= γ=(i+2)/I =(3+2)/3 = 5/3 γ-1=5/3 -1 =2/3= 0.667 W=- {(vRT₁)/(γ-1)} ...

Physics
15 V

phy
F₁=G•m•M/R₁² F₂ =G•m•M/R₂² F₁/F₂=R₂²/R₁² F₂=F₁•R₁²/R₂²= …

physic
F₁=G•m•M/R₁² F₂ =G•m•M/R₂² F₁/F₂=R₂²/R₁² F₂=F₁•R₁²/R₂²= …

Physics Please Answer
The charge of He ion = e The aceleration of ion in the electric field ma=eE a=eE/m KE=mv²/2= m(at)²/2= = (eEt)²/2m ℇ=KE ℇ = hc/λ hc/λ=(eEt)²/2m t={sqrt(2mhc/λ)}/eE= ={sqrt(2•6.65•10⁻²⁷•6.63•10&...

physic
mv²/R=GmM/R ² v= sqrt (GM/R) v₁/v₂= sqrt(R₂/R₁) =sqrt(1/4.5)=0.47

physic
See answer to a similar question below under related questions

Physics
0 = m₁v-m₂u u= m₁v/m₂=175•2.75/2400= ...

Physics
F=Δp/Δt=mΔv/Δt= =0.063•45/0.03=94.5 N

physics
KE=PE=mgh

Physics
PE=KE mgh=mv²/2 v=sqrt(2gh)

Physics
PE=KE mgh=mv²/2 v=sqrt(2gh)

physics
m₁v-m₂u=0 u= m₁v/m₂= =1150•26.7/2030=15.13 m/s

gen physics
(a) KE₁ =m₁v²/2 =85.6•4.58²/2=897.8 =898 J. I also can’t obtain the suggested answer (b) and, as a result, the answer (c) (b) According to the law of conservation of linear momentum m₁v =(m₁+m₂)u u= m₁v/(m₁+m₂...

Physics
KE(ini) =mv₁²/2 =8•4²/2=…

Physics
KE(ini) =mv₁2 =8•4²/2=… KE(fin)= mv₂²/2 =8•12²/2=…. W= KE(fin)- KE(ini)= …

Physics
(a) N=q/e=3.2•10⁹/1.6•10⁻¹⁹= 2•10²⁸ (b) The mass of one lead atom is m₀=207.2 amu =207.2•1.67•10⁻²⁷=3.46•10⁻²⁵kg The number of atoms in 8 g of lead N₀=m/m₀=0.008...

physics
F=k•q₁•q₂/r² k =9•10⁹ N•m²/C² q₂ =F•r²/k •q₁

physics
KE=PE mv²/ 2 =kx²/2 k=m(v/x) ²

physics
Pt =E =mv²/2 v=sqrt(2Pt/m) = =sqrt{2•2000•60/1400)= =13.09 m/s

Physics
m₁v=(m₁+m₂)u u= m₁v/(m₁+m₂)= =17000•23/(17000+5100)=17.7 m/s

physics
ma=Fcosα-F(fr) ma=0 F(fr) = μmg Fcosα= μmg μ=Fcosα/mg = =20•cos30/5•9.8=0.35

physics
mv²/R =μmg v=sqrt(μgR) = =sqrt(0.45•9.8•0.12)=0.73 m/s T=2πR/v = 2π•0.12/0.73 = 1.03 s.

science
4πR²3/(4πR³) = 3/R = 3/3960=0.00076

physics
m₁g+m₂g =(m₁+m₂)g =380+175=555 (m₁+m₂) =555/g=56.6 kg m₁a =T m₂a=-T+m₂g m₂a = - m₁a +m₂g a=(m₂g)/(m₁+m₂) = =175/56.6=3.1 m/s²

physics[
(a) a=5.0 m/s² (b) a depends on power of the engine which doesn’t depend on the mass of fuel

physics
ma=mg-F(res) F(res) = m(g-a) = 78(9.8-7.4) = 187.2 N

physics
F=m₁ a₁ => m₁ =F/a₁ . If m₂=m₁/2 a₂=F/m₂=F/(m₁/2) =2F/m₁ = 2a₁

Physics
s₁ = 100 ya=91.44 m v=s₁/t₁ t₂=s₂/v= s₂•t₁/s₁= =100•9/91.44 =9.84 s

Physics
λ=v/f => f = v/ λ, v = sqrt(TL/m ), λ=2L, f = sqrt(TL/m )/ 2L= =sqrt(573•0.803/0.363•10⁻³)/2•0.803= =701 Hz

Physics
b. A Foccault pendulum (a large mass hanging from a tall structure using on a long wire) T=const during the long period of time

Physics
All explanations on the base of formula for period os spring pendulum T=2πsqrt(m/k) (a) m↓=>T↓ i. Shorter (b) iii. Unchanged (c) k↑↓ => T ii. Longer (d) iii. Unchanged

Physics
m₁=3.21 kg m₂=15.3 kg m₂g=T m₁v²/R=T m₁v²/R= m₂g v=sqrt{ m₂gR/ m₁}= =sqrt{15.3•9.8•0.855/3.21} = 1.8 m/s

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