Question #250774

A light 300mm diamter pulley is held stationairy and carries a 10kg mass haning on a light cord passing around the pulley. Find the vertical acceleration of the mass when the pulley is released. Frictional torque is the pulley bearings is 3N.m.




Clearly show the following value


Ek=?


Ep=?


E=?


Energy equation=??


v=??


1
Expert's answer
2021-10-13T15:41:12-0400

g=9.8ms2g = 9.8\frac{m}{s^2}

d=300mmd = 300mm

r=d2=150mm=0.15mr = \frac{d}{2}= 150mm= 0.15m

Ifr=3NmI_{fr}= 3N*m

Ifr=FfrrI_{fr}= F_{fr}*r

Ffr=Ifrr=30.15=20NF_{fr}= \frac{I_{fr}}{r}=\frac{3}{0.15}=20N

Let the load descend a distance h\text{Let the load descend a distance }h

Ek=mv22E_k =\frac{mv^2}{2}

Ep=mghE_p= -mgh

Efr=FfrhE_{fr}=F_{fr}h

Ek+Ep+Efr=0E_k+E_p+E_{fr}=0

mv22mgh+Ffrh=0\frac{mv^2}{2} - mgh +F_{fr}h=0

v2=2h(mgFfr)m(1)v^2= \frac{2h*(mg-F_{fr})}{m}(1)

v=2h(mgFfr)mv=\sqrt{ \frac{2h*(mg-F_{fr})}{m}}

v2=2ahv^2 = 2ah

From (1)\text{From (1)}

2ah=2h(mgFfr)m2ah = \frac{2h*(mg-F_{fr})}{m}

a=(mgFfr)m=109.82010=7.8ms2a = \frac{(mg-F_{fr})}{m}=\frac{10*9.8 -20}{10}=7.8\frac{m}{s^2}


Answer: a=7.8ms2\text{Answer: }a =7.8\frac{m}{s^2}



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