Answer to Question #179446 in Physics for john vincent burlas

Question #179446

What is the average power dissipated by a 2kg grinding wheel of radius 0.1 m brought to rest in 10 rev from an initial velocity of 3000 rpm? Assume constant acceleration. 


1
Expert's answer
2021-04-12T06:58:11-0400

n=10n=10


ω=3000 rpm=314 rad/s\omega=3000\ rpm=314\ rad/s


I=mr2/2=20.12/2=0.01 kgm2I=mr^2/2=2\cdot0.1^2/2=0.01\ kg\cdot m^2



W=ΔKE=Iω22=0.0131422493 (J)W=\Delta KE=\frac{I\omega^2}{2}=\frac{0.01\cdot314^2}{2}\approx493\ (J)


P=W/tP=W/t


ϕ=ωtϵt2/2\phi=\omega t-\epsilon t^2/2


ωf=ωϵtϵ=(ωωf)/t=(ω0)/t=ω/t\omega_f=\omega-\epsilon t\to \epsilon=(\omega-\omega_f)/t=(\omega-0)/t=\omega/t


ϕ=ωtϵt2/2=ωtωt22t=ωt2\phi=\omega t-\epsilon t^2/2=\omega t-\frac{\omega t^2}{2t}=\frac{\omega t}{2}


2πn=ωt2t=4πnω=43.1410314=0.4 (s)2\pi n=\frac{\omega t}{2}\to t=\frac{4\pi n}{\omega}=\frac{4\cdot 3.14\cdot10}{314}=0.4\ (s)


P=W/t=493/0.4=1232.5 (W)P=W/t=493/0.4=1232.5\ (W) . Answer










Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment