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The-flywheel-of-a-punch-press-has-a-moment-of-inertia-of-16kgm-2-and-runs-at-300rev-min-The-flywheel-supplies-all-the-energy-needed-in-a-quick-punching-operation-a-Find-the-speed-in-rev-min-to-which




Question Number 31934 by NECx last updated on 17/Mar/18
The flywheel of a punch press has  a moment of inertia of 16kgm^2   and runs at 300rev/min.The  flywheel supplies all the energy  needed in a quick punching  operation.  a)Find the speed in rev/min to  which the flywheel will be reduced  by a sudden punching operation  requiring 5000J of work.  b)What must be the constant  power supply to the flywheel to  bring it back to its initial speed  in a time of 5s?
$${The}\:{flywheel}\:{of}\:{a}\:{punch}\:{press}\:{has} \\ $$$${a}\:{moment}\:{of}\:{inertia}\:{of}\:\mathrm{16}{kgm}^{\mathrm{2}} \\ $$$${and}\:{runs}\:{at}\:\mathrm{300}{rev}/{min}.{The} \\ $$$${flywheel}\:{supplies}\:{all}\:{the}\:{energy} \\ $$$${needed}\:{in}\:{a}\:{quick}\:{punching} \\ $$$${operation}. \\ $$$$\left.{a}\right){Find}\:{the}\:{speed}\:{in}\:{rev}/{min}\:{to} \\ $$$${which}\:{the}\:{flywheel}\:{will}\:{be}\:{reduced} \\ $$$${by}\:{a}\:{sudden}\:{punching}\:{operation} \\ $$$${requiring}\:\mathrm{5000}{J}\:{of}\:{work}. \\ $$$$\left.{b}\right){What}\:{must}\:{be}\:{the}\:{constant} \\ $$$${power}\:{supply}\:{to}\:{the}\:{flywheel}\:{to} \\ $$$${bring}\:{it}\:{back}\:{to}\:{its}\:{initial}\:{speed} \\ $$$${in}\:{a}\:{time}\:{of}\:\mathrm{5}{s}? \\ $$
Answered by mrW2 last updated on 17/Mar/18
(a)  (1/2)×16×[(((300)/(60))×2π)^2 −((u_2 /(60))×2π)^2 ]=5000  ⇒u_2 =182 rev/min  (b)  ((5000)/5)=1000 Watt
$$\left({a}\right) \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{16}×\left[\left(\frac{\mathrm{300}}{\mathrm{60}}×\mathrm{2}\pi\right)^{\mathrm{2}} −\left(\frac{{u}_{\mathrm{2}} }{\mathrm{60}}×\mathrm{2}\pi\right)^{\mathrm{2}} \right]=\mathrm{5000} \\ $$$$\Rightarrow{u}_{\mathrm{2}} =\mathrm{182}\:{rev}/{min} \\ $$$$\left({b}\right) \\ $$$$\frac{\mathrm{5000}}{\mathrm{5}}=\mathrm{1000}\:{Watt} \\ $$

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