Question Number 31934 by NECx last updated on 17/Mar/18
$${The}\:{flywheel}\:{of}\:{a}\:{punch}\:{press}\:{has} \\ $$$${a}\:{moment}\:{of}\:{inertia}\:{of}\:\mathrm{16}{kgm}^{\mathrm{2}} \\ $$$${and}\:{runs}\:{at}\:\mathrm{300}{rev}/{min}.{The} \\ $$$${flywheel}\:{supplies}\:{all}\:{the}\:{energy} \\ $$$${needed}\:{in}\:{a}\:{quick}\:{punching} \\ $$$${operation}. \\ $$$$\left.{a}\right){Find}\:{the}\:{speed}\:{in}\:{rev}/{min}\:{to} \\ $$$${which}\:{the}\:{flywheel}\:{will}\:{be}\:{reduced} \\ $$$${by}\:{a}\:{sudden}\:{punching}\:{operation} \\ $$$${requiring}\:\mathrm{5000}{J}\:{of}\:{work}. \\ $$$$\left.{b}\right){What}\:{must}\:{be}\:{the}\:{constant} \\ $$$${power}\:{supply}\:{to}\:{the}\:{flywheel}\:{to} \\ $$$${bring}\:{it}\:{back}\:{to}\:{its}\:{initial}\:{speed} \\ $$$${in}\:{a}\:{time}\:{of}\:\mathrm{5}{s}? \\ $$
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](Q31936.png)
$$\left({a}\right) \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{16}×\left[\left(\frac{\mathrm{300}}{\mathrm{60}}×\mathrm{2}\pi\right)^{\mathrm{2}} −\left(\frac{{u}_{\mathrm{2}} }{\mathrm{60}}×\mathrm{2}\pi\right)^{\mathrm{2}} \right]=\mathrm{5000} \\ $$$$\Rightarrow{u}_{\mathrm{2}} =\mathrm{182}\:{rev}/{min} \\ $$$$\left({b}\right) \\ $$$$\frac{\mathrm{5000}}{\mathrm{5}}=\mathrm{1000}\:{Watt} \\ $$