Question

1 Required information NOTE This is a multi part question. Once an answer is submitted, you will be unable to return to this part The flywheel shown has a radius of 20 in a weight of 320 lbs, and a radius of gyration of 15 in A 100-b block Ais attached to a wire that is wrapped around the flywheel, and the system is released from rest. The effect of friction is neglected Part 1 of 2 4 Determine the acceleration of block A [You must provide an answer before moving on to the next part) The acceleration of block Ais ft/s2

Answer 1

O! Step! show the free ebody diagram of given system as in figure (1): = mFd B By W = ang mag Istep 2 show the kinetic diagram of given system as in figure (2) Id . An hould mea 02 Istep 3 a) Take moment about point B since, the system of external force is Equivalent to System of effective forces, Therefore, express the system of external forces as: E MB E (MB)eft Take clockwise moment as positive Step 47 From Figure (1) calculate E MB. E MB (MAG) mass of block A 9- gravity r=radine of flywheel Here, ma 03 Foom Figure (2) calculate e (Moleht E (Model Id+(mA a) Here, I - moment of inertia of flywheel d = angular åcceleration of flywheel a= Acceleration of block a Step 5 From equation (2) substitucte (mag)o for Z Mo and Id+(ma)x for EModelt Id + (m, ar Express the formula for angular acceleration of flywheel as (mag) 98 d = а ONO Scanned with CamScanner CS Scanned with CamScanner

+104) toy Step 6 Express the formula for moment of Inertia of flywheed (I) as I= m₂ k² Here, mi= mass of flywheel K - radius of gyration of flywhee) Now express the formula for weight of block A (WA) as i mag Step 7 For equation (2) substitute a fora mak² for I, WA for Mag (WA) +(malg mpk?) ( 8 = a 8. 05 WA = (M= K²) ( 2 ) + maa 2 WA (MEK tma ma) a 82 WA a = K me Steps substitute WE for me WA for MA, and g WE 9 WA wg) St Hube 82 Here, we = Weight of the flywheel WA = Weight of block A (06 Step 9 substitute WA 100 lb WE 320 lb 9 = 322 Als in. K 15 20 in. in egn ♡ 100 lb a= 320 lb 15 in 100 lb + 32.264/52 32-2fa15 coin 100 lb ft/5² a= 8.6957 a = 11.4999 filoz Hence the acceleration of block is 11.5 fts2 Scanned with CamScanner CS Scanned with CamScanner