Question

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The 38-in. drum rotates about a horizontal axis with a constant angular velocity 5.4 rad/sec. The small block A has no motion relative to the drum surface as it passes the bottom position ø = 0. Determine the coefficient of static friction (u s) which would result in block slippage at an angular position ø: plot your expression for 0 < ø ≤ 180°. Determine the minimum required coefficient value (u min) which would allow the block to remain fixed relative to the drum throughout a full revolution. For a friction coefficient slightly less than (u min) at what angular position ø would slippage occur?

If ø = 35°, u = ?
If ø = 54°, u = ?
If ø = 112°, u = ?

Minimum coefficient, u min = ?
For u slightly less than u min, øslip = ?

Answer 1

+ mr2² -U. Sesh radys F- 2. F Value N= mycose 4 m2.12 imgsint mga meni Sof? N= mg cose + mgsino. putting in egres MAN =(ong cose + me22) Me mgsino Asing. geoset geosetes Be Given, 2 = 5.4 rad/s, s= 19 in. - 386.22 in/s2. 2 F2 = Us ma loset me ez megsin e 2 go M = 386.22 sin o. 386.22 COS8 + (1975.42) Ms = 20 386.22 sino 38672/cose + 1.4345) sa sino. cose + 1.4345 30=35, 0=35 us= Sin 35° 30.2545 Cos 35°t 1.9345 48-5407 Tus = Sin sy us= Sin 54° cos54 +1.4345 = 0.4

40-12, a Msa Sin 112° cos/12° +1.4345 0.8748 For Minimum required Coefficient value (Umin) differentiate List wiele reipet to ó' and then equate to zero de 2.0 do di sino do coso +1.43451 450) O- 134. 195° / -at which Mmin. min = 0.9723 Forel at will occur slightly less than Morin, sup Ogline 134.8196°