Question

5J A person applies a force of magnitude F as shown to the axle of a uniform disc with mass Mand radius R (such that the force is applied at the center of mass of the disc). The ground has a coefficient of static friction of 0.500 and a coefficient of kinetic friction of 0.400. a) Below a critical F, the disc rolls without slipping. Find this critical F in terms of M, R, and g. F b) Calculate the acceleration of the center of mass and the angular acceleration of the disc below this critical F as a function of F, M, R, and g. c) Calculate the acceleration of the center of mass and the angular acceleration of the disc above this critical Fas a function of F, M, R, and g. d) Draw a diagram showing how the acceleration of the center of mass and how the angular acceleration of the disc varies as we vary F.

Answer 1

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qN a Уа yet I = MR? a) If body is purely rolling Static friction acts on the body. M = 0.4 Ms=0.5 F - fs = ma also, T=IX { x = met ( 9 0 fm @ & F = (M + mja also to EMN for sung - to so. Smg F -0.5Mg = F = 1. 5M +0.5M > F-0.5mg = ma= xx 2 F = F = 2F to sing = F = 1.5 My Soul 5) acceleration (a) = ? and And you may put a Angular acceleratim = L = 2F 3 MR E lusing Uwe is napting. sliding then kinetic fiction c) If body roll with acto.

F - fx = ma > F-0.4mg = Mao adeo u. a= acceleration - F - 0.4mg M kul for Angular Motion T=It fox R = It 0.4 Mg xf = MR XL Hrgular Acceleration g R - 1.5Mg rolling with sliding Zone Pure rolling tone