Question

3. A very thin circular hoop of mass m and radius r is made to roll, without slipping, down a ramp with an angle of inclination (with respect to the horizontal), as shown in the figure below. See Figure 3. Note: The moment of inertia of the thin circular hoop is given by: I houp = mra Consider a system consisting of a ladder with a painter climbing said ladder. The ladder has a length 1 = 5,00 meters and mass (which is uniformly distributed) m. The mass of the painter is M = 3m; ie the mass of the painter is throu times the mass of the ladder. If the ladder begins to slip (at the base) when the painter has traversed a distance (along the ladder) d = 1, determine the coefficient of static friction between the ladder and It has been demonstrated, during lecture, that the linear) acceleration of the center of the hoop is (then) given by the following: a = sin(o). the floor Suppose, now, that the circular hoop is to be replaced by a hollow sphere of mass Mund radius R. Note: Assume that the surface of the wall is frictionless. See Figure 4. Determine the linear) acceleration of the center of the hollow sphere. Note: The moment of inertia of the hollow sphere is given by: Ikollow sphere = MR? 18 For Fc 4.0 m 2.8 m mg Mg P in tim. Int. Figure 3 -3.0 m 2.1 m Figure 4 "How often have I said to you when you have eliminated the impossible, whatever remains, however improbable, must be the truth?"

Answer 1

Afn Ay fs = Static frichon mg Sin8 = X-Component of ng mgloss = y-component of mg En I normal force on Sphere het Torque about point c=T== fs R R= radius of sphere By and low of motion for rotation, T= Im [x = Angular queelera bon) + fs R = I1 I = ZMR2 (Moment of Inesha fsR=(2MR3) foo hollow Sphere) fFR = ZMRC) [asă (formulare in terms of formula in terms of Quelerebon)

fs= 2 Ma Noco, Net force along X-exis, Fnet - Mg Sino - fs By Ind lowo of mohon, Fhet = Ma » Mg Sino - fs= Ma My Sing- ŽMQ = Ma [from 0] gSino – 24 = Q g Sino = zate gSino = za [a= 2 gsing Aus