A block with mass ?m? = 5.00 kg slides down a surface inclined 36.9O to the horizontal (?Fig. P10.62?). The coefficient of kinetic friction is 0.25. A string attached to the block is wrapped around a flywheel on a fixed axis at ?O?. The flywheel has mass 25.0 kg and moment of inertia with respect to the axis of rotation. The string pulls without slipping at a perpendicular distance of 0.200 m from that axis. (a) What is the acceleration of the block down the plane? (b) What is the tension in the string?
Solution 70P Step 1 of 3: a)The free body diagram of flywheel we know that = Iz z = TR z Now TR = I z Step 2 of 3: The free body diagram of the block F =yma y n mg cos 36.9 = 0 0 n = mg cos 36.9 0 fk= nk= mgkos 36.9 F =xma x 0 0 mg sin 36.9 T mgcks 36.9 = ma 0 0 mg(sin 36.9 cok 36.9 ) T = ma we know that a = R and = a block wheel R Ia TR = R I T = R2a = ma mg(sin 36.9 kcos 36.9 ) a = 2 2 5 kg+0.5 kg.m /0.2 m) 2 = 1.12 m/s