Question

A 10 kg box resting on a horizontal, frictionless surface is attached to a 4 kg block by a thin light rope that passes over a frictionless pulley. The pulley has a shape of a uniform solid disk of mass 4.5 kg and a radius of 0.55 m. After the system is released 10 kg box moves to the right, 4 kg block moves down and the pulley rotates clockwise. 7 Find: (a) the magnitude of the tension (in N) of the rope on the end attached to 10 kg box; (b) the magnitude of the tension (in N) of the rope on the end attached to 4 kg block; (c) the magnitude of the acceleration in m/s) of the 10 kg box;

Answer 1

Ans: Given data :- r = 0.55m m mass of the box resting m, = lokg mass of the hanging weight my = mg = 4kg mass of the cylindrical pulley M = 4.5kg. radius å Free body diagram 키 let a) be the acceleration of in the horizontal direction a be the acceleration of my in the vertical direction. since the books are.connected by an inextensible string , mist their accelerations must be, of equal magnitude, T that is a sa, sa a) Model mi as a particle under a net force in the horizontal direction E Fx = Tiam, a To =m, a

particle under a net force in the model my as a verit cal direction Efy = mag-T₂ = mga T₂ = my g-maa net torque model Pulley as a rigid object under E1 = (1, - 1.) v = 1a I = ² mr2 (72 -T.) r = 12 mr 20 7-T = ₂2 ma mag-mga-m,a = 1/2 ma ₂ Matm, atm, a = m₂ g a mg /M + Mytm, 4 x 9.8 a. **4.5+4+10 2.41 m/s²

a) The magnitude of the tension at lokg Toam, a = 10 x2.41 1- 84. N 4kg b) The The magnitude of the tension at m₂ g mga me (9-3) = 4(9.8 - 2.41) Tz = 29.56 c) The magnitude of the acceleration of the lokgher ܘ . ܢܘ: ܕܘ .'. Therefore la, = 2.41 m/s²