Question

A square block with mass m 50 kg uniformly distributed and side length L. Sm is connected to the edge of a table by a hinge. The hinge is at the bottom right corner of the block. A cable is attached to the top right corner of the block and to the table such that the cable forms an angle a 40 below the horizontal. Someone pulls the block with a force 250N to the left. Futis applied at the lower left corner of the block M a) If the system is in static equilibrium what is the tension in the cable? b) What is the force from the hinge on the block? The system is again statie. Leave your answer in terms of components. c) The force full and the cable are both removed. The block is free to rotate around the hinge without friction. The moment of inertin for the square rotating around a corner is - ML. If the block starts from rest what is the change in the height of its center of mass when the angular speel in dinas per second

Answer 1

son EL- T cosa My fTsina Fonell' Nx mg Hinge a. System is in static equilibrium the net acceleration of block is zero. Net force and net torque is also zero b. Taking moments of forces about hinge Tnet = 0 Mg 18(1) - Tcosa X (L) = 0 Mg T= 2 x cosa (50) x (9.8) TE 2 x cos40 T = 319.825N c. F = 0 Tcosa+N - F pull = 0 Tcos40+ N2 - 250 = 0 N = 250 - Tcos 40 N = (250) - (319.825) * (cos40) N = 5

EF, = 0 N, - Mg - Tsina = 0 N = Mg + Tsina N, = (50) (9.8) + Tsin 40 N, = (50) (9.8) + (319.825) * (sin40) N = 695.58N C. If change in center of the mass height is h then gravitational potential energy is converted into kinetic energy of the block Mgh = {1002 Mgh }(22) gh = {{?co2 h- L02 3g (0.3)2 (7) h= (3) (9.8) h = 0.15m