1. The problem statement, all variables and given/known data Two particles of masses 6 kg and 8 kg rest on two horizontal tables.The coefficient of friction between both particles and their respective tables is (1/2).The particles are connected by a smooth inextensible string which passes over smooth pulleys and under a smooth movable pulley of mass M kg Show that none of the particles will move if M is less than or equal to 6 2. Relevant equations F=MA 3. The attempt at a solution t = Tension a = acceleration of 6 kg particle b = acceleration of 8 kg particle for the six kg particle 3g - t = 6a a = (3g - t)/6 for the eight kg particle 4g - t = 8b b = (4g-t)/8 for pulley M 2t -Mg = M(a+b)/2 4t -2Mg = M(3g-t)/6 + M(4g-t)/8 96t -48Mg = 4M(3g-t) + 3M(4g -t) multiplied my 24................ 96t = 48Mg + 12Mg -4Mt + 12Mg - 3Mt 96t + 7Mt = 72Mg t(96 + 7M)= 72Mg t = 72Mg / (96 + 7M) Since its not accelerating 2t - Mg = (3g - t) + (4g -t) Sum of the forces are equal 4t= Mg + 7g 288Mg = (Mg + 7g)(96 + 7M) Substituting value for t 288Mg = 96Mg + 672g +7Mg^2 + 49Mg 7Mg^2 - 143Mg +672g = 0 68.6M^2 - 1401.4M + 6585.6 When I use the minus b formula i get M = 13.1 and 7.32 I'm convinced I've done this completely wrong.I was hoping I would get a solution of M = 6. Any help would be appreciated.