Exercício de Dinamica Aplicada (154)

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315 
 
 
PROBLEM 12.14 
Solve Problem 12.13, assuming that the coefficients of 
friction between block A and the incline are 0.25sμ = and 
0.20.kμ = 
PROBLEM 12.13 The two blocks shown are originally at 
rest. Neglecting the masses of the pulleys and the effect of 
friction in the pulleys and between block A and the incline, 
determine (a) the acceleration of each block, (b) the tension 
in the cable. 
 
SOLUTION 
We first determine whether the blocks move by computing the friction force required to maintain block A in 
equilibrium. T = 175 lb. When B in equilibrium, 
 req0: 175 200sin 30 0xF FΣ = − ° − = 
 req 75.0 lbF = 
 0: 200cos30 0 173.2 lbyF N NΣ = − ° = = 
 0.25(173.2 lb) 43.3 lbM sF Nμ= = = 
Since req , blocks will move ( up and down).mF A B> F 
We note that 
1
.
2B Aa a= 
Block A 
 
 (0.20)(173.2) 34.64 lb.kF Nμ= = = 
 
200
0 : 200sin 30 34.64
32.2x A A AF m T aΣ = − ° − + = (1)