OK...There are two weights here. I don\'t know how to evaluate this problem. Ple

Question

OK...There are two weights here. I don't know how to evaluate this problem. Please solve.

Determine the tensions in CD, CB, and BA and the angle theta required for the equilibrium of the 30n lb cylinder E and the 60 lb cylinder F.

Explanation / Answer

Let tension in AB = x lb, in BC = y lb and in CD = z lb. For equilibrium of F and E in the horizontal direction, xcos45° = ycos? = zcos30° => x/v2 = (v3/2) z ... ( 1 ) For equilibrium of F and E in the vertical direction, 60 - xsin45° = ysin? = zsin30° - 30 => x/v2 = 90 - z/2 ... ( 2 ) From (1) and (2), (v3/2) z + z/2 = 90 => z = 180/(v3 + 1) = 90(v3 - 1) = 65.88 N Plugging in (1), x = v(3/2) z = v(3/2) * (65.88) = 80.69 N Next, squarring and adding, ycos? = zcos30° and ysin? = zsin30° - 30 => y^2 = z^2 - 30z + 900 => y = v[(65.88)^2 - (30)*(65.88) + 900] = 57.13 N Also, ycos? = zcos30° => cos? = (z/y)cos30° = [(65.88)/(57.13)] cos30° = 0.9987 => ? = 2.96° Tension in CD = 65.88 N Tension in CB = 57.13 N Tension in BA = 80.69 N ? = 2.96°

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