Final answer:
To maintain equilibrium, the tension in the rope connecting the cylinders must be greater than or equal to the weight of cylinder D. The range of the mass m of cylinder D for which equilibrium is maintained is 14.23 kg ≤ m ≤ 175.7 kg.
Step-by-step explanation:
In order for equilibrium to be maintained, the tension in the rope connecting the two cylinders must be greater than or equal to the weight of cylinder D. The maximum tension in the rope occurs when the static friction force between the rope and the rods reaches its maximum value.
Using the equation for static friction μs = Fs / N, where Fs is the maximum static friction force and N is the normal force, and substituting the given coefficient of static friction μs = 0.40, we can calculate the maximum static friction force as 0.40 times the normal force.
Since the normal force is equal to the weight of cylinder D, we can set up an inequality: 0.40 times the weight of cylinder D ≥ weight of cylinder D. Solving for the weight of cylinder D, we find that the range of the mass m of cylinder D for which equilibrium is maintained is 14.23 kg ≤ m ≤ 175.7 kg.