Final answer:
To calculate the maximum counterclockwise moment of a couple that can be applied without disturbing the equilibrium of the system, consider the frictional forces acting on the spool and block. Multiply the coefficient of static friction by the normal force for the spool and block, and sum the results to find the maximum counterclockwise moment.
Step-by-step explanation:
The maximum counterclockwise moment of a couple that can be applied without disturbing the equilibrium of the system can be calculated by considering the frictional forces acting on the spool and block.
First, let's analyze the spool. The maximum clockwise moment that can be applied due to the static friction under the spool can be found by multiplying the coefficient of static friction under the spool (0.15) by the normal force acting on the spool. The normal force is equal to the weight of the spool, which is given as the product of its mass (50 kg) and the acceleration due to gravity (9.8 m/s^2).
Next, let's analyze the block. The maximum clockwise moment that can be applied due to the static friction under the block can be found by multiplying the coefficient of static friction under the block (0.2) by the normal force acting on the block. The normal force is equal to the weight of the block, which is given as the product of its mass (30 kg) and the acceleration due to gravity (9.8 m/s^2).
The maximum counterclockwise moment of the couple Co is equal to the sum of the clockwise moments due to the static friction under the spool and block. Therefore, the maximum counterclockwise moment is given by:
Co = (0.15 * (50 kg * 9.8 m/s^2)) + (0.2 * (30 kg * 9.8 m/s^2))
Simplifying this expression will give you the answer.