Final answer:
To determine the mass of the counterweight needed to balance the assembly at point O, one must apply the principle of torque balance around point O, considering the product of each mass, gravitational acceleration, and respective distance from point O.
Step-by-step explanation:
To determine the mass mc of the counterweight so that the center of mass of the assembly is at point O, we can use the concept of torque balance. In a system where the center of mass is desired at a specific point (in this case, point O), the sum of the torques about that point must equal zero. Torque is calculated by the product of the mass, the gravitational acceleration (g = 9.8 m/s²), and the distance from the pivot point. For a basic example, consider a meter stick with masses attached at various points. If the stick itself has a mass, it too must be factored into the balance. The torque produced by each mass is the product of the mass, gravity, and distance from the pivot. To balance the system, the torques on one side of the fulcrum must be equal to the torques on the other. If we have a mass m1 at a distance d1 from the fulcrum and mass m2 at a distance d2, and we wish to find the mass m3 at a distance d3 to balance the system, we would solve for m3 in the equation m1 × d1 + m2 × d2 = m3 × d3. Then solve for the counterweight mass mc where mc × dc = (mass of flywheel + mass of bolt + any other masses) × their respective distances to point O.