Final answer:
The reaction at the pin O just after the cord AB is cut can be calculated using Newton's third law of motion. The reaction force at pin O is equal in magnitude and opposite in direction to the gravitational force acting on the pendulum. By adding up the gravitational forces acting on the sphere and the rod, we can find the total reaction force at pin O.
Step-by-step explanation:
When cord AB is cut, the 30-lb sphere and 10-lb slender rod will experience a downward force due to gravity. This force will cause a reaction at the pin O, which can be calculated using Newton's third law of motion. According to Newton's third law, the reaction force at the pin O will be equal in magnitude and opposite in direction to the gravitational force acting on the pendulum.
To calculate the reaction force, we can add up the gravitational forces acting on the sphere and the rod separately. The gravitational force acting on the sphere is given by F_sphere = mg_sphere, where m_sphere is the mass of the sphere and g is the acceleration due to gravity (approximately 9.81 m/s^2). Similarly, the gravitational force acting on the rod is given by F_rod = mg_rod, where m_rod is the mass of the rod. Adding up these forces, the reaction force at pin O is given by F_o = F_sphere + F_rod.
Since the mass of the sphere is 30 lbs and the mass of the rod is 10 lbs, we need to convert these masses to kilograms before plugging them into the equations. 1 lb is equal to 0.4536 kg. So the mass of the sphere in kilograms is (30 lbs)(0.4536 kg/lb) = 13.608 kg, and the mass of the rod in kilograms is (10 lbs)(0.4536 kg/lb) = 4.536 kg. Plugging these values into the equations, we get F_sphere = (13.608 kg)(9.81 m/s^2) = 133.51968 N and F_rod = (4.536 kg)(9.81 m/s^2) = 44.57016 N. Adding these forces together, we find that the reaction force at pin O, Fo, is equal to F_o = F_sphere + F_rod = 133.51968 N + 44.57016 N = 178.08984 N.