To find the acceleration and tension in a pulley system, apply Newton's second law to both blocks, then solve the resulting equations. The acceleration can be found by considering the net force on each block, and the speed of a falling block can be determined using kinematic equations.
To solve for the acceleration and tension in a system of two blocks connected by a massless rope over a massless frictionless pulley, we will apply Newton's second law of motion. Based on the given information, we will draw free-body diagrams for each block. The force of gravity acting on the hanging block creates acceleration for the system, while tension exists in the rope due to this force.
Consider the 4.0 kg block on the table and the 1.0 kg hanging mass. Let's denote the acceleration as 'a' and the tension as 'T'. For the 1.0 kg block, the only force is gravity, so Fnet = m * g - T, which gives us T = m * g - m * a. For the 4.0 kg block, we have no other forces, so T = m * a. By solving these two equations simultaneously, we will get the values of 'a' and 'T'.
The speed of the hanging mass when it hits the floor can be found using kinematic equations since it starts from rest and is initially 1.0 m from the floor.