Final answer:
To analyze the velocity of the center of mass in a system with blocks connected by a string over a frictionless pulley, we apply Newton's second law and use kinematic equations, and in the case of a frictionless collision, the center-of-mass velocity remains constant.
Step-by-step explanation:
When two blocks are connected by a light string and pass over a pulley, we assess the system's movement by applying the laws of motion. With negligible mass and friction of the pulley, we can analyze the forces acting on the blocks to determine the system's acceleration, tension in the string, and final velocity.
For example, consider a system where a 4.0 kg block is on a table and a 1.0 kg block is hanging. To find the acceleration, we apply Newton's second law to each block. The hanging mass experiences the force of gravity (m*g), where m is mass and g is the acceleration due to gravity (9.8 m/s^2).
This force causes the entire system to accelerate. The tension in the string acts upward on the hanging mass and horizontally on the mass on the table, counteracting the system's acceleration due to gravity. Since the pulley is frictionless, tension is the same on both sides of the pulley.
To find the speed after the block fell 2.0 meters, we can use kinematic equations, knowing the system started from rest (initial velocity is zero) and we've already calculated the acceleration.
In cases involving a frictionless collision, the center-of-mass velocity remains constant both before and after the collision due to the conservation of momentum.