Final Answer:
When released and sticking together upon collision, the two sticks will swing to a height equal to the length of one stick. This is due to the conservation of energy, where the combined system's potential energy is proportional to the height, and the mass doubling upon collision maintains the same potential energy as a single stick.
Step-by-step explanation:
When the initially horizontal stick is released, it experiences simple harmonic motion as it swings back and forth. This motion occurs because the gravitational potential energy is converted into kinetic energy as the stick descends, and vice versa as it ascends. The release point is crucial, as it determines the maximum potential energy the system can reach. Upon collision with the stationary stick, the two sticks stick together, forming a single system with twice the mass.
The collision between the sticks is assumed to be perfectly elastic, conserving both kinetic and potential energy. As a result, the combined system of the two sticks, now acting as one, continues to conserve the total energy of the system. The potential energy at the highest point of the swing is proportional to the height reached. Since the mass of the system has effectively doubled due to the collision, and potential energy is directly proportional to mass, the height attained is the same as if a single stick of the same length had been released from the horizontal position.
Understanding the principles of energy conservation and the dynamics of collisions enhances our grasp of fundamental physics concepts. It sheds light on how seemingly complex systems can be analyzed by considering the conservation laws governing energy and momentum.