As shown in the figure, two objects a and B with mass m are connected by a light spring with stiffness coefficient K. A is lifted in the air by hand with external force F, and B is h above the ground. After letting go, a and B fall, and B does not rebound after colliding with the ground. When the spring force is mg, what is the falling distance of object a?

As shown in the figure, two objects a and B with mass m are connected by a light spring with stiffness coefficient K. A is lifted in the air by hand with external force F, and B is h above the ground. After letting go, a and B fall, and B does not rebound after colliding with the ground. When the spring force is mg, what is the falling distance of object a?

When two objects are held in hand, B is in balance, so the elastic force is mg. According to Hooke's Law: F = KX, the spring extends X1 = MGK. After landing, when the elastic force is mg, the spring is compressed x2 = MGK. Therefore, the common falling distance of a is x = X1 + x2 + H = H + 2mgk. A: the falling distance of object a is H + 2mgk