Task id11962

A student observes a stone falling from a height A above the Earth's surface in a reference frame associated with the Earth. At the initial moment of time, the stone was at rest, therefore, its kinetic energy was equal to zero: Ek1=0. Potential energy of the “Earth - stone” system: Ep1=mgh. A stone flies up to the Earth's surface with a speed v, which can be calculated from the expressions: v=gt, from which v=|/2gh. Consequently, its kinetic energy at the Earth's surface is Ek2=mv2/2=m2gh/2=mgh. The potential energy of the “Earth - stone” system in this position is zero: Thus, the student is convinced that in his frame of reference the law of conservation of mechanical energy is satisfied: Ek1 + Ep1=0 + mgh=mgh, Eh2 + Ep2=mgh + 0=mgh . Therefore, Ek1 + Epl=Ek2 + Ep2. The second student observes the fall of the same stone in a frame of reference associated with an elevator moving vertically downward with speed and relative to the surface of the Earth. At the initial moment of time, the stone in the reference frame associated with the elevator has a speed v directed vertically upward, therefore, its kinetic energy E,k1=mv2/2. In this case, the stone is located at a height h above the surface of the Earth, therefore; potential energy of interaction of the “Earth - stone” system E,p1=mgh. At the Earth's surface, the kinetic energy of the stone in this reference frame is equal to zero, since the speed of the stone relative to the Earth becomes equal to the speed of the elevator: E,k2=0. The potential energy of the “Earth-stone” system in this position is also zero: E,p2=0. Since E,k1 + E,p1=mv2/2 + mgh, E,k2 + E,p2=0, the second student comes to the conclusion that the mechanical energy of the “Earth-stone” system is not conserved. How can this paradox be resolved?