Final answer:
The question revolved around the conservation of energy principle in a system involving a spring. The student correctly equated the spring's initial potential energy to the sum of its potential energy after release and the subsequent kinetic energy of the mass.
Step-by-step explanation:
The student is asking about energy conservation in the context of a physics problem involving a spring. The equation they've set up indicates that the spring's initial potential energy is partly converted into gravitational potential energy and partly into kinetic energy.
This conversion follows the law of conservation of energy, which states that the total energy in an isolated system remains constant.
Therefore, when the spring is compressed or stretched, work is done on it, and this work is stored as potential energy (PE) in the spring.
When the spring is released, this stored energy is transformed into kinetic energy (KE) of the moving mass and any other forms of energy, such as sound or heat due to friction, if present in the system.
The equation they have used takes the initial potential energy of the spring (1/2)kx2, and equates it to the sum of the potential energy in the spring after being released, plus the kinetic energy of the mass (v is the velocity).
If there are no non-conservative forces or if their work is being taken into account separately, the equation should correctly yield the final velocity of the mass attached to the spring.