An object of mass m is resting on top of a spring - Edexcel - A-Level Physics - Question 3 - 2023 - Paper 1

To solve this question, we need to understand the energy transfer when the spring is released. Initially, when the spring is compressed by a distance Δx, the potential energy stored in the spring can be expressed as:

PE_{spring} = rac{1}{2}k riangle x^2

where $k$ is the spring constant.

When the spring returns to its original length, this potential energy is converted into kinetic energy of the object and gravitational potential energy. At the moment Δx becomes zero, the energy conservation principle can be applied:

rac{1}{2}k riangle x^2 = rac{1}{2}mv^2 + mg riangle x

Rearranging this leads us to:

F riangle x = rac{1}{2}mv^2 + mg riangle x

Thus, the correct choice from the provided options is B:

F riangle x = rac{1}{2}mv^2 + mg riangle x