107 The only force acting on a particle is conservative force F⃗. If the particle is at point A,

step 1 So this problem on the topic of conservation of energy, we're told that the only force acting on

107 The only force acting on a particle is conservative...

107 The only force acting on a particle is conservative force $\vec{F}$. If the particle is at point $A$, the potential energy of the system associated with $\vec{F}$ and the particle is $40 \mathrm{~J}$. If the particle moves from point $A$ to point $B$, the work done on the particle by $\vec{F}$ is $+25 \mathrm{~J}$. What is the potential energy of the system with the particle at $B$ ?

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Key Concepts

Potential Energy

Potential energy is the stored energy of a system related to the position or configuration of objects within a conservative force field. It quantifies energy that can be converted into work or kinetic energy when the configuration changes, and its value depends on the relative positions of the components of the system.

Relationship Between Work and Potential Energy

In the context of conservative forces, the work done by the force is equal to the negative change in potential energy. This fundamental relationship allows for the easy computation of energy changes; for instance, if a conservative force does positive work on a particle while moving it between two points, the potential energy of the system correspondingly decreases by the same amount.

Conservative Force

A conservative force is characterized by the property that the work done by the force in moving a particle between two points is independent of the path taken. This property allows the force to be associated with a potential energy function, making it possible to analyze energy changes without regard to the specific trajectory of the particle.

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