Question

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

Short answer

The potential energy of the particle at B is 15 J.

Step-by-step solution

Given data:

Work done, W = 25 J

Potential energy at point A,$U_A=40J$

To understand the concept:

When conservative force works on an object, the change in potential energy is negative of work done.

Formula:

The work done is equal to the change in potential energy.

Workdone = - Change in PE

Calculate the potential energy of the system with the particle at B:

As work done is as same as the change in potential energy. Therefore,

$$\begin{gathered} Workdone=-ChangeinPE \\ W=-\left(U_B-U_A\right) \\ 25\mathrm{J}=-\left({\mathrm{U}}_{\mathrm{B}}-40\mathrm{J}\right) \\ 25\mathrm{J}=-{\mathrm{U}}_{\mathrm{B}}+40\mathrm{J} \\ {\mathrm{U}}_{\mathrm{B}}-\left(40-25\right)\mathrm{J} \\ =15\mathrm{J} \end{gathered}$$

Hence, the potential energy of the system with the particle at B is 15 J .