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Q107P

Expert-verifiedFound in: Page 211

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**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?**

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

Work done, W = 25 J

Potential energy at point A, ${U}_{A}=40J$

**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*

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

$Workdone=-ChangeinPE\phantom{\rule{0ex}{0ex}}W=-\left({U}_{B}-{U}_{A}\right)\phantom{\rule{0ex}{0ex}}25\mathrm{J}=-\left({\mathrm{U}}_{\mathrm{B}}-40\mathrm{J}\right)\phantom{\rule{0ex}{0ex}}25\mathrm{J}=-{\mathrm{U}}_{\mathrm{B}}+40\mathrm{J}\phantom{\rule{0ex}{0ex}}{\mathrm{U}}_{\mathrm{B}}-\left(40-25\right)\mathrm{J}\phantom{\rule{0ex}{0ex}}=15\mathrm{J}$

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

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