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Found in: Page 211

Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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

See the step by step solution

Step 1: Given data:

Work done, W = 25 J

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

Step 2: 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

Step 3: 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,

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

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