First slide

Concept of potential energy

Question

A conservative force $\vec{F} = (- a x + b x^{2}) \hat{i}$ is acting on a particle where a ,b are constants. The change in potential energy when particle is displaced from x=3m to x=4m (Take U=0 at x=0)

Moderate

A

$\frac{37 b}{3} - \frac{7 a}{2}$
B

$16 b - 4 a$
C

$7 b - a$
D

$\frac{7 a}{2} - \frac{37 b}{3}$

Solution

$\begin{array}{l} \int d U = - \int \vec{F} \cdot \vec{d r} \\ \int d U = - \int_{3}^{4} (- a x + b x^{2}) \vec{i} \cdot (d x \vec{i} + d y \vec{j} + d z \vec{k}) \\ ΔU = - [\begin{matrix} \int_{3} - a x d x + \int_{3}^{4} b x^{2} d x \\ 3 & 3 \end{matrix}] \\ ΔU = + {[\frac{a x^{2}}{2}]}_{3}^{4} - b {[\frac{x^{3}}{3}]}_{3}^{4} \\ ΔU = \frac{7 a}{2} - \frac{37 b}{3} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App