First slide

Concept of potential energy

Question

The potential energy of a configuration is expressed as $U(x,y)= 5 x^{2} y$ . The force acting the particle at (1m,1m,1m) is

Moderate

A

$-5(\hat{i} + \hat{j})$
B

$-10 \hat{i} - 5 \hat{j}$
C

$- 5 \hat{i} -10 \hat{j}$
D

$10 \hat{i} + 5 \hat{j}$

Solution

$\begin{array}{l} \vec{F} = \frac{- \partial U}{\partial x} \hat{i} - \frac{\partial U}{\partial y} \hat{j} - \frac{\partial U}{\partial z} \hat{k} \\ \vec{F} = - 10 x \hat{y} - 5 x^{2} \hat{j} - 0 \hat{k} \\ A t (1, 1, 1) \vec{F} = - 10 \hat{i} - 5 \hat{j} \end{array}$

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