First slide

Concept of potential energy

Question

The potential energy of a 2kg particle is given by $U = (a x + b y) J$ , Where a and b constants, x and y are coordinates of particle in metre. Initially the particle is at rest and at (4a,4b).The coordinates after 2 seconds is $(x a, x b)$ , where x is______

Moderate

Solution

$\begin{array}{l} \vec{F} = \frac{- \partial U}{\partial x} \hat{i} - \frac{\partial U}{\partial y} \hat{j} \\ \vec{F} = - a \hat{i} - b \hat{j} \\ a_{x} = \frac{F_{x}}{m} = - \frac{- a}{2}; a_{y} = \frac{F_{y}}{m} = \frac{- b}{2} \\ S_{x} = \frac{1}{2} a_{x} t^{2} = \frac{- 1}{2} \times \frac{a}{2} \times 4 = - a \\ S_{y} = \frac{1}{2} a_{y} t^{2} = \frac{1}{2} \times (\frac{- b}{2}) 4 = - b \\ ∴ Find coordinates \\ = [(4 a - a), (4 b - b)] \\ = (3 a, 3 b) \end{array}$

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