First slide

Concept of potential energy

Question

The potential energy of a particle is determined by the expression $U = α (x^{2} + y^{2})$ , where $α$ is a positive constant. The particle begins to move from a point with coordinates (3, 3), only under the action of potential field force. Then its kinetic energy T at the instant when the particle is at a point with the coordinates (1, 1) is

Moderate

A

$8 α$
B

$24 α$
C

$16 α$
D

Zero

Solution

As the particle moves only under the action of conservative force, its mechanical energy must be conserved. So $ΔT + ΔU = 0$ (T stands for kinetic energy)
$\begin{array}{l} ΔT = - ΔU = U_{i} - U_{f} \\ = α (3^{2} + 3^{2}) - α (1^{2} + 1^{2}) = 16 α \end{array}$

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