Question

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

• A. $8\alpha$
• B. $24\alpha$
• C. $16\alpha$
• D. Zero

Answer 1

The correct option is C $16\alpha$

As the particle moves only under the action of conservative force, its mechanical energy must be conserved. So $\Delta T+\Delta U=0$ ($T$ stands for kinetic energy)

or $\Delta T=-\Delta U=\Delta U_i-{\Delta }_f$

$=\alpha (3^2+3^2)-\alpha (1^2+1^2)=16\alpha$