The potential energy of a particle is determined by the expression U=α(x2+y2), where α is a positive constant. The particle begins to move from a point with the coordinates (3,3)( m ), 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)( m ) is 32 α / n. Find n.

Question

The potential energy of a particle is determined by the expression U=α(x2+y2), where α is a positive constant. The particle begins to move from a point with the coordinates (3,3)( m ), 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)( m ) is 32 α / n. Find n. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

U =α( x 2+ y 2) Total Mechanical energy = KE + PE =0+α(32+32) =18 α At x =1,1 PE =α(12+12)=2 α KE + PE = C T +2 α =18 α T =16 α n =2

U=α(x2+y2) Total Mechanical energy =KE+PE =0+α(32+32) =18α At x=1,1 PE=α(12+12)=2α KE+PE=C T+2α=18α T=16α n=2

$U = α (x^{2} + y^{2})$
Total Mechanical energy $= K E + PE$
$= 0 + α (3^{2} + 3^{2})$
$= 18 α$
At $x = 1, 1$
$PE = α (1^{2} + 1^{2}) = 2 α$
$K E + PE = C$
$T + 2 α = 18 α$
$T = 16 α$
$n = 2$