The $2-$lb box slides on the smooth circular ramp. If the box has a velocity of $\backslash (30\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash )$ at $\backslash ($ A $\backslash ),$ determine the velocity of the box and normal force acting on the ramp when the box is located at $\backslash ($ B $\backslash )$ and C$.$ Assume the radius of curvature of the path at $\backslash ($ C $\backslash )$ is still $5$ ft $.$

$[$Use the Principle of work and energy$]$