HW$16\mathrm{.}2-$ The $0\mathrm{.}2-kg$ ball is propelled through a smooth

vertical tube whose shape is defined by $r=(0\mathrm{.}6sin)m,$ is

in radians. The angle is given by $=(t^2)rad,$ where $t$ is in

seconds. When $=45,$ find:

The angle $$ between hat$(u{)}_r($the unit vector in the radial

direction$)$ and hat$(u{)}_T($the unit vector in the direction that is

tangent to the path or the particle$).$

The non$-$zero components of vec$(v)$ and vec$(a)$

The directions of hat$(u{)}_r,$hat$(u{)}_{},$ and vec$(a)$

The normal force between the tube and the ball

The force acting on the ball $($tHe force propelling it through

the tube$).$ answers are given but show work

$=45$

$F_N=2\mathrm{.}37N$

$F=2\mathrm{.}72N$