Problem Statement:

In a facility that processes consumer shipments, certain packages are redirected by the track pictured. A motor $($not pictured$)$ is mounted below the flat, horizontal surface, and drives the arm to rotate and

push one package at a time around the curve. The curved portion of the track is described by the equation $r()=5(2+sin())ft.$ The package weighs $23$ lb $.$ Neglecting friction and the size of the

package, determine the following when $=25,{}^{}=6\mathrm{.}5ra\frac{d}{s}$ and ${}^{}=0\mathrm{.}3ra\frac{d}{s^2}$ :

Tip: The track is drawn to scale. Consider printing the figure, drawing the arm at your value of $,$ then drawing the unit vectors accordingly. The answers depend on proper definition of the unit vectors. You

can enlarge the figure by clicking on it$.$

Answers $($with units$)$:

The value of $r^{}$:$29\mathrm{.}455003f\frac{t}{s}$

The value of $r^{}$ :

The angle between the arm and the direction of package motion $($i$.$e$.$ the angle $)$:

The normal force between the package and the track:

The normal force between the package and the arm: