Problem Statement:

A toy car weighing $0\mathrm{.}72$ lb has been released at the top of the track. The curved portion of the track is described by the equation

$r()=8(1-cos())$ ft$.$ When the car reaches a position of $=252,$ its speed is $30\mathrm{.}3f\frac{t}{s},$ and the radius of curvature of the track

is $8\mathrm{.}62951$ ft $.$ Neglecting the car's size and friction, determine the following for the instant in question.

Tip: The track is drawn to scale. Consider printing the figure, drawing the car at your value of $,$ then drawing the unit vectors

accordingly. You can enlarge the figure by clicking on it$.$ The answers depend on proper definition of the unit vectors.

The angle $=$

The angle $=$

$($i$.$e$.$ the angle between gravity and tangent; it will be obtuse if the car has already passed the

bottom of the track.$)$

The normal component of acceleration:

The tangential component of acceleration:

The net normal force on all wheels at the instant in question.

Finally, resolve the acceleration into cylindrical components:

The radial acceleration component, $a_r=$

The transverse acceleration component, $a_{}=$