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## Homework Statement

The original problem was as follows:

A civil engineer wishes to redesign a curved roadway in such a way that a car will not have to rely on friction to round the curve without skidding. In other words, a car moving at the designated speed can negotiate the curve even when the road is covered with ice. Such a ramp is usually banked, meaning the roadway is tilted toward the inside of the curve. Suppose the designated speed for the ramp is to be 11.2 m/s (25.1 mi/h) and the radius of the curve is 34 m. At what angle should the curve be banked?

I am getting a conflict if I do this problem in different ways:

## Homework Equations

I can resolve N into its vertical and horizontal components. Since the car is supposed to be in vertical equilibrium,

[tex]\begin{array}{l}

N\cos \theta - mg = m{a_{ycar}} = 0\\

or\quad N\cos \theta = mg

\end{array}[/tex]

If I do the problem the second way:

I resolve mg into the component along the plane and the component perpendicular to the plane:

Then

[tex]\begin{array}{l}

N - mg\cos \theta = m{a_{y'}} = 0\\

or\quad N = mg\cos \theta

\end{array}[/tex]

**WHAT'S WRONG WITH MY REASONING!**