- #1
vadiraja
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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!