Solved: A rider on a Ferris wheel moves in a vertical
Chapter 5, Problem 5ED(choose chapter or problem)
To negotiate a flat (unbanked) curve at a faster speed, a driver puts a couple of sand bags in his van aiming to increase the force of friction between the tires and the road. Will the sand bags help?
The banking of curves can reduce the chance of skidding. The normal force exerted by a banked road, acting perpendicular to the road, will have a component toward the center of the circle (Fig. 5-14), thus reducing the reliance on friction. For a given banking angle \(\theta\), there will be one speed for which no friction at all is required. This will be the case when the horizontal component of the normal force toward the center of the curve, \(F_{N} \ \sin \theta\) (see Fig. 5-14), is just equal to the force required to give a vehicle its centripetal acceleration-that is, when
\(F_{N} \ \sin \theta=m \frac{v^{2}}{r}\) [no friction required]
The banking angle of a road, \(\theta\), is chosen so that this condition holds for a particular speed, called the “design speed.”
Equation Transcription:
FN sin
FN sin = m
Text Transcription:
theta
FN sin theta
FN sin theta = m v^2/r
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