pezmachine9000
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A section of a high speed test track is circular with a radius of curvature R = 1860 m.
At what angle of θ should the track be inclined so that a car traveling at 61.0 m/s (136 mph) would keep moving in a circle if there is oil on that section of the track, i.e., it would not slip sideways even with zero friction on that section. (Hint: The car's vertical acceleration is zero.)

A Section Of A High Speed Test Track Is Circular With A Radius Of Curvature R 1860 M At What Angle Of Θ Should The Track Be Inclined So That A Car Traveling At class=

Sagot :

Using Newton's second law, the car is experiencing a net force parallel to the banked curve such that

[tex]mg \sin(\theta) = \dfrac{mv^2}r \implies \sin(\theta) = \dfrac{v^2}{rg}[/tex]

where [tex]v[/tex] is the tangential speed of the car and [tex]r[/tex] is the radius of the curve. Solve for [tex]\theta[/tex] :

[tex]\sin(\theta) = \dfrac{\left(61.0\frac{\rm m}{\rm s}\right)^2}{(1860\,\mathrm m)g} \approx 0.204 \implies \theta = \sin^{-1}(0.204) \approx \boxed{11.8^\circ}[/tex]

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