pezmachine9000
Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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]

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.