Max Speed for Car on Concrete Curve of Radius 80.0m, 19.0^\circ Angle

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SUMMARY

The maximum speed for a 1900 kg rubber-tired car navigating a banked concrete curve with a radius of 80.0 m and a 19.0° angle is calculated using the formula v(max) = sqrt(rg * u(coeff. static friction)). With a static coefficient of friction of 1.0, the correct maximum speed is determined to be 28.8 m/s. The initial attempts using v = sqrt(rg * tan(theta)) were incorrect due to misapplication of the formulas. Properly analyzing the forces through a free body diagram is essential for accurate calculations.

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Homework Statement



A concrete highway curve of radius 80.0 m is banked at a 19.0^\circ angle.

What is the maximum speed with which a 1900 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)

The Attempt at a Solution



I used the equation v = sq rt (rg*tan(theta)) but that didn't work, so I used
v(max) = sq. rt. (rg*u(coeff. static friction)) and got 28.8 m/s2, but that didn't work either.

If anyone can tell me what I'm missing or went wrong, I'd greatly appreciate it.
 
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If you are trying to use some formula directly, it is the wrong formula.
If you have drawn free body diagram and then tried to get the formula, you have missed something. Show your attempt.
 
I'm not really sure how I should approach the problem. Can you tell me how I can start?
 

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