Physics: Ahighway curves to the left with radius of curvature of 36 m and is banked at 26, so that cars can take this curve at higher speeds. consider a car of mass 1477 kg whose tires have a static friction coefficient 0.61 against the pavement.how fast can the car take this curve without skidding to the outside of the curve?

KN= 15 unitsNM= 20 unitsStep-by-step explanation:...

Ahighway curves to the left with radius of curvature

mikki93

15.01.2022

Explanation:

Given

radius of track $r=36\ m$

inclination $\theta =26^{\circ}$

mass of car $m=1477\ kg$

coefficient of kinetic friction $\mu =0.61$

From diagram

$N\cos \theta -f_r-mg=0---1$

Where N=Normal reaction

f_r=friction

$N\cos \theta +f_r\cos \theta =\frac{mv^2}{r}---2$

$f_r=\mu N----3$

From 1 2 and 3 we get maximum velocity without skidding

$v=\sqrt{gr}\times \sqrt{\frac{\tan \theta +\mu}{1-\mu \tan \theta }}$

$v=\sqrt{9.8\times 36}\times \sqrt{\frac{\tan 26+0.61}{1-0.61\cdot \tan 26}}$

$v=\sqrt{551.366}$

$v=23.78\ m/s$

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