5.10/20 points | Previous Answers Tipler6 5.P.097. Ask Your Teacher My Notes Que

Question

5.10/20 points | Previous Answers Tipler6 5.P.097. Ask Your Teacher My Notes Question Part Points Submissions Used A curve of radius 24 m is banked so that a 940 kg car traveling at 43.2 km/h can round it even if the road is so icy that the coefficient of static friction is approximately zero. You are commissioned to tell the local police the range of speeds at which a car can travel around this curve without skidding. Neglect the effects of air drag and rolling friction. If the coefficient of static friction between the road and the tires is 0.300, what is the range of speeds you tell them?

I got the V Maximum which is 58.32 Km/h, I need the V Minimum please.

Explanation / Answer

43.2 km/h = 12 m/s

The normal force has increased to mgcos where is the angle between the resultant force on the car Fr and the normal to the track surface. Fr itself is m((V²/r)²+g²) and its angle from the vertical ß = arctan(V²/rg).
Letting the bank angle of the track be ,
= ß- and putting the rest of it together,
µ = tan
ß = + and
V² = rg*tanß
Using your numbers,
= arctan(12²/(24*9.81)) = 31.45°
= arctan(0.3) = 16.7°
ß = 48.15° and finally,

V = (rgtanß) = 16.21 m/s = 58.36 km/hr

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