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ArbitrLikvidat [17]
3 years ago
5

How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius

110 m at a speed of 101 km/h
Physics
1 answer:
mixas84 [53]3 years ago
6 0

The magnitude of static friction is

<em>f</em> = <em>mv</em> ²/<em>r</em>

(i.e. the net force acting on the car parallel to the road points toward the center of the curve)

while the net vertical force must be

∑ <em>F</em> = <em>n</em> - <em>mg</em> = 0

because the car is otherwise in equilibrium. Then

==>   <em>n</em> = <em>mg</em>

==>   <em>f</em> = <em>µn</em> = <em>µmg</em> = <em>mv</em> ²/<em>r</em>

==>   <em>µ</em> = <em>v</em> ²/(<em>rg</em>)

We have

<em>v</em> = 101 km/h ≈ 28.1 m/s

<em>r</em> = 110 m

<em>g</em> = 9.80 m/s²

so that

<em>µ</em> = (28.1 m/s)² / ((110 m) <em>g</em>) ≈ 0.730

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