Answer :
The speed that will cause the car to slide as it travels around a level curve with a 34.7 m radius is 17.06 m/s (or) 61.416km/hr.
What is speed ?
In contrast to speed, velocity describes the rate and direction of an object's motion as it travels along a path. In other words, speed is a scalar quantity while velocity is a vector.
As the car rounds the curve, the amount of its acceleration is determined by v²/R.
where v is the vehicle's speed and R is the curve's radius Only the frictional force of the road on the tires, due to the horizontal nature of the road, allows for this acceleration. The Newton's second law's horizontal part is f=mv²/R. [tex]F_{N}[/tex] The vertical component of Newton's second law results in if f is the normal force of the road acting on the car and m is its mass[tex]F_{N}[/tex]=mg. The greatest amount of static friction is therefore determined by Eq.
[tex]f_{s.max} = \mu_{s} F_{N} =\mu_{s} mg\\[/tex]
Unless the vehicle sways, f ≤ [tex]\mu_{s}[/tex]mg. This means
V²/R = [tex]\mu_{s}[/tex]g ⇒ v ≤ [tex]\sqrt{\mu_{s}Rg}[/tex]
As a result, the top speed at which the vehicle can navigate the curve without slipping
[tex]V_{max}[/tex] = [tex]\sqrt{\mu_{s}Rg}[/tex] = [tex]\sqrt{(0.859)(34.7)(9.8)}[/tex]
[tex]V_{max}[/tex] = 17.06m/s = 61.416km/hr
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