Answer:
The speed the car must travel to experience no friction is approximately 16.9 m/s
Explanation:
The car and road data are;
The mass of the car, m = 1,200 kg
The radius of the road, r = 80 meters
Given that the angled at which the road is banked, θ = 20°
The friction between the tires and the road, at the required speed, [tex]\mu_s[/tex] = 0, No friction
We have;
[tex]\dfrac{v^2}{r \cdot g} = \dfrac{\left( sin \, \theta + \mu_s \cdot cos \, \theta \right)}{\left( cos\, \theta + \mu_s \cdot sin\, \theta \right)}[/tex]
Where [tex]\mu_s[/tex] = 0, we get;
[tex]\dfrac{v^2}{r \cdot g} = \dfrac{ sin}{ cos} = tan \, \theta[/tex]
∴ v² = r·g·tan(θ)
Where;
g = The acceleration due to gravity ≈ 9.81 m/s²
v = The speed at which the car travels
∴ v² = 80 m × 9.81 m/s² × tan(20°) = 285.64384 m²/s²
v = √(285.64384 m²/s²) ≈ 16.9 m/s
The speed with which the car must travel to experience no friction, v ≈ 16.9 m/s
