Respuesta :
Answer:
The speed of the car safely make the curve, V = 65.23 Km/h
Explanation:
Given,
The radius of the curve, r = 78 m
The designed speed of the curve, v = 85 km/h
= 23.61 m/s
The coefficient of static friction, μₓ = 0.3
The static friction of the curve is given by the relation,
Fₓ = μₓ η
The acceleration responsible for the static friction
aₓ = μₓ x g
Substituting the values in the equation
aₓ = 0.3 x 9.8
= 2.94 m/s²
The designed acceleration of the curve
a₀ = v²/r
= 23.61²/78
= 7.15 m/s²
The acceleration supported by the static friction, aₓ can be subtracted from the designed acceleration of the curve.
Therefore the net acceleration,
a = a₀ - aₓ
= 7.15 - 2.94
= 4.21 m/s²
The centripetal velocity associated with this acceleration is
a = V²/r
∴ V² = a x r
V = √(a x r)
=√ (4.21 x 78)
= 18.12 m/s
= 65.23 Km/h
Hence, the speed required by the car to safely make the curve is, V = 65.23 Km/h
