A highway curves to the left with radius of
1 answer:
Answer:
29.131 m/s
Explanation:
Draw a free body diagram. There are three forces: weight force mg pulling down, normal force N pushing perpendicular to the road, and friction force Nμ pushing parallel to the road downwards.
Sum of forces in the centripetal direction:
∑F = ma
N sin θ + Nμ cos θ = m v² / r
N (sin θ + μ cos θ) = m v² / r
Sum of forces in the vertical direction:
∑F = ma
N cos θ − Nμ sin θ − mg = 0
N (cos θ − μ sin θ) = mg
N = mg / (cos θ − μ sin θ)
Substituting:
mg (sin θ + μ cos θ) / (cos θ − μ sin θ) = m v² / r
g (sin θ + μ cos θ) / (cos θ − μ sin θ) = v² / r
v² = gr (sin θ + μ cos θ) / (cos θ − μ sin θ)
Plugging in values:
v² = (9.8 m/s²) (39 m) (sin 30° + 0.72 cos 30°) / (cos 30° − 0.72 sin 30°)
v = 29.131 m/s
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