Question

If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 105 m radius curve banked at 15°. Correct: Your answer is correct. m/s (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 30.0 km/h?

Answer 1

a)      Calculate Initial speed

Given –

Radius(r) = 105m

Angle (ϴ) = 15⁰

By using formula,

Weight component due to gravity = Component of centrifugal force

mgsinϴ = (mv²/r) cosϴ

Now calculate v, so take square root on right hand side

v = √ (9.8m/s²)*(105m)*(tan15⁰)

v = 16.60 m/s

v = 17m/s

The initial speed of car is v = 17m/s

b)      Calculate minimum coefficient of friction needed for a frightened drive to take the same curve at 30.0km/h.

Convert speed 30.0km/h into m/s

(30.0km/h)(1000m/s)(h/3600) = 8.333m/s

Weight component due to gravity = Component of centrifugal force + friction

mgsinϴ = (mv²/r) cosϴ+ u*[(mv²/r) sinϴ+mgcosϴ]

u = [gsinϴ - (v²/r) cosϴ] / [(v²/r) sinϴ + gcosϴ]

u = [(9.8m/s²)*sin15⁰ – ((8.333)²/105)*cos15⁰ / ((8.333)²/105)*sin15⁰+[(9.8m/s²)*cos15⁰

u = 0.20

The minimum coefficient of friction is u = 0.20

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