Posted by **Mike Joseph** on Saturday, June 16, 2012 at 5:20pm.

A 1400 kg car rounds a curve of 57 m banked at an angle of 14 degrees

If the car is traveling at 98 km/h, will a friction force be required? If so, in what direction?

May someone please walk me through this problem step by step? Thank you

- Physics of Vehichle -
**Elena**, Sunday, June 17, 2012 at 8:09am
Let the x-axis point toward the center of curvature and the y-axis point upward. Use Newton’s second law

ΣFy = N• cos θ = mg, N

ΣFx = N• sin θ = m•v²/R,

Dividing the 2nd equation by the 1st equation, we obtain

tan θ = v² /R•g

v=sqrt(R•g•tan θ)=sqrt(57•9.8•tan14)=11.8 m/s,

V = 98 km/h =98000/3600 =27.2 m/s

V>v => the friction force is required (directed to the center of the curvature)

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