If a curve with a radius of 90 m is properly banked for a car traveling 63 km/h, what must be the ?

Question

If a curve with a radius of 90 m is properly banked for a car traveling 63 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 98 km/h?

Jonathon Rolfson · Accepted Answer

Let:v0 be the ideal speed for the curve, a be the banking angle,r be the radius,g be the acceleration due to gravity,v be the increased speed,u be the necessary coefficient of static friction. 63 km/hr = 63 / 3.6 = 17.5 m/sec.98 km/hr = 98 / 3.6 = 27.222 m/sec.When the curve is ideally banked:v0^2 = rg tan(a)rg tan(a) = 17.5^2tan(a) = 17.5^2 / (90 * 9.81)= 0.3469The coefficient of friction required for a car going at speed v is:u >= [ v^2 – rg tan(a) ] / [ v^2 tan(a) + rg ]Putting u = 17.5 m/su >= [ v^2 – v0^2 ] / [ v^2 tan(a) + rg ]u >= [ 27.222^2 – 17.5^2 ] / [ 27.222^2 * 0.3469 + 90 * 9.81 ]u >= 0.381.

Jonathon Rolfson · Answer

trick question? does it especially say static friction? mu N is friction stress, mu N r is frictional torque. so if friction is = to the stress outward, then mu N r = m a r

Natalie Goodwin

If a curve with a radius of 90 m is properly banked for a car traveling 63 km/h, what must be the ?

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