a car drives around a curve with radius 410 m at a speed of32m/s. The road is ba

Question

a car drives around a curve with radius 410 m at a speed of32m/s. The road is banked at 5 degree. the mass of car is 1400kg. a) what is the frictional force on the car? b) at what speed could you drive around this curve sothat the force of friction is almost zero? a car drives around a curve with radius 410 m at a speed of32m/s. The road is banked at 5 degree. the mass of car is 1400kg. a) what is the frictional force on the car? b) at what speed could you drive around this curve sothat the force of friction is almost zero?

Explanation / Answer

Let n= normal force on car =5 degrees bank R=radius=410m v=32m/s f=frictional force m=car mass=1400kg Sum of forces in x direction gives: nsin+f=mv2/R nsin=mv2/R-f  ................................................(1)
Sum of forces in y gives: ncos-mg=0 ncos=mg    .......................................................(2) Dividing (1) by (2) and solving for f yields: f=mv2/R-mg(tan) Substituting values: f=2296N (b) Find v such that f is almost 0. In this case mg(tan)=mv2/R v2=Rgtan v=18.75m/s v2=Rgtan v=18.75m/s

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