Question

A car rounds a banked curve where the radius of the curvature is 100m, the banking angle is 10^o and the coefficient of the static friction is 0.10. Determine the range of speeds the car can travel without slipping up or down the bank.

Answer 1

going slower, the friction force is In the case of a car down toward the bottom of the bank. The freebody diagram in this case is shown below going to oppose the car's sliding Faformal cos θ Norma, sin θ FNormal friction Sin g 2 friction sin θ friction COS θ F. werghtmg

We now add up the forces in thex and v directions. ma rmv mv mv NcoFiction sine-Fweighe - mg (cos θ + uSin6) Substituting for N in the other equation, mv g(sin- cos cos@+ usin θ (100 m)(9.8m/s)(sin10-(0.10)cos10*) cos10+(0.10)sin 10 23.7 m/s

To solve for the maximum speed the car can travel at without sliding off the top of the track: In this case friction is going to be working to oppose the sliding off the car upward, so the free-body diagram is as below: ormat Sin e ,formal COS θ FNorma Ffriction sin θ F. friction Cos e Fweighe mg

Again, the equations are developed as below ma F _mv mv fre ion mv cost_ which gives N-cose-μ sin θ Substituting for N in the other equation, mv mv or (sin θ + μ cos@)-- or g(sin θ + μ cos9) v2 rg (sin θ + μ cos θ) cos- lSind (100 m) (9.8 m/s )(sin10 +(0.10)cos10°) cos10 (0.10)sin 10 - 60.6 m/s