A 10kg advertising sign is mounted to the roof of a car using magnets. These magnets are able to provide an attractive force between the sign and the roof of 100N. When the car is moving, wind loading applies a force (in Newtons) to the sign in the opposite direction to the velocity of 0.1(v^2), where v is the speed of the car in m/s.
The coefficient of static friction between the sign and the roof is static friction = 0.25.
(a) Calculate the highest constant speed the car can drive at without the sign sliding off the roof.
(b) Calculate the highest constant speed that the car can go around a corner with a radius of curvature of 50m
Adjust your answer for part (b) based on the assumption that the car tilts over on its suspension by an angle of 5 degrees.