A person is riding a motorcycle in a hollow, transparent plastic sphere in a horizontal circle. The radius is 13 m, the mass of the motorcycle is 40 kg, and the mass of the person is 70 kg. The speed is 15 m/s.
a) What is the minimum coefficient of static friction for the tires to not slip?
b) What total force does the motorcycle exert on the rider?
The Attempt at a Solution
First I thought there would be a force of weight pulling the motorcycle down, a normal force of the sphere on the motorcycle, and a force of friction perpendicular to the normal force/opposite the direction of motion. In this case, wouldn't the normal force be equal to mv^2/r? But then how does this tell you when the tires will slip?
Then I was looking at some diagrams of cars traveling in circles, and the diagram showed the friction force going to the center/perpendicular to the direction of motion. If this is the case, then wouldn't mv^2/r be equal to the sum of the normal force and the friction force? But then how do you know what the normal force even is?