The problem: A concrete highway curve of 80 meters is banked at a 19 degree angle. What is the maximum speed with which a 1800kg rubber-tired car take this curve without sliding? (static coefficient of friction of rubber on concrete = 1)
So would I set up something like this?
The answer is 40.1m/s, but I get 31.6m/s. So I need help to figure out what I'm not getting. I have the force of gravity in the y direction equal to 16,679.0N and in the x direction it is equal to 5,743.0N. The max friction would equal the normal force since the coefficient is 1, so the max friction would equal the force of gravity in the y direction. Add the max friction and Fgx and I have 22,422.0N. That means I can have the force in the opposite direction before sliding, right? If so F=ma or F=m(v^2)/r so 22,422.0=(1800/80)v^2. That's how I got v=31.6m/s