If a curve with a radius of 88m is perfectly banked for a car traveling 75km/h, what must be the coefficient of static friction for a car not skid when traveling at 95 km/h?

Answer 1

change velocities to m/s

Then, sketch the bank and force vectors parallel to the bank.

1) mg*sinTheta=mv^2/r * cosTheta

where v=75km/hr in m/s
solve for tan theta (sin/cos).

verify that. Now, you increase speed, same angle.

mg*sinTheta+mu*mg*cosTheta=mv^2/r * cosTheta

so find mu. How is the easy way? divid e by cos theta , you know tan theta.
v= new speed (95 in m/s), solve for mu.

Answer 2

Can you show me step by step with the numbers in there? I am confused..

Answer 3

-0.327

Answer 4

You forgot the normal force due to centripetal force.
mg*sinTheta+mu*mg*cosTheta+mu*v^2/r*sinTheta=mv^2/r * cosTheta
m cancels out so the equilibrium is stated in acceleration.
mu= ((v^2/r)*cosTheta-g*sinTheta)/(g*cosTheta+(v^2/r)*sinTheta)