Max Speed of Car on Wet Ramp Turn at 20° Bank

[Balsam]

Homework Statement

A car is making a turn on a wet highway ramp. The coefficient of static friction between the tires and the road is 0.25. Determine the maximum speed at which the car can safely negotiate a turn of radius 200m with a banking angle of 20 degrees.
radius= 200m
μs=0.25
angle(θ)=20°

Homework Equations

Fs=μs(Fn)

Fc=mv/r

The Attempt at a Solution

I tried solving this by drawing an FBD. I drew my x and y axes so they could follow the incline and the normal and friction forces would run along the axes. The only force I broke down into components was Fg. I used the first formula to solve for Fs by plugging in the given coefficient of static friction and plugging in +mgcosθ for Fn. I got Fs=0.25(mucosθ). Then, I plugged that into the second formula with all other given values. I divided out my 'm' variables, and then isolated for 'v'. The answer I got was 22.14609185m/s. The correct answer is 36m/s. I don't know what I did wrong.

 

[ehild]

Homework Statement

A car is making a turn on a wet highway ramp. The coefficient of static friction between the tires and the road is 0.25. Determine the maximum speed at which the car can safely negotiate a turn of radius 200m with a banking angle of 20 degrees.
radius= 200m
μs=0.25
angle(θ)=20°

Homework Equations

Fs=μs(Fn)

Fc=mv/r

The second formula is wrong, check.

The Attempt at a Solution

I tried solving this by drawing an FBD. I drew my x and y axes so they could follow the incline and the normal and friction forces would run along the axes. The only force I broke down into components was Fg. I used the first formula to solve for Fs by plugging in the given coefficient of static friction and plugging in +mgcosθ for Fn. I got Fs=0.25(mucosθ). Then, I plugged that into the second formula with all other given values. I divided out my 'm' variables, and then isolated for 'v'. The answer I got was 22.14609185m/s. The correct answer is 36m/s. I don't know what I did wrong.

 

[Balsam]

The second formula is wrong, check.

I typed it wrong, but in solving the problem, i used mv^2/r

 

[ehild]

Without seeing your FBD and work in detail, we can not help you. The car goes along a horizontal circle, so the centripetal force is horizontal, while the friction acts along the slope. They are not equal. And friction is not the only force that keeps the car on track.