Need help finding the banking angle of a curved road please

[Coronita]

A highway curve of radius 500m is designed for traffic moving 90 km/hr. What is the correct banking angle of the road?




I made a force diagram and wrote out the sums of the forces in the x and y then tried to solve for theta I got:

sumFx= -nsin theta=ma=mv^2/r

and

sumFy= -mg+ncos theta=0 --> n=mg/cos theta

then substituted n into the first


I ended up getting 89.6 degrees though...did I just make an algebra mistake or did I go about it the wrong way?

 

[Doc Al]

I suspect you made an arithmetic mistake. Show the final steps where you solved for theta.

 

[AsuraSky]

Your net Fx is incorrect, it should be Nsin(theta)=mv^2/R not -Nsin(theta)=mv^2/R

 

[Coronita]

mg/cos(theta)*sin(theta)=mv^2/r

mg sin(theta)/cos(theta)=m(90^2)/500


10tan(theta)=8100/500

tan(theta)=162

theta=arctan 162

theta=89.6

 

[Doc Al]

mg/cos(theta)*sin(theta)=mv^2/r

mg sin(theta)/cos(theta)=m(90^2)/500

Wrong units for the speed. Convert km/h to m/s.

 

[Coronita]

Thanks! You're right on that one but now I get 89.8 degrees :P

 

[Doc Al]

Thanks! You're right on that one but now I get 89.8 degrees :P

What's the correct speed?