You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 1.00 × 102 mi/h without the aid of friction. You estimate that when elements like downforce and grip in the tires are considered the cars will round the turns at a maximum of 175 mi/h. Find the banking angle necessary for the racecars to navigate these turns at 1.00 × 102 mi/h and without the aid of friction or other forces.

Question

caozeyuan · Answer

@Poeticalto take a look pls!

caozeyuan · Answer

I am Chinese so I have NEVER dealt with lb, ft, mi and other useless units

caozeyuan · Answer

Seriously, why don't human agree on using SI unis?

anonymous · Answer

Units doesn't really matter in any problem, as long as you understand what is going on and how to solve it.
Anyways, I don't know if this is right or not, but I'm using this equation: v^2=r*g*tan(theta)
Divide by rg to solve for tan(theta)
(v^2)/(r*g)=tan(theta)
now take the tan inverse of both sides.
tan^-1((v^2)/(r*g))=tan(tan^-1(theta))
Tan and tan inverse cancel on the right side, so all you have is theta, which is the angle you're solving for.
Now you can plug numbers in. You have the velocity (102), the radius (1000) and gravity (9.8 or 9.81 depending on whatever your problem wants)
theta=tan^-1((102^2)/(1000*9.8))
theta=46.712 degrees

Again, I don't know if that's right or not, but I hope that helps. Mass shouldn't be affected by this, but I don't know where the max speed comes in.