How do I answer these physics questions and what answer should I get?

Question

You want to design the automobile racing circuit in Los Angeles to attract tourists to boost

economy during Spring. First, you design the banked road for the racing cars to speed at 100mph

for a circular circuit of radius 1000 m. If you want to allow the speed of racing cars up to 200

mph, how much of the friction between the tire and the road should be added to banked road?

(a) Draw the free-body diagram with all the forces acting on a race car without friction.

(b) Set the equations of motion for the race car in your coordinate system.

(c) Find the banking angle for a speeding car at 100 mph.

(d) Include frictional force to your free-body diagram.

(e) Find the minimum coefficient of static friction to allow the speed of 200mph.

Answer 1

Hi Mike I.,

Why the confusion? Your instructor left you detailed steps to solve this one. You must first apply the equation for uniform circular motion a = v^2/r to get that value for a. Then decompose it (via F=ma; carry the m of the car passively through all the calculations), in addition to the static force of gravity on the car, and solve for the banking angle of the track. The banking angle is the angle for which the net lateral force in the plane parallel to the banked track surface (as in the figure) is zero. That makes the car easy to steer. Now recalculate the acceleration required for 200 mph, and decompose it and gravity (as above) at the same banking angle as you found for 100 mph. There will be a substantial unbalanced force "laterally"; relate that to the force perpendicular to the track surface to get your required coefficient of friction. Note that the "down" force on the car increases slightly as the speed increases, due to the banking of the track; the "circular" acceleration vectors a bit into it. But you'll still be losing rubber way faster!

-- Cheers, --Mr. d.