Question
need help on these problems
1. Slippery Road. A banked, circular highway curve was designed and constructed with a radius of curvature R= 200 m and banking angle to accommodate traffic moving at the speed limit of 60 km/h. Suppose you are late for class and want to speed at 100 km/h around the curve. What minimum coefficient of friction do you require between your tires and the road that pwill allow you to speed around the turn without skidding off the side of the road? (Assume that the weight of your car remains evenly distributed on all four tires, and there is no negative lift due to spoilers or other performance-enhancing features of your car.) 2. Extinction-Level Event. Buried underneath Mexico's Yucatán Peninsula is the Chicxulub crater, more than 180 km in diameter. The impact that created this crater released an estimated energy equivalent to 100 Teratons of TNT (4.2x1023 J), and has been implicated in causing the extinction of the dinosaurs 65 million years ago. Let's assume that the object responsible for this event was a sphere of rock with density of 3 g/cm3 (typical for asteroids and comets), and it entered Earth's atmosphere at a speed of 30,000 m/s (comparable to Earth's orbital speed around the Sun). Assume also that atmospheric drag did not slow the object down significantly before impact (see part b). a. What was the estimated mass (in kg) and diameter (in m) of the object? Show all of your work!
Explanation / Answer
1] banking angle theta = arctan(v^2/rg) = arctan((60*5/18)^2/(200*9.8)) = 0.1408 rad
we know that, Vmax = sqrt[rg(sin theta + u cos theta)/(cos theta - u sin theta)]
(100*5/18)^2 = 200*9.8*[ sin 0.1408 + u cos 0.1408]/[cos 0.1408 - u sin 0.1408]
771.6 = 1960 [ 0.1403+0.9901u]/[0.9901-0.1403u]
solving for u, u = 0.239 which is close to 0.24 answer
