1. The problem statement, all variables and given/known data A 1200 kg car rounds a banked curve of radius 70 m. If the banked angle is 12° and the car is travelling at 90 km/h, show that friction is necessary in order for the car to safely make the turn. 2. Relevant equations Force of gravity: Fg=m*g to calculate the normal force: opposite side of angle: Fncos(12°)=mg centripetal force: Fc=mv2/R Fc=Ff μ=Ff/Fn 3. The attempt at a solution So these are the things we know: m=1200kg R=70m θ=12° v=90km/h=25m/s car is travelling on a banked curve With this information we can start off by calculating the Fg=mg=(1200kg)*(9.8m/s2)=11760N The normal force can be calculated from: Fncos(12°)=mg Fn=11760N/cos(12°)= 12022.725N From here, I calculated the Fc: Fc=(1200kg)*(25m/s)/(70m)= 10714.286 N I think we are to assume that Fc=Ff, because its a banked curve? Im not entirely sure on this reasoning... some clarification would be appreciated :) so from here I calculated μ: μ=Ff/Fn=10714.286N/12022.725N= 0.89 END OF MY FIRST ATTEMPT _________________________________________ BEGINNING OF SECOND ATTEMPT (for this attempt I used another problem as a guide that I found online... not entirely sure of the explanation given at the end, I have a hard time visualizing it) I calculated the Force trying to pull the car down the bank: from the adjacent side: F=mgsin(12°)= (1200kg)*(9.8m/s2)sin(12)= 2445.041N The needed centripetal force: Fc=mv2/R= (1200kg)*(25m/s)2/(70m)= 10714.286N The component of Fc that is parallel to the road surface is: opposing side: Fc*cos(12°)=10480.153 N The difference between component of centripetal force parallel to the roadway and the force due to gravity component parallel to the roadway is: 10480.153 N- 2445.041 N= 8035.111N This force must be made up by friction, toward the center of the circle but parallel to the roadway surface. _____________________________ SO, if anyone could lend me a hand and let me know where I went wrong and which attempt better suites this type of problem that would be greatly appreciated! Thank you so much in advance!