Banked curve We will analyze the physics of a car going around a highly banked curve: The banking angle is O and the radius of the turn is R. The car is moving at a speed v that you must determine (as a function of 0, R, m, g, and, in a later part, Us). Part A. No friction Assuming there is no friction (imagine the road is covered with ice if you'd like): 1. Draw the free body diagram for the car. 2. Split the forces into components along a normal (not tilted) x-y coordinate system, and use Newton's law(s) in the y direction to solve for the normal force (from the road on the car), in terms of m, g and 0. 3. Use Newton's law(s) in the x direction to solve for the car's speed v, in terms of g, R and 0.Part B. Friction, high speed. Put friction back into the problem: there is static friction with coefficient us between the tires and the road. 1. Draw the free body diagram for the car. Assume the car is driving faster than the speed v from part A3. Think carefully about the direction of the static friction! 2. We want to solve for the maximum speed Vmax the car can round the curve without slipping. Split the forces into components along a normal (not tilted) x-y coordinate system, and use Newton's law(s) in the y direction to solve for the normal force (from the road on the car), in terms of m, g, 0 and us. 3. Use Newton's law(s) in the x direction to solve for the car's speed Vmax, in terms of g, R, 0 and us.Part C. Friction, low speed Repeat part B, assuming the car is driving slower than the speed v from part A. 1. Draw the free body diagram for the car. Think carefully about the direction of the static friction! 2. Solve for the normal force and the minimum speed Vmin. If you look carefully at your equations, you should be able to just take your work from part B and adapt it with a couple of strokes of a pen. You don't need to re-solve everything!centripetal force N, normal force Fg:mg gravitational force Explanation As there is no frictional force only two types of force will be there. Step 22' 3 Normal force in y direction Fy = 0 = NCOSE} mg Explanation In the y direction, there is no component of friction as there is no friction or other forces. Step 3:3 2 . Normal force In x direction FX 2 mVT = Nsml here the centripetal force is countering the horizontal component of the normal force. Explanation In the x direction, the only component is centripetal force. part B 1) the F.B.D is shown in the first 2) the normal force N mg Assin O+cos 0 3) maximum velocity V(gR) sin 0-Us V max Assin O+cos 0