1. The problem statement, all variables and given/known data To measure the combined force of friction (rolling friction plus air drag) on a moving car, an automotive engineering team you are on turns off the engine and allows the car to coast down hills of known steepness. The team collects the following data: (1) On a 2.70° hill, the car can coast at a steady 20 m/s. (2) On a 5.50° hill, the steady coasting speed is 30 m/s. The total mass of the car is 1150 kg. (a) What is the magnitude of the combined force of friction at 20 m/s (F20) and at 30 m/s (F30)? (b) How much power must the engine deliver to drive the car on a level road at steady speeds of 20 m/s (P20) and 30 m/s (P30)? (c) The maximum power the engine can deliver is 46 kW. What is the angle of the steepest incline up which the car can maintain a steady 20 m/s? (d) Assume that the engine delivers the same total useful work from each liter of gas, no matter what the speed. At 20 m/s on a level road, the car gets 14.2 km/L. How many kilometers per liter does it get if it goes 30 m/s instead? 2. Relevant equations W(ext) = Delta E(mech) + Delta E(therm) Delta E(mech) = Delta K + Dela U Delta E(therm) = F(friction) * s 3. The attempt at a solution Parts c and d are the the ones I can't figure out. For part a, I used W(ext) = Delta E(mech) + Delta E(therm). Since there are no external forces, Delta E(therm) = - Delta E(mech). Delta E(mech) = Delta K + Delta U, and since the car is coasting at a constant speed, Delta K is 0. I set the gravitational potential energy to be 0 at the top of the hill, so Delta U = U(final), which is -mgssin(theta) if s is the length of the hypotenuse of the incline. So then Delta E(therm) = mgssin(theta), and since Delta E(therm) = F(friction) * s, F(friction) = mgsin(theta). Plugging the numbers, I got that the frictional force at 20 m/s was 531N and at 30 m/s was 1080N, which was correct. For b, I just used P = F * v to find the power at 20 m/s and 30 m/s. For c, I plugged the equation for F into the Power equation, which gave me P = mgsin(theta) * v. Then I solved for theta, and got theta = arcsin(Power / (mgv)). I tried plugging in 46000 W for power along with the other given information to get theta = 11.8 degrees, and I also tried plugging in my answer for b at 20 m/s in, neither of which were right. For d, I'm not really sure where to start, or what equations/relationships to use. Maybe I could use the ratio between the power needed at 20 m/s and 30 m/s somehow? Any help would be appreciated.