Question

A 1000 kg car has a maximum power output of 120 hp. How steep a hill can it climb at a constant speed of 74 km/h if the frictional forces add up to 600 N?

Answer 1

From the force diagram for the car, we have:

            x-component:   F – F_fr= mg sin q.

Because the power output is P = Fv, we have

            (P/v) – F_fr= mg sin q.

      The maximum power determines the maximum angle:

            (P_max/v) – F_fr= mg sin q_max ;

            (120 hp)(746 W/hp)/[(74 km/h)(1000 m/3600 s] – 600 N =

                                    (1000 kg)(9.80 m/s²) sin q_max ,

      which gives sin q_max = 0.383,orq_max = 22.52 degree