A 1235.2 kg car climbs a 9.4° slope at a constant speed of 94.4 km/h. Assuming that air resistance may be neglected, at what rate (in kW) must the engine deliver energy to the drive wheels of the car



Answer :

Answer:

51.8 kW

Explanation:

Power is equal to work over time, and work is equal to force times distance. Thus we can show that power is equal to force times velocity. By drawing a free body diagram and applying Newton's second law of motion, we can find the required force to move the car up the slope.

There are 3 forces on the car:

Weight force mg pulling down,

Normal force N pushing up perpendicular to the slope,

and applied force F pushing up parallel to the slope.

Sum of forces in the parallel direction:

∑F = ma

F − mg sin θ = 0

F = mg sin θ

F = (1235.2 kg) (9.8 m/s²) (sin 9.4°)

F = 1977 N

The speed of the car is 94.4 km/h. Converting to m/s:

v = 94.4 km/h × (1000 m/km) × (1 h / 3600 s)

v = 26.22 m/s

So the power is:

P = Fv

P = (1977 N) (26.22 m/s)

P = 51,843 W

P = 51.8 kW