Question

A 710 kg car drives at a constant speed of 23 m/s. It is subject to a drag force of 500 N. What power is required from the car's engine to drive the car

a) on level ground?

b) up a hill with a slope of 2.0°?

Answer 1

Explanation:

Given that,

Mass of the car, m = 710 kg

Speed of the car, v = 23 m/s

Drag force, F = 500 N

(a) Let P is the power is required from the car's engine to drive the car on the level ground. Power is given by :

$P=F\times v\\\\P=500\ N\times 23\ m/s\\\\P=11500\ W$

(b) Let P is the power is required from the car's engine to drive the car on up a hill with a slope of 2 degrees.

At this slope, force will be, $F=mg\ \sin\theta$

Total force will be :

$F=710\times 9.8\times \sin(2)+500\\F=742.83\ N$

Power is given by :

$P=F\times v\\\\P=742.83\times 23\\\\P=17085.09\ W$

or

P = 17 kW