Answer to Question #157174 in Classical Mechanics for Ivo

Question

A car mass 1400kg moves with a steady speed of 20 m/s on a straight rough road with its engine working at a constant rate of 36KW.
(a) Calculate the resistance R to the motion of the car if the road is horizontal.
Given that R is proportional to the square of the speed of the car,
(b) Show that R = 9v^2 /2 .

Answer 1

$\text{2 forces act on the car along the X axis}$

$R - \text{resistance to movement}$

$F_m-\text{car motor power}$

$\text{the direction of these forces is opposite}$

$\text{the car moves at a constant speed according to Newton's first law,}$

$\text{the resultant of forces is 0}$

$F= F_m-R;F=0;R=F_m$

$a)P= F_m*v$

$F_m=\frac{P}{v}=\frac{36000}{20}=1800$

$R=F_m = 1800 N$

$b)R =k*v^2$

$k= \frac{R}{v^2}= \frac{1800}{20^2}= \frac{9}{2}$

$R= \frac{9v^2}{2}$

Answer:$a)R = 1800N$ $b)R= \frac{9v^2}{2}$