Question

car travels 60 km/h will skid 30 m when its brakes are locked. if the same car is traveling 180 km/h, what will be the skidding distance?

Answer 1

Answer:

270 m

Explanation:

When the driver hits the brakes, the kinetic energy of the car is converted by friction into heat. The kinetic energy K is given by:

(1) $K=\frac{1}{2} mv^{2}$

The work W done by friction is:

(2) $W = F_fd$

where the force of friction is:

$F_f = \mu mg$

d: distance sliding

μ: friction coefficient

m: mass

g: gravitational constant

setting equation 1 and 2 equal:

(3) $\frac{1}{2}mv^{2}=\mu mgd$

simplifying:

(4) $d = \frac{v^{2} }{2\mu g}$

Use equation 4 to find the ratio between the two cases gives:

(5) $\frac{d_1}{d_2} = \frac{v_1^{2} }{v_2^{2} }$

plugging in:

$\frac{30}{d_2}=\frac{60^{2} }{180^{2}}$

$d_2=270$