Answer to Question #276229 in Mechanics | Relativity for Aslam

Question

Consider an automobile moving at v mph that skids d feet after its brakes lock. Calculate how far it would skid if it was moving at 2v and the brakes were locked.

Answer 1

Explanations & Calculations

• The maximum friction force that acts on the wheels of the car during the skid does work against the motion thereby draining the car's kinetic energy making it stop.

• Work done by the force is $\small W = fs$ .

• Since the tire & road conditions do not change, the maximum friction force remains constant.
• Then, the calculation should look like this,

$\qquad\qquad \begin{aligned} \small W_1&=\small fs_1\\ \small \frac{1}{2}mv^2&=\small f(d)\cdots(1)\\\\ \small W_2&=\small fs_2\\ \small \frac{1}{2}m(2v)^2&=\small fs_2\cdots(2)\\\\ (2)\div(1)\\ \small \frac{4}{1}&=\small \frac{s_2}{d}\\ \small s_2&=\small 4d \end{aligned}$

• The car would skid 4times the previous distance.