Answer to Question #276229 in Mechanics | Relativity for Aslam

Question #276229

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.



1
Expert's answer
2021-12-06T16:42:31-0500

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 W=fs\small W = fs .


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

W1=fs112mv2=f(d)(1)W2=fs212m(2v)2=fs2(2)(2)÷(1)41=s2ds2=4d\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.

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