Keating, Erick asks:

CATAGORY: Mechanics QUESTION: We have the length of a car tire's skid mark. We are guessing that the co-efficient of friction for car tires is about .5 or so. What is the proper formula for the calculating of the velocity of this vehicle?

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We want to dissipate the kinetic energy of the car into work done on the
by friction.  Thus

(1)       Change in kinetic energy = work done by friction

             final KE - initial KE = work done by friction
                  0  - (1/2)mv^2   = -Uk mg L
Where m is the mass of the car v is the initial speed of the car, Uk is
coefficient of friction, g = magnitude of the acceleration due to gravity
= 9.8
m/s^2 and L is the length of the skid.  The work is negative because the
acting against the displacement and thus drains energy away from the car.
mass cancells in (1). Also divide by -1 to give

(2)                   (1/2)v^2   =  Uk g L

solving for v in terms of L gives

(3)                      v = sqrt(2 Uk g L)

So your "proper" formula is

                 *                        *
                 *   v = sqrt(2 Uk g L)   *
                 *                        *
It of course assumes that ALL the kinetic energy is dissipated in the skid
and not part in the skid and part in colliding with something else.

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