You testify as an \"expert witness\" in a case involving an accident in which ca

Question

You testify as an "expert witness" in a case involving an accident in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill. You find that the slope of the hill is = 12.0°, that the cars were separated by distance d = 24.0 m when the driver of car A put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car A at the onset of braking was v0 = 19.5 m/s. (a) With what speed did car A hit car B if the coefficient of kinetic friction was 0.60 (dry road surface)?

Explanation / Answer

The net force on the sliding car, along the incline, would be the component of the weight down the incline - the friction up the plane.

The weight down the plane = mgsin(angle)

The frictional force is uFn and the normal force on an incline is mgcos(angle), so...

mg(sin angle) - umgcos(angle) = the net force

By Newtons second Law, F = ma, so...

ma = mg(sin angle) - umgcos(angle) (mass cancels)

a = (9.8)(sin 12) - .6(9.8)(cos 12)

a = -3.71 m/s2 (Negative means its slowing down)

Then apply vf2 = vo2 + 2ad

vf2 = 19.52 + 2(-3.71)(24)

vf = 14.2 m/s

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