You have been called to testify as an expert witness in a trial involving a head

Question

You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 1515 lb and was traveling eastward. Car B weighs 1125 lb and was traveling westward at 45.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 17.5 ft before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750. How fast (in miles per hour) was car A traveling just before the collision? (This problem uses English units because they would be used in a U.S. legal proceeding.)

Explanation / Answer

let east be +x

m1 = 1515 lb, initia velocity u1

m2 = 1125 lb, u2 = -45 mph

d = 17.5 ft = 5.334 m

u2 = -45*1.607*5/18 = 20.1 m/s


let v is the velocity of the cars aftre the collision

work done by friction = chnage in kinetic enrgy of the cars


mue*(m1+m2)*g*d = 0.5*(m1+m2)*v^2

v = sqrt(mue*g*d)

= sqrt(0.75*9.8*5.334)

= 6.26 m/s


m1*u1 + m2*u2 = (m1+m2)*v


1515*u1 - 1125*20.1 = (1515+1125)*6.26


u1 = ((1515+1125)*6.26 + 1125*20.1)/1515

u1 = 25.83 m/s

= 25.83*(18/(5*1.607))

= 57.87 mph

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