Problem 8.76 You are called as an expert witness to analyze the following auto a

Question

Problem 8.76 You are called as an expert witness to analyze the following auto accident: Car B, of mass 2100 kg ,was stopped at a red light when it was hit from behind by car A, of mass 1400 ______ kg The cars locked bumpers during the collision and slid to a stop. Measurements of the skid marks left by the tires showed them to be 7.25 m long, and inspection of the tire tread revealed that the coefficient of kinetic friction between V = mph the tires and the road was 0.650. Part A What was the speed of car A just before the collision? v= mph Part B By how many mph was car A exceeding the speed limit 350 mph? Delta v= mph

Explanation / Answer

here,

mb = 2100 kg
ma = 1400 kg
D = 7.25

s = 7.25 m
uk = 0.650

Ff = uk * N
Ff = 0.6650(2100+1400)*9.8
Ff = 22809.5 N

Work Done by frictional Force
Wf = F*D
Wf = 22809.5 * 7.25
Wf = 165368.875 N/m

as after the collision both stick together and comes to rest due to fricitional force :

0.5*(ma+mb)v^2 = Work down by frictional Force
v = sqrt(2*Wf/(ma+mb))
v = sqrt(2*165368.875/(2100+1400))
v = 9.721 m/s

A)
From conservatin of Momentum we have :
mava + mbvb = (ma+mb)V
mava + 0 = (ma+mb)V
va = (ma+mb)V / ma
va = ((2100+1400) * 9.721) / 1400
va = 24.302 m/s

as 1 mph = 0.44704 m/s
va = 24.302 / 0.44704
va = 54.362 mph

B)
Excedded velocity
Ve = Va - 35
Ve = 54.362 - 35
Ve = 19.362 mph

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