In the \"before\" part of Fig. 9-60, car A (mass 970 kg)is stopped at a traffic

Question

In the "before" part of Fig. 9-60, car A (mass 970 kg)is stopped at a traffic light when it is rear-ended by carB (mass 1500 kg). Both cars then slide with locked wheelsuntil the frictional force from the slick road (with a lowk of 0.20) stops them, at distancesdA = 8.8 m and dB = 6.8 m.What are the speeds of (a) car A and(b) car B at the start of the sliding,just after the collision? (c) Assuming that linearmomentum is conserved during the collision, find the speed of carB just before the collision.

Explanation / Answer

(a)
   if f is the frictional force then from newtonssecond law of motion we get
   f = m a
   the frictional force is given by
   f = k n
     = k m g
   the deccelration of each car will be
   a = f / m
      = k m g /m
      = k g
   if d is the stopping distance using the equation ofmotion we get the speed v of the car just after
   the impact as
   v2 = vo2 + 2 ad
   as vo = 0
   the speed of car A will be
   v2 = 2 a d
   vA = (2 a d)
      = (2k g dA)
        = ........ m /s
(b)
   the speed of car B will be
   vB = (2 a d)
        = (2k g dB)
        = ........ m /s
(c)
   if we take that v is the speed of car B justbefore the impact then from the law of conservation of
   linear momentum we get
   v = [(mA vA) +(mB vB)] / mB
      = ....... m / s

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