Chapter 09, Problem 056 before part of the figure, car A 4.4 m. What are the spe

Question

Chapter 09, Problem 056 before part of the figure, car A 4.4 m. What are the speeds of (a) car A and (b) cr n the and gre part of the figure, car A ( mass 1000 kg) is stopped at traffic light when it is rear-ended by car B ot the start of the sliding, just after the collision? (c) Assuming that inear momentum is conserved during the collision, find the speed of car B just before the collision S.& m and de mass 1400 kg). Both cars then slide with locked wheels until the frictional force from the slick road with a low k of 0.25) stops them, at distances stopa A- ar B just before tx Before (a) Number (b) Number (e) Number Click if you would like to Show Work for this question Units Units Units Open Show Work

Explanation / Answer

   if f is the frictional force then fromnewtons second law of motion we get

   f = m a

   the frictional force is given by

   f = k n

     = k mg  

   the deccelration of each car will be

   a = f / m

      =k m g / m

      =k g

   if d is the stopping distance using the equationof motion we get the speed v of the car just after

   the impact as

   v2 = vo2 +2 a d

   as vo = 0

   the speed of car A will be

   v2 = 2 a d

   vA = (2 a d)

      = (2k g dA)

        = 5.23 m /s

(b)

   the speed of car B will be   vB = (2 a d)

        = (2k g dB)

        = 4.64m /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

      = 8.37 m / s

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