An automobile has a mass of 1710 kg and a velocity of 17.2 m/s. It makes a rear-

Question

An automobile has a mass of 1710 kg and a velocity of 17.2 m/s. It makes a rear-end collision with a stationary car whose mass is 2220 kg. The cars lock bumpers and skid off together with the wheels locked. (a) What is the velocity of the two cars just after the collision? (b) Find the impulse that acts on the skidding cars from just after the collision until they come to a halt. (c) If the coefficient of kinetic friction between the wheels of the cars and the pavement is ?k = 0.420, determine how far the cars skid before coming to rest.

Explanation / Answer

a)

conserving momentum just before and after the collision
1710 * 17.2 = (1710+2220) * v

v = 7.484 m/sec

b)

velocity of cars become zero after time 't' sec

  v - uk * g * t

t = 1.782 sec ( if g =10 m/sec2)

total frictional force ( f ) = (1710 + 2220) * uk *g = 16506 N

   impulse acting on cars = f * t = 29413.692 N.sec

c)

   for calculating distance traveled by cars before stopping

   use v * v - u * u = 2 * a * s

  substituting v =0 , u = 7.484 m/sec , a = - 4.2 m/sec2

we get s = 0.891 mts.

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